lll'lllll/Illllllllsl llllllTl

312903

      
 

LARY
Michigan State
University

 

This is to certify that the
dissertation entitled
Ion Association and Complexation of Alkali Cations
by Crown Ethers and Cryptands in Various Solvents

presented by

Sadegh Khazaeli

has been accepted towards fulfillment
of the requirements for

Ph.D. degeehi Physical Chemistry

' 2
Major professor

Dam August 4, 1982

MSU is an Affirmative Anion/Equal Opportunity Instilutiou 0— 12771

 

 

 

 

MSU

LIBRARIES

»

 

 

 

RETURNING MATERIALS:
Place in book drop to
remove this checkout from
your record. FINES will
be charged if boOk is
returned-after the date
stamped below.

 

 

NM 1 51994

 

 

 

 

 

 

 

 

ION ASSOCIATION AND COMPLEXATION OF ALKALI
CATIONS BY CROWN ETHERS AND CRYPTANDS IN

VARIOUS SOLVENTS

By

Sadegh Khazaeli

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements

for the degree of

DOCTOR OF PHILOSOPHY

Department of Chemistry

1982

 

~}

/'3¢'&S

 

ABSTRACT

ION ASSOCIATION AND COMPLEXATION OF ALKALI
CATIONS BY CROWN ETHERS AND CRYPTANDS IN

VARIOUS SOLVENTS
By
Sadegh Khazaeli

The concentration and temperature dependence of the
13303 chemical shift, 6, for cesium salts in methylamine
was fit by a model involving ion—pairs and triple—ions.

Formation constants for ion—pairing, K. at 25.0°C and

ip’
standard deviations are: (2.65:0.19) x 105 and (1.30i

0.19) X lOLl M_1 for CsI and CsBPhu respectively, and the

corresponding enthalpies of association are: 3.7:O.3 and

l. The value for (K. obtained

lp)CSI

from conductance measurements depended on the conductance

A.O:l.0 kcal.mole_

equation used. The Onsager limiting law fit the data best

A —l

with (K. ) (3.u3io.2o) x 10 M at —15.7°c which is

ip 051 =
only about 35% of the value obtained from the NMR data at
this temperature.

The variation of 5 with temperature and with

 

 

 

Sadegh Khazaeli

(l8—Crown—6)/(Cs+) mole ratio (R) in methylamine and am—
monia solutions indicated the formation of both 1:1 and 2:1
complexes. The concentration and temperature dependence

of 6 for the 1:1 complex in methylamine was described by

 

K K
the equilibria: Cs+ + C‘-f Csc+, Csc+ + X‘ :A Csc+.x‘,
ARC . AHX

K
+_ X +— _
and Cs .X -+C EH0 CsC .X , where C and X are the ligand
x

and the anion respectively. Values of KC = (1.07:0.08)

x 10L1

M‘1 at 25.000 and AH: = —l6.72i0.08 kcai.moie‘l were
obtained. The ion—pair formation constants of the 1:1

complex at 25.0°C are: (KA)CSI = (l.51i0.06) x 105 and

 

(KA)CsBPhh = (1.16:0.34) x 10A M—l. Other parameters have
the values: KX = (8.4ii.u) x 103, (6.33:0.uo) x 103,
and (4.87:0.53) x 103 M‘1 at 25.000 with AH; = —l8.80i0.95,
—16.uoio.53, and —13.50i0.73 keg-iihoie‘l for CsBPhu, CsI,
and CsSCN, respectively.'

The mole ratio'data for R > 1 were analyzed for solu-

. . . + _
tions in methylamine according to the equilibrium CsC .X

K

+ C A§§2 CEC:.X_ with corrections introduced for ion—associa-
x2

tion of the salt and the 1:1 complex. The thermodynamic

parameters are: (Kx2)CsI = “-03:0'05’ and (Kx2)CsBPhh =
22.82i0.35 M“1 at 25.000 with (AH;2)C8I = —6.05i0.08, and

< = —7.35:O.l2 kcal.mole_l. The corresponding

0
AHx2)CsBPhh
approximate values in ammonia are: (Kx2)CsBPh4 = 649i44

M“1 at 25.000 with (AHO = -u.9i:o.28 keai.moie‘l.

x2)CsBPhu
Rubidium-87 chemical shifts of some rubidium salts were

Studied as a function of concentration. Attempts to use

 

¥

Sadegh Khazaeli

87Rb NMB to study complexation of the Rb+ ion by l8—crown—6
and cryptand-222 failed.

The exchange of the Li+ ion between the free and 211—
cryptated species in methylamine solutions, while slow on
the NMR time scale, occurs within seconds of mixing. The
chemical shift of Li+ in the complex is the same in methyl-
amine and ammonia, indicating that the complexant effec—

tively isolates Li+ from the solvent and anion.

 

 

To my wife and

in memory of my father

ii

 

- ' ' 3 ~77 - ' ' _. v‘L. "~ “(1’35 ;’j.."‘". T ..- _
‘T-‘mf. 7.. A .

ACKNOWLEDGMENT

The author wishes to express his deepest appreciation
to Professor J. L. Dye for his encouragement, enlighten—
ing suggestions and invaluable assistance, and to Professor
A. I. Popov for his guidance, whole-hearted support, and
friendship throughout the course of this investigation.
Gratitude is extended to the Department of Chemistry,

Michigan State University, and the National Science Founda—

tion for financial support under Grants DMR-79—2lA79 and
CHE—80-lO808.

Thanks are also extended to the members of the research
groups of both Professor Popov and Professor Dye for their
help and moral support, and to the friends at Michigan State
University and elsewhere without whose friendship this study
would have been more difficult.

Many thanks go to MSU's technical and clerical staff

especially Mr. Wayne Burkhardt and Mr. Tomas Clarke for the

maintenance of the NMR spectrometers, Mr. Keki Mistry for
his excellent glassblowing service and secretary Sharon
Corner for her assistance.

Above all, the author wishes to thank his family and

his wife's family for their unending encouragement, under—

standing, and financial aid.

 

 

 

 

I am deeply grateful to my wife, Afsaneh, for her love,
patience, and encouragement through the years of graduate

study and for her constant care of our sons, Javad and

Nima.

To her and in memory of my father, I dedicate this

thesis.

iv

 

 

 

(Iv.

...-~ -

'0.-

--» .

 

TABLE OF CONTENTS

Chapter Page

LIST OF TABLES. . . . . . . . . . . . . . . . . . . xi
LIST OF FIGURES . . . . . . . . . . . . . . . . . . xx
CHAPTER I - INTRODUCTION AND HISTORICAL . . . . . . I
Introduction. . . . . . . . . . . . . . . . . . 2
Historical Background 3
1. Ion Association 3
A. Theoretical Aspects 3
B. Methods of Studying Ion-
Association . . . . . . . . . 1A
i. ESR, Electronic, and Vibra-
- tional Spectroscopy . . . . . . 15
a. ESR spectroscopy. . . . .i. 15
b. Electronic spectroscopy . . 16
c. Vibrational spectroscopy. . 18
ii. Electrical Conductance Measure-
ment. . . . . . . . . . . . . . 20
iii. Alkali Metal Nuclear Magnetic
Resonance Spectroscopy. . . . . 27
a. Introduction. . . . . . . . 27
b. Relaxation Studies. . . . . 28
0. Chemical Shift Studies. . . 31
2. Complexation of Alkali Cations
by Crown Ethers and Cryptands . . . . . A5
A. Introduction. . . . . . . . . . . . A5
B. Selectivity of Complexation . . . . A9
1. Relative Sizes of Cation and
Ligand Cavity . . . . . . . . . U9

.'.

.’.

Chapter

ii. Arrangement of Ligand Binding
Sites .

iii. Type and Charge of Cation
iv. Type of Donor Atom.
v. Number of Donor Atoms

vi. Substitution of the Macro—
cyclic Ring

Vii. Solvent and Anion Effects
C. Thermodynamics of Complexation.
D. The Use of Alkali Metal NMR
to Study Thermodynamics and
Kinetics of the Complexation.
CHAPTER II — EXPERIMENTAL
1. Purification of Materials
A. Ligands
B. Solvents.
C. Salts
2. Glassware Cleaning.
3. NMR Techniques.
A. NMR Instruments
B. Data Handling
C. NMR Sample Preparation. . . .
A. Conductance Method.
A. Conductance Equipments.
B. Data Handling

C. Sample Preparation for Conductance
Measurements. . . . . . . . .

CHAPTER III — THERMODYNAMICS OF ION—ASSOCIATION
OF CESIUM SALTS IN METHYLAMINE.

vi

Page

53
53
55
55

56
57
58

61
6A
65
65
67
69
70
7O
7O
72
75
8O
8O
81

83

85

‘ nu. '.‘.~.‘ . . A _:

 

a“!'

”1.
n
a
.
o
o

‘1'

Chapter

 

Introduction.

Cesium-133 NMR Studies of Cesium
Salts in Methylamine. . . .

A. Concentration Dependence of 133Cs
Chemical Shifts of Cesium Salts
in Methylamine. . . . . . .

B. Ion Association of Cesium Salts
in Methylamine.
i. Simple Ion—Pair Model
ii. Formation of Triple—Ions.
a. One type of triple-ion.
b. Two types of triple-ions.

C. Complimentary Experiments

i. Cesium Tetraphenylborate in
90% V/v Methylamine in Dimethyl-
sulfoxide Solutions . .

ii. Mixtures of Cesium Iodide and
Cesium Thiocyanate in Methyl—
amine . .

iii. Mixtures of Cesium Iodide and
Cesium Tetraphenylborate in
Methylamine

D. Conclusions

Electrical Conductance Measurements
of Cesium Iodide in Methylamine

A. Introduction.
B. Results

1. Calibration of the Conductance
Cell. . .

ii. Conductance of Cesium Iodide in
Methylamine at -15.7°C.

C. Discussion.

D. Conclusion.

vii

Page

86

87

87

103

103
108
108
110

129

130

133

137
1A3

1A5
1A5
1A6

1A6

149
152

155

 

 

 

 

Chapter Page

A. Comparison of NMR and Electrical
Conductance Measurements. . . . . . . . . . 156

CHAPTER IV — COMPLEXATION OF CESIUM SALTS BY
18-CROWN-6 IN METHYLAMINE AND

 

LIQUID AMMONIA . . . . . . . . . . . . 159
1. Introduction. . . . . . . . . . . . . . . . 160
2. Complexation of Cesium Salts by

18—crown-6 in Methylamine . . . . . . . . . 161

A. Mole Ratio Dependence of 13303
Chemical Shift in Methylamine . . . . . 161
i. Results . . . . . . . . . . . . . . 161
ii. Discussion. . . . . . . . . . . . . 169

B. Concentration Dependence of the 133Cs
Chemical Shift of the 1: 1 Complex

 

in Methylamine. . . . . . . 176
i. Results . . . . . . . . . . . . . . 176
ii. Discussion. . . . . . . . . . . . . 183
a. General discussion. . . . . . . 183
b. The chemical shift of the

1:1 complex, 5MC+ . . . . . . . 185

c. Enthalpy of formation of the
ion—paired complex. . . . . . . 189
iii. Analysis of the Data. . ; . . . . . -191
a. Cesium iodide . . . . . . . . . 191
b Cesium tetraphenylborate. . . . 194
c. Cesium thiocyanate. . . . . . . 197
d Summary . . . . . . . . . . . . 201

C. Thermodynamics of Formation of 2: 1
Complexes of 18- crown-6 With Cesium

Salts in Methylamine. . . . . . . . . . 205
3. Complexation of Cesium Tetraphenyl—
borate by 18— crown-6 in Liquid Ammonia. . . 221
A. Results . . . . . . . . . . . . . . . . 221
viii

 

'.-.--;fl

I
.
up.

‘0
q
I
‘0
'\
i“
.-' -‘
e ‘
.~.
'§
‘\
e
.. i.
.' ‘5
.
‘p.
C‘
I
.
._.
I
h
'n
|
V
O

II,

It

 

 

 

Chapter Page

B. Discussion. . . . . . . . . . . . . . . 226
C. Summary . . . . . . . . . . . . . . . . 231
A. Conclusion. . . . . . . . . . . . . . . . . 233

 

CHAPTER V — l. RUBIDIUM-87 NMR INVESTIGA-
TION OF RUBIDIUM SALTS AND THEIR
COMPLEXES IN AQUEOUS AND NON-
AQUEOUS SOLVENTS
2. LITHIUM—7 NMR STUDY OF COM-
PLEXATION OF LITHIUM SALTS BY C211
IN METHYLAMINE AND LIQUID AMMONIA . . . 237

1. Introduction. . . . . . . . . . . . . . . . 238

2. Investigation of Rubidium Salts and
Their Complexes in Aqueous and Non-

 

Aqueous Solvents ....... . . . . . . . . . . 239

A. Salt Solutions. . . . . . . . . . . . . 239

B. Complexation. . . . . . . . . . . . . . 2AA
3. Complexation of the Lithium Cation by

C211 in Methylamine . . . . . . . . . . . . 2A8
A. Complexation of the Lithium Cation by

C211 in Liquid Ammonia. . . . . . . . . . . 252
5. Conclusion. . . . . . . . . . . . . . . . . 252

CHAPTER VI - SUMMARY AND SUGGESTIONS FOR

FURTHER STUDIES. . . . . . . . . . . 255

1. Summary . . . . . . . . . . . . . . . . . . 256

2. Suggestions for Further Studies . . . . . . 261
APPENDICES. . . . . . . . . . . . . . . . . . . . . 26A

APPENDIX 1 - DETERMINATION OF ION-ASSOCIATION
PARAMETERS BY NMR TECHNIQUES: DES—
CRIPTION OF THE COMPUTER PROGRAM

KINFIT AND SUBROUTINE EQN. . . . . . . 265

A. Simple Ion—Pair Formation . . . . . . . . . 265
B. Ion-Pairs and Anionic Triple-Ion

Formation . . . . . . 267

0- Ion-pairs and Two Kinds of Triple Ions. . . 27A

ix

 

 

Chapter

APPENDIX 2 - DETERMINATION OF ION-PAIR FORMA—
TION CONSTANTS BY CONDUCTANCE
MEASUREMENTS, DESCRIPTION OF THE
COMPUTER PROGRAM KINFIT AND SUB-
ROUTINE EQN. . . .

A. The Onsager Limiting Law.
B. Extended Conductance Equation

i. Pitt's Equation Linearized by
Fernandez-Prini

ii. Fuoss-Hsia Equation Linearized
by Fernandez Prini.

iii. Fuoss-Hsia Equation Corrected
by Chen

iv. Justice Equation.

APPENDIX 3 - DETERMINATION.OF COMPLEX FORMATION
CONSTANTS BY THE NMR TECHNIQUE;

DESCRIPTION OF THE COMPUTER PROGRAM

KINFIT AND SUBROUTINE EQN.

A. 1:1 Complex Formation in Media of Low
Dielectric Constant

B. 2:1 Complex Formation in Media of Low
Dielectric Constant

REFERENCES.

Page

28A
28A
286

290

291

298
298

302

302

315
32A

_._—.._ . . _........._._..__.....

 

 

 

.’~-.

Table

LIST OF TABLES

Page

Nuclear Properties of Alkali Nuclei . . . . . 29
Chemical Shifts/ppm at Infinite
Dilution for 7Li+, 23Na+, 39K+

1330s;+ Ions in Various 801-

and
vents. . . . . . . . . . . . . . . . . . . A2
Diamagnetic Susceptibility Correction

of Various Solvents on DA-60 and WH-180
Instruments . . . . . . . . . . . . . . . . 7A

133Cs

Concentration Dependence of
Chemical Shift of CST in Methylamine

at Various Temperatures . . . . . . . . . . 88
Concentration Dependence of the 13305
Chemical Shift of CsBPhu in Methyl-

amine at Various Temperatures . . . . . . . 91
Variation of the 13305 Chemical

Shift with the Mole Ratio (18C6)/

(CsBPhu) in Methylamine Solutions at

Different (Cs+) Concentrations and

Various Temperatures. . . . . . . . . . . . 93
Concentration Dependence of the 13305
Chemical Shift of CsSCN in Methylamine

at Various Temperatures . . . . . . . . . . 95

xi

‘Table

10

11

12

13

Concentration Dependence of the

133CS Chemical Shift of Csi3 in
Methylamine at 25.00 and 5.6°C.
Cesium-133 Chemical Shifts of
Saturated Solutions of CsBr, CsClOu,
CsNO3 in Methylamine at 25.000.
Calculated Thermodynamic Parameters
of Ion-Association of Cesium Salts in
Methylamine at 25.0°C According to a
Simple Ion—Pair Model

Calculated Thermodynamic Parameters
for Ion-Association of Cesium Salts
in Methylamine at 25.000 According to
the Ion-Pair and Anionic Triple—Ion
Model

Thermodynamic Parameters for Ion—
Association of Cesium Salts in Methyl—
amine at 25.0°C; Obtained with the
Assumptions that Ion-Pairs and Two
Kinds of Triple Ions are Present, and
That 50s = 60.73 ppm at 25.000.
Thermodynamic Parameters for Ion-
Association of Cesium Salts in Methyl-
amine at 25.000; Obtained with the

Assumptions that Ion-Pairs and Two

xii

Page

98

100

107

111

117

Table

13

1A

15

16

17

Kinds of Triple Ions are Present, and
That 6C3 = A0 ppm

Thermodynamic Parameters for Ion-~
Association of Cesium Salts in Methyl-
amine at 25.000; Obtained With the
Assumption that Ion-Pairs and Two
Kinds of Triple Ions are Present, and
That 603 = 80 ppm

Thermodynamic Parameters for Ion—
Association of Cesium Salts in Methyl-
amine at 25.0°C; Obtained with the
Assumptions that Ion-Pairs and Two
Kinds of Triple Ions are Present, and
That Kt/Kip is a Known Constant
Thermodynamic Parameters for Ion-
Association of Cesium Salts in Methyl-
amine at 25.0°C; Obtained with the
Assumptions that Ion-Pairs and Two
Kinds of Triple-Ions are Present,

and that Kt/Kip is an Adjustable
Parameter

Thermodynamic Parameters for Ion-
Association of Cesium Salts in Methyl-
amine at 25.0°C; Obtained with the

Assumptions that Ion-Pairs and Two

xiii

Page

118

119

122

12A

Table

17

18

19

20

21

22

Page

Kinds of Triple Ions are Present,

with Equipartition of the Chemical

Shifts. . . . . . . . . . . . . . . . . . . 127
Thermodynamic Parameters for Ion-

Association of Cesium Salts in Methyl-

amine at 25.0°C; Obtained with the

Assumptions that Ion-Pairs and Two

Kinds of Triple Ions are Present, and

is Temperature Dependent . . . . 128
133Cs

that 60$.X
Concentration Dependence of the
Chemical Shift of CsBPhu in 90% v/v
Methylamine-DMSO at 25.0°C. . . . . . . . . 131
133Cs Chemical Shifts of Different

Mole Ratios of (I-)/(SCN-) + (I-)

in Mixtures of CsI and CsSCN in

Methylamine at Various Temperatures;

(Cs+) = 0.005A E- . . . . . . . . . . . . . 13A
Cesium-133 Chemical Shifts of Dif-

ferent Mole Ratios of (I-)/(BPhE) +

(I‘) for 0.0007 and 0.003 g 0s+ in

Methylamine Solutions at 2A.6°C . . . . . . 138
Resistances of the 90.9k0 Standard

Resistor, Water, and Aqueous Potas-

sium Chloride Solutions at 25.0:0.0A°C. . . 1A7

xiv

 

 

Table

23

2A

25

26

Equivalent Conductances of Cesium
Iodide Solutions in Methylamine at
—15.7°C . . . . .

Values of the Association Constant

and Limiting Equivalent Conductance

of Cesium Iodide in Methylamine at
—15.7°C Obtained by Various Conductance
Equations

Mole Ratio Study of 18C6, CsI Complexes
in Methylamine at Various Temperatures;
(08+) = 0.0206i0.0008 1_v1_ .

Mole Ratio Study of 1806, CsBPhu
Complexes in Methylamine at Various
Temperatures; (Cs+) = 0.0108i0.0005 M
Thermodynamic Parameters for the

Formation of the 2:1 Complex of 18-

.Crown—6 and CST in Methylamine. K i

1

10M

Thermodynamic Parameters for the Forma—
tion of the 2:1 Complex of 18—Crown-6
and CsBPhu in Methylamine. Kl : 10M
Concentration Dependence of the 133Cs
Chemical Shift of the 1:1 Complex of
CsI and 18C6 in Methylamine at

Various Temperatures.

XV

Page

150

15A

162

 

 

 

Table

30

31

32

33

3A

35

 

 

Page

Concentration Dependence of the 13305
Chemical Shift of the 1:1 Complex of

CsBPhM and 18C6 in Methylamine at

 

Various Temperatures. . . 178
Concentration Dependence of the 133Cs
Chemical Shift of the 1:1 Complex of
CsSCN and 1806 in Methylamine at ‘
Various Temperatures. . . . . . . . . . . . 179

Thermodynamic Parameters for the.

Formation of the 1:1 Complex of 18-

Crown—6 and CsI in Methylamine at

25.000; with Adjustment of AHZ. . . . . . . 190

Thermodynamic Parameters for the

Formation of the 1:1 Complex of 18C6

and CsI in Methylamine at 25.000; with

Calculation of AH: from Other Adjustable

Parameters. . . . . . . . . . . . . . . . . 193

Thermodynamic Parameters for the

Formation of the 1:1 Complex of 18C6

and CsBPhu in Methylamine at 25.000;

with AH: = Ang . . . . . . . . . . . . . . 195

Thermodynamic Parameters for the

Formation of the 1:1 Complex of 1806

and CsBPhu in Methylamine at 25.000;

KC was Used as a Constant . . . . . . . . . 198

 

 

Thermodynamic Parameters for the
Formation of the 1:1 Complex of 18C6
and CsSCN in Methylamine at 25.0°C.
Thermodynamic Parameters of the
Complexation of Cesium Salts by 18—
Crown—6 in Methylamine at 25.0°C.
Thermodynamic Parameters for the
Formation of the 2:1 Complex of CsI
with 18—Crown-6 in Methylamine at
25.000; Assuming Complete Ion-Pair

Formation of the MC+ Complex at

Thermodynamic Parameters for the
Formation of the 2:1 Complex of CsI
with 18—Crown-6 in Methylamine at
25.0°C; Assuming Complete Ion—Pair
Formation of Both the MC+ and MC+
Complexes at (Cs+)
Thermodynamic Parameters for the
Formation of the 2:1 Complex of CsBPhu
with 18—Crown—6 in Methylamine at 25.0°C;
Assuming Complete Ion—Pair Formation of

both the MC+ and MC+ Complexes at (Cs+)

Page

200

202

207

210

211

 

Table

A1

A2

A3

AA

A6

A7

-Concentration Dependence of the

Thermodynamic Parameters for the
Formation of the 2:1 Complexes of Cesium
Salts with 18-crown-6 in Methylamine

at 25.0°C . . .
133CS
Chemical Shift of CST in the Presence
of a 6.0-Fold Excess of 18—Crown—6

in Methylamine at Various Temperatures.
Mole Ratio Study of 18C6.CsBPhu Com—
plexes in Liquid Ammonia at Various
Temperatures; (Cs+) = 0.001 M .

Mole Ratio Study of 18C6.CsBPhu Com—
plexes in Liquid Ammonia, at Various
Temperatures; (08+) = 0.0075 M.

133CS

Concentration Dependence of the
Chemical Shift of CsBPhuin Liquid
Ammonia at 6.0°C.

Complexation Formation Constant,
Limiting Chemical Shifts, and Thermo-
dynamic Parameters for the 2:1 Complex
of 1806, CsBPhu in Liquid Ammonia at
Various Temperatures, Assuming K1 1 10A
Thermodynamic Parameters for the
Formation of the 2:1 Complex of 1806
and Cesium Salts in Methylamine and,

Ammonia Solutions . . . . . . . . . .

xviii

 

Page

216

219

222

225

227

232

Table - Page

A8 Rubidium—87 Chemical Shifts and

Linewidths of Rubidium Salts in Three

Solvents at Ambient Temperatures. . . . . . 2A0
A9 Rubidium~87 Chemical Shifts versus

(Ligand)/(Rb+) Mole Ratio . . . . . . . . . 2A5
50 Lithium—7 Chemical Shifts of the Free,

5F, and C211—Cryptated, 0C, Lithium

Cation in Methylamine as a Function

of Time. (211)/(Li+) = 0.5, (Li+)

= 0.069 M . . . . . . . . . . . . . . . . . 2A9

7Li Chemical

51 Mole Ratio Study of the
Shift of LiBr in the Presence of
Cryptand 211 in Liquid Ammonia.

(Li+) = 0.07 g. . . . . . . . . . . . . . . 253

 

 

 

LIST OF FIGURES

 

 

Figure Page

1 Cesium—133 chemical shift as a

function of concentration. . . . . . . . . 35
2 Cesium-133 shifts against concentra—

tion for CsBr+HOAc-H20 systems . . . . . :7 "38
3 Sodium-23 chemical shifts YE Gutmann

donor numbers. . . . . . . . . . . . . . . A0
A Naturally occurring and synthetic

macrocycles. . . . . . . . . . . . ... . . A6
5 (a) Various stoichiometries of K+-crown

ether complexes. (b) Exclusive CS

0222 complex . . . . . . . . . . . . . . . ' A8
6 Selectivity of 18-crown—6: log K values

for the reaction of 18—crown—6 with
metal cations in H2O YE: ratio of

cation diameter to l8—crown—6 cavity

diameter .‘. . . . . . . . . . . . . . . . 51
7 Selectivity of cyclic polyethers of
various sizes: log K values for re—

action of several crown ethers with

alkali metal ions K§.cation radius . . . . 52

XX

 

Figure

10

Ill
:12

3.3

3.4

:1

1-7'

55

Selectivity of cryptands: log K values
for reaction of several cryptands with
alkali metal cations gs. cation radius
Cryptand sublimation apparatus
Calibration curve for 10 mm NMR tubes
at 0°C .

Extended NMR tube for high vacuum.
Extended NMR tube for the kinetic ex-
periment

The conductance cell . .

Concentration and temperature depend-
ence of the 133Cs chemical shift of
cesium iodide in methylamine
Concentration and temperature depend-
ence of the 133CS chemical shift of
cesium tetraphenylborate in methyl—

amine.

Cesium-133 chemical shift versus

(18-crown-6)/(CSBPhu) mole ratio at
different concentrations of CsBPhu
and various temperatures .
Concentration dependence of the 13303
chemical shift of cesium thiocyanate

in methylamine at various tempera;

tures.

xxi

Page

5A
66

76
77

79

82

90

92

9A

96

Figure

18

19

220

2323

214

255

Concentration dependence of the 133Cs

chemical shift of cesium triiodide in
methylamine at 25.0 and 5.6°C.
Concentration dependence of the 133CS
chemical shifts of some cesium salts
in methylamine at 25.0°C
Concentration dependence of 13303
chemical shifts of CsI and CsBPhu

in methylamine at 25.0°C

Cesium-133 chemical shifts of cesium
thiocyanate solutions versus tempera-
ture

Concentration dependence of the 133Cs
chemical shift of cesium tetraphenyl-
borate in 90% v/v methylamine in di-
methylsulfoxide at 25.0°C.

A comparison of 133Cs chemical shifts
of pure cesium salts and the mixture
of cesium salts in methylamine at
25.0°C

Plot Of (5obs‘50sl)/(50sSCN‘50sl)
versus mole fraction of iodide

A comparison of 133CS chemical shifts

of pure cesium salts and mixtures of

cesium salts in methylamine at 25.0°C.

xxii

Page

99

101

106

116

132

135

136

139

Figure

26

27

£28

2259

3ZL

322

333

Plot of (Gobs'GCsI)/(SCsBPhu-SCSI)

versus mole fraction of iodide

Calculated 13305 chemical shifts of mix-

tures of CsI and CsTPB as a function

of concentration

Plot of equivalent conductance versus

the square root of the molar concentra-

tion of cesium iodide in methylamine

at ~15.7°C

Cesium-133 chemical shift versus

(l8-crown-6)/(CsI) mole ratio and

temperature in methylamine; (CsI)

= 0.02 M .

Cesium—133 chemical shift versus

(l8-crown-6)/(CsBPhu) mole ratio

and temperature in methylamine;

(CsBPhu) = 0.01 M.

Ln"K2" XE l/T for the 2:1 complex of

18-crown—6 and CsI in methylamine.

Kl Z 10”, (C31) = 0.02 M .

Ln "K2" gs l/T for the 2:1 Complex of

18-crown-6 and CsBPhu in methylamine.
A

K1 3 10 , (CsBPhu) = 0.01 g.

Concentration dependence of the 133Cs

chemical shift of the 1:1 complex of

XXiii

Page

1A1

1A2

151

16A

168

173

17A

Figure

33

3A

35

36

37

38

39

 

 

7' "' W. ,' _ '..' '
—: WEI—m —'

18-crown-6 and CsI in methylamine at
various temperatures . . . .
Concentration dependence of the 1330s
chemical shift of the 1:1 complex of
18-crown—6 and CsBPhu in methylamine at
various temperatures . . . .
Concentration dependence of the 133Cs
chemical shift of the 1:1 complex of
18—crown—6 and CsSCN in methylamine at
various temperatures

Limiting 1330s chemical shift of the
1:1 complex of 1806 and CsSCN XE tem—
perature in methylamine. . . . . . . .
Concentration dependence of the 133Cs
chemical shift of CST in the presence
of a 6.0—fold excess of lB—crown—6
in methylamine at various tempera-
tures. . . . .

Cesium—133 chemical shift versus
(18—crown—6)/(CsBPhu) mole ratio
and temperature in liquid ammonia;
(Cs+) = 0.001 g. . .

CeSium—133 chemical shift versus

(18—crown—6)/(CsBPhu) mole ratio

in liquid ammonia at various tem—

Page

180

181

182

 

187

220

. . . 223

peratures; (Cs+) = 0.0075 M, . . . . . . . 22h

xxiv

Figure

A0

A1

U42

Page

Cesium-133 chemical shift versus

concentration of CsBPhu in liquid

ammonia at 6.0°C . . . . . . . .l. . . . . 228
Rubidium-87 chemical shifts of rubidium

bromide versus concentration (—) or

mean molar activity (---) in aqueous

solutions. . . . . . . . . . . . . . . . . 2A2
Rubidium-87 chemical shifts of rubidium

bromide in methanol (-) or rubidium

iodide in propylenecarbonate (-—-)

versus concentration (0) or mean molar

activity (A) of the solution . . . . . . . 2A3

XXV

CHAPTER I

INTRODUCTION AND HISTORICAL

 

1

INTRODUCTION

Since the discovery of crown ethers by Pederson (1—3)

 

and cryptands by Lehn and coworkers (A-7), the thermo—
dynamics and kinetics of complexation of alkali cations by
these novel compounds have been studied in aqueous and
nonaqueous solvents by various physicochemical techniques.

Most of the research in this area has been performed in

 

relatively high dielectric media, where ionic association

occurs to a limited degree if at all. Little is known

about the effect of different ion—association processes

upon complexation in low dielectric solvents. The high

sensitivity of 133Cs NMR along with its narrow lines al—

lowed us to investigate extensively the thermodynamics of

the complexation of cesium salts by l8—crown—6 in the low

dielectric constant solvent methylamine. The results of

this study are presented in Chapters III and IV of this

Dissertation and are compared with the data in liquid am—

monia and in other solvents.

The thermodynamics of complexation of all the alkali

cations except the rubidium cation by crown ethers and

cryptands has been studied by the alkali metal NMR tech—

nique. To fill the gap, attempts were made to use 87Rb

NMR to study the complexation of rubidium salts in solu—

tion. This work will be described in Chapter V.

 

The kinetics of complexation of alkali cations with

crown ethers and cryptands has been investigated mostly

by line shape analysis of NMR signals. It was suggested

that the rate of exchange of Li+ ion between the solvated

 

and C211 cryptated states in methylamine is very slow

the exchange rate can be determined directly
Chapter

(8). If so,
from the time dependence of the 7Li chemical shift.

V also describes the kinetic study of the complexation of

the lithium cation by C211 in methylamine.

 

HISTORICAL BACKGROUND
1. Ion Association

A. Theoretical Aspects

Michael Faraday (9) was the first to realize that ions

play an important role in the behavior of electrolytic

solutions. He assumed, however, that in solutions ions

are formed only under the influence of an electrical field.»
Arrhenius, after extensive studies on the conductivity of
electrolytic solutions, proposed that molecules of an
electrolyte are spontaneously dissociated, to a certain

extent, into free ions (10). His theory could explain

the behavior of weak electrolytes where only a small frac—
tion of the molecules are dissociated but the behavior of

strong electrolytes shows considerable deviations from

Arrhenius' theory.

 

The concept of "ionic atmosphere" which is characterized
by a certain regularity in the distribution of ions and the
use of Poisson's equation by Debye resulted in the Debye-
Hfickel limiting law (11) (DHLL) for the activity coefficient
of ions.. The DHLL describes the behavior of strong elec-
trolytes only at very low concentrations which is a conse-
quence of the approximation used to linearize the Poisson—
Boltzmann distribution function. A modification of the
DHLL considers ions with finite size instead of point
charges by introducing an ionic parameter "a" which is
the minimum average distance to which two ions can ap—
proach each other.

The Debye-Hfickel theory was successful in describing
experimental data at low concentration (<0.01 M) for 1:1

electrolytes in high dielectric constant solvents. At
biggier concentrations, and for ions with high charges, the
lirnsarized Poisson-Boltzmann equation is not valid, and
true short—range forces between the ions also becomes im-
portant.

Grunwall, LaMer, and Sandved (12) improved the Debye-
Pfiickel theory by using higher order terms in the Poisson-
Ekoltzmann equation. Their treatment predicts departures
iflwmlthe Debye-Hackel theory for electrolytes of high
‘falence type, for electrolytes whose "a" parameters are
53nm11,2u1d for electrolytes in solvents with low dielectric

clonstants. However, their treatment has been criticized

 

because of internal mathematical inconsistencies.
Although the theory of Debye-HUckel including the ion
size parameter is very successful in describing many experi—
mental data (13,1A), there remain some unsolved problems
such as the question about the validity of the linearized

Poisson-Boltzmann equation and the consideration of short—

range forces between the ions. It also does not seem to

be possible to extend this theory to more general models

nor to higher concentrations (m0.5 M). For these reasons

much theoretical research has been done on the basis of
the exact statistical treatment of the problem (15—18).

A complete solution of the Poisson—Boltzmann equation

is not possible due to mathematical difficulties. Bjerrum,

who realized such difficulties, suggested a much simpler

approach by introducing the concept of ion—pair forma—

tion (19). He proposed a model of rigid nonpolarizable

spheres in a medium of fixed macroscopic dielectric

constant (primitive model). The ion—solvent interaction

as well as nonpolar bonds were neglected. The probability

that an ion is at a distance r from another ion was given

by the Maxwell—Boltzmann distribution function. The Bierrum

distance q is defined as the distance at which the energy

of interaction of the ions is 2kT. Two ions within a
distance q 1 r 2 a are considered as ion—pairs. Within

this region the potential energy of the two ions was taken

as the Coulombic energy. The probability of finding two

 

 

 

 

7l""""'[_ 6 - ' 7' l

ions 1 and 2 in this region is,

o [Z1Z2le2/DrkT 2
e r dr

 

probability = 1 — a 1000

 

(l—l)

 

where d is the degree of dissociation of the ion—pair,

N is Avogadro's number, C is the molar concentration,
4

Z1 and 22 are the valences of the ions, D is the bulk di—

electric constant, k is the Boltzmann constant, and T is

 

the temperature in OK. If y E IZlZ2Ie2/erT and b

IZlZ21e2/aDkT, then it can be shown that,

2
IZlZ2le 3 fb y -A

 

_ AHNC
l ’ a ' 1000 DkT 2 e y dy
2
— ””NC ’lezle >3 0(b) <1—2)

 

— 1000 DkT
b
where Q(b) E f e y dY-
2

The ion-pair formation constant KA can be written as,

l-d (1—3)

 

 

l I -—:—-———-——-—“mr gLA'fi_‘- _.‘... . .. .
I 7
|

where r+ is the mean activity coefficient. As concentration

decreases the mean activity coefficient and a2 approach

unity, then,

 

 

Introducing a from Equation (1—2) gives.

[le2le2)3

KA =1‘0‘0‘0 ( DKT Q(b) (1—5)

Values of Q(b) have been tabulated by Bjerrum for the range

1 3 b i 15. Values of Q(b) in the range 15 g b 5 80 were

obtained by Fuoss and Kraus (20). Despite the mathematical

artifacts and the oversimplification of the model, the
Bjerrum theory has been able to describe systems of 1:1

electrolytes (20) as well as polyvalent electrolyte

systems (21) in water and mixed solvents.

One of the problems of the Bjerrum theory was that

the probability function diverges for r > q and so cannot

have any physical meaning. Furthermore, at low dielectric

constants the value of q becomes extremely large. Fuoss

(22) in 1958 defined ion-pairs to include only those ions

in physical contact. The solvent was taken as a continuum

dielectric and ions as rigid spheres. Upon formation of an

ion-pair, the solvent molecules between the ions were

 

 

 

 

 

squeezed out. Cations were taken as conducting spheres
of radius "a" and the anions as point charges. This is
equivalent to considering both cations and anions as spheres

of radius a/2. By a statistical treatment the following

 

expression for the ion—pair formation constant was ob—

tained,

 

 

 

1—d
K =
A d2Cy
- _ AiTNa3 b _
KA — 3000 e (l 6)

The value of "a" corresponding to the minimum in KA can be
obtained by differentiating the above equation with re—

spect to "a". This yields,

2
— 'le2le - g <1-7>
amin-W-sq
The Fouss expression consists of two terms (23). The pre—

eXponential factor has an entropic nature and stands for a
probability factor which increases with the Size of the
C01liding ion. When 'legl = 0 the value of KA is a measure
Of the excluded volume from the solution occupied by the

ions. The exponential term is energetic in nature and

 

I . A _3_

 

expresses a shielding factor caused by the ionic charges.
The Fouss theory considers the solvent to be a continuum
dielectric and includes only electrostatic forces between

the ions.

Fouss and Kraus (2A,25) obtained an expression for the

 

formation constant of triple—ions, by assuming equal prob-
ability of the formation of cationic and anionic triple—
ions. Their final equation for the case in which the

centers of the three ions lie on a straight line is,

 

3
~ 311: I<b3) (1—8)

where a3 is the distance of closest approach of the ion—

pair and the other ion, and b3 = lZlZ2Ie2/a3DkT. Values of
I(b3) for values of b3 from 3.5 to 36.6 were calculated and
tabulated (2A,25). Consideration of boundary conditions
leads to the conclusion that triple-ions are unstable

(K3 - 0) with respect to thermal agitation when b3 : 8/3,

therefore ion-triples can form in solvents with

2
3lZlZ2le

D < -————————
— 8a3kT

(1-9)

Denison and Ramsey (26) calculated ion—pair association

constants from a Born cycle. Their thermodynamic theory

considers two ions as an ion—pair when they are in contact,

that is separated by the distance of closest approach. The

 

 

10

ion-pair formation constant calculated from their model

is expressed as,

b . (1-10)

According to the above theories the ion-pair association

constants of a salt in two solvents with the same dielectric

constant should be equal (isodielectric rule). Gilker-

son (27) noted that ion-pair association constants of some

tetraalkylammonium salts are different in 1,2-dichloro-
ethane (D = 10.2), 1,1-dichloroethane (D = 10.0), and g—

dichlorobenzene (D = 9.93) which have practically the same

dielectric constants. Gilkerson tried to rationalize the

above facts by including ion-solvent effects in the

tflueoretical expressionfku°the ion-association constant (27),

arki obtained the following expression,

KA = [(2nukT/h2)3(gvo)exp(-Es/kT)]_lexp(e2/DakT) (l-ll)
iri which u is the reduced mass, g is the internal rotational
811d.vibrational contributions to the partition function,

\’ is fine free volume available to each particle, and o is
The

a. facUn? varying from unity for solids to e for gases.

IDEuemeter' ES is the difference between the solvent-ion

al'ldsolvent-ion-pair interaction energies. To a first

 

11

approximation ES is proportional to the dipole moment of the

solvent molecule. This approach could explain the dif-

ferences in the ion-pair association constants in solvents

with the same dielectric constant. Later GilkerSOn (28)

substituted for the energy term, Es’ the free energy change

of the solution upon dissociation and came up with,

2
K = AuNa3 ex [A s _ Ass + [ZlZZIe (1 12)
A 3000 p RT R aDkT ‘

Pettit and Bruckenstein (29) have extended the Denison—
Ramsey theory by the introduction of the entropic term in
the ion-association constant expression. Their theory is
applicable mainly to solventsof low dielectric constant
(D g 10) where contact ion—pair formation must be ex—
pected.

Eigen and Tamm (30) attacked the ion-association problem
by a kinetic approach with a multistep model for associa—
tion.

From the ion—association theories mentioned, the

behavior of strong electrolytes can be explained in suf-

ficiently dilute solutions. The extension of these theories

to more concentrated electrolytes must take into account
the short—range forces between the ions which makes the

theoretical treatment complicated. The short range forces

are due to (23),

 

 

l. Repulsive forces from quantum mechanical effects.
2. The molecular structure of the solvent which results

in deviations from Coulomb's law for a continuum

dielectric medium.

 

Attractive contributions to the interaction forces
from mutual polarization of the ions, from Van—

der Waals forces, and from attractive forces of co—
valent bond formation.

A. Solvation effects.

(31),

These effects have been considered by Levine et a1.
Stecki (32), Marcus (33), and others (3A,35).
Specific ion—solvent interactions influence the extent

of ion—association and can also lead to the formation of

 

different types of ion—pairs. No quantitative theory is

available for ion—solvent interactions,but consideration of

the dielectric constant, the dipole moment, and the donor

ability of the solvent can lead to a qualitative description

of the problem.
In 195A Winstein (36) and Fuoss (37) simultaneously and

independently suggested that two kinds of ion-pairs may

exist - contact and solvent separated. Solvent separated

ion-pairs may exist only in those solvents in which one
(solvent shared) or both (solvent separated) ions have tight
solvation shells. When interaction of the solvent with both

ions is weak a contact ion—pair forms. In solvents of

 

13

medium dielectric constant, the association constant of the‘
two kinds of ion pairs can be separated by the combination
of appropriate experimental techniques (38). The extent
of formation of different kinds of ionepair cannot be
explained by simple electrostatic considerations. The be-
havior can best be explained by the donor-acceptor concept.
In strong donor solvents, ions are tightly solvated and
therefore the formation of solvent separated ion-pairs is
favored. On the other hand, in solvents of low donor ability.
contact ion-pair formation is favored.

Recently Fuoss (39,A0) proposed a model in which the sol-
vent-separated ion—pair was introduced as an intermediate
transition state between unpaired ions and contact pairs,

according to the following equilibria,

(1—13)

KA = KR(1 + KS) (1—1A)
wtierre A+ ... B- denotes a solvent separated ion—pair. The

ffilrst step in Equation (13) is diffusion controlled and

311355 equilibrium constant can be obtained from,

 

 

1A

2
in which 8 = UET’ and R is the diameter of the Gurney
coesphere. The second step is controlled by short-range

ion-solvent and cation-anion interactions with,

KS = exp(ES/kT) (1—16)

where Es is the difference in free energy between solvent

separated pairs and contact pairs.

B. Methods of Studying Ion-Association

Ion-association in solutions can be studied by dif-
ferent experimental techniques such as electrical conduc-
tance measurements, potentiometry, polarography, and a
variety of spectroscopic techniques such as electronic and
Vibrationa1,electron spin resonance and nuclear magnetic
resonance spectroscopy.

Ion—association studies by electronic, vibrational,
and electron spin resonance spectroscopy will be discussed
briefly in Section (1).

The oldest method used to study ion—association in
electrolytes is the measurement of electrical conductance.
The accuracy of association constants derived from such
measurements dependscnlthe accuracy of the theoretical

conductance equation. This method will be given more

attention in Section (ii).

 

 

15

Alkali NMR spectroscopy is one of the most informative
techniques for the study of alkali ions in solutions. Im—
provements in instrumentation have resulted in extensive

and growing applications of this technique for the study of

different association processes in solution. A detailed

review of alkali NMR technique will be given in Section

(iii).
(1) ESR, ElectronicJ and Vibrational Spectroscopy

(a) ESR Spectroscopy - Electron spin resonance

studies have yielded the most detailed description of ion—

pair structures but require paramagnetic species. Detailed

study of ion-pairing is possible because of the appearance

of hyperfine structures in the ESR spectra of radical an—

ions. The hyperfine splitting is caused by the interaction

between the unpaired electrons and nuclei of the diamag—

netic cations.

Weissman and coworkers (A1,A2) discovered that each
line in the ESR spectra of the benzophenone ketyl anion and

the naphthalene radical anion splits into four lines by

coupling to 23Na, as a result of close association of the

‘anion with the sodium cation. The effect of ion—pairing

on the g—value has been studied by Williams e: a1.(A3).

Electron spin resonance spectroscopy also gives in—

formation about different types of ion—pairs and the extent

 

 

 

of solvent participation. For example, deelmann, Jagur—

Grodzinski, and Szwarc (AA) observed two sets of metal hyper-

fine couplings for sodium naphthalenide. Sodium naphthal-

enide forms contact ion—pairsiiltetrahydropyran but solvent

separated ion—pairs form on addition of tetraglyme. The

intensity of the line due to the solvent separated ion—pair
increases with increasing tetraglyme concentration. The
authors determined the equilibrium constant between the two

kinds of ion-pairs (N200 M_l). Other evidence for the

presence of two types of ion—pair is given by Hirota and
coworkers (A5,A6) and by Van Willigen 3: a1. (A7).

Triple ion formation has also been detected by ESR.
The addition of sodium tetraphenylborate to sodium—2,5-
di—p—butyl-p—benzosemiquinone in tetrahydrofuran results in
a spectrum characteristic of the triple cation (A8).

Symons (A9) recently reviewed the application of ESR

spectroscopy to the study of solvation.

(b) Electronic Spectroscopy — Symons and coworkers
(50) reported the earliest spectrophotometric studies of

ion—pair formation. They observed marked shifts in the

position of the first electronic absorption band of a
variety of iodides as a result of changes in the solvent

polarity, counterion, and temperature. The interesting

properties of the optical spectracu‘pyridinium iodide led

Kosower to establish a scale of solvent polarity (51,52),

 

 

   

 

 

17

called theEZparameter, which is defined as the transition
energy in Kcal/mole of the longest wavelength absorption
band of l-ethyl—A-carbomethoxy pyridinium iodide dissolved
in a particular solvent. Another solvent parameter ET

was introduced by Dimroth pp a1. (53). Smid and coworkers
(5A) observed a trend in the shift of the absorption band
of the fluorenyl contact ion—pair in tetrahydrofuran with
the size of the cation. A shift to higher wavelength
results as the radius of the cation increases. The trend
in Amax was,free ion > N+Butu > Cs+ > K+ > Na+ > Li+. A

similar trend was observed by Zaugg and Schaefer (55) in

 

the spectra of alkali enolates and alkali phenolates.

The existence of different kinds of ion-pairs can be
detected by optical spectroscopy. Changes in solvent
polarity and struCture can affect the equilibrium between
contact and solvent separated ion—pairs. The absorption
bands caused by solvent separated ion—pairs are often in—
dependent of the cation and solvent, but the absorption
bands of contact ion—pairs usually show a shift to higher
wavelength as the solvent polarity increases (5A). The
equilibrium between the two kinds of ion-pairs also depends
on temperature, pressure, and anion structure. For ex-
ample, 9—(2—hexy1)fluorenyllithium in 2,5—dimethyltetra—
hydrofuran solution is predominantly in the form of contact
ion pairs at -20°C, but in the form of solvent separated

ion—pairs at —A0°C (5A). Szwarc and coworkers showed that

 

 

 

 

for fluorenyl
equilibrium 3
pressure incr
on the anion
solvent separ
Fox and Hz
the position <
tion bands of
for solvated i
tahnd a linea
electron and v
311110113 (58) ha

tion.

(0) V
found a band i
salts in benze
Edgell and cow
bands of alkal
sulfoxide. The

A the nature 0

anion. It was

3180193. POpOV

of
“Age numb

A? [R bands We

18

for fluorenyllithium and sodium salts in tetrahydrofuran, the
equilibrium shiftstowanS solvent separated ion-pairs as the
pressure increases (56). The presence of large substuents
on the anion also shifts the equilibriumtowards formation of
solvent separated ion—pairs.

Fox and Hayon (57) found a linear correlation between
the position of the absorption maxima of the first absorp-
tion bands of bromide and chloride ions and Vmax (cm—l)
for solvated iodide in the same solvent. They also ob—
tained a linear relationship between Vmax of the solvated

electron and Vmax of the solvated iodide in 38 solvents.

Symons (58) has reviewed uv spectroscopic studies of solva—

tion.

 

(c) Vibrational Spectroscopy — Evan and Lo (59)
found a band in the far IR spectra of tetraalkylammonium
salts in benzene which was assigned to ion—aggregates.
Edgell and coworkers (60,61) observed similar far IR broad
bands of alkali solutions in tetrahydrofuran and dimethyl—
sulfoxide. The frequencies of these bands depend largely
on the nature of the cation and, to some extent, on the
anion. It was suggested that the bands are due to the
cation—anion Vibration of ion-pairs or higher aggregate
Species. Popov and coworkers (62) obtained far IR spectra
of a large number of alkali salts in dimethylsulfoxide.

Far IR bands were observed which could not be assigned to

 

 

 

 

either solve

were strongly

 

of the anions

 

tion of the c
of 6Li+, NDZ,
indicated that
vibration.
Popov and
spectrum of 11'
mixtures. The
chlorate ion 8
acetone/Li+ mo
broadens and SI
behavior Shows

l.

The effect
on the far IR
were investiga
human and IR d
the existence 0
m the anion i
that NaCo ( co ) A

contact ion-pai

th
e I‘l’chofco)!l S

lhethoxyethane

19

either solvent or salts. The frequencies of the bands

were strongly cation dependent, but completely independent
of the anions (63). These bands were assigned to the vibra-
tion of the cation in a solvent cage. Isotopic substitutions
of 6Li+, NDZ, d6DMSO for 7Li+, NHZ, and DMSO, respectively
indicataithat both cation and solvent participate in the
vibration.

Popov and coworkers (64,65) studied the mid infrared
spectrum of lithium perchlorate in nitromethane—acetone
mixtures. The symmetric stretching vibration of the per—
chlorate ion shows a narrow and symmetrical band when the

.+ .
acetone/Ll mole ratio is greater than M. This band

 

broadens and shifts with decreasing mole ratio. This
behavior shows that the solvation number of Li+ is
M.

The effects of cation, anion, solvent, and concentration
on the far IR band of NaCo(CO)u in tetrahydrofuran solution
were investigated by Edgell at al. (60,61). The additional
Raman and IR data for the Co(CO); anion was explained by
the existence of different sites (or kinds of ion—pairs)
for the anion in tetrahydrofuran. The authors concluded
that NaCo(CO)u exists mainly as solvent separated and
contact ion-pairs (66—68). Addition of cryptand C221 to
the NaCo(CO)u solutions (69) in tetrahydrofuran and 1,2—
dimethoxyethane solutions converts the mix of ion sites to

a single solvent separated ion site of tetrahedral symmetry.

 

 

 

 

 
 

In tetrahydI’O

site of 02v 3

 

is some inter
sodium cation
Popov (70

of electrolyte

(ii) Elec

Arrhenius
behavior of we
sociation of a
measured equiv;
and A0 is the e
At low concent
equilibrium AB

equation (72) ,

The Oswald (111

 

20

In tetrahydropyran and 2-methyl tetrahydrofuran a new
site of 02v symmetry formed. This indicates that there

is some interaction between the anion and the cryptated

sodium cation.

Popov (70) and Irish (71) reviewed IR and Raman studies

of electrolytes.

(ii) Electrical Conductance Measurement

Arrhenius (10) was the first to explain the conductance
behavior of weak electrolytes by defining the degree of dis—
sociation of an electrolyte a as a = A/AO where A is the
measured equivalent conductance at a given concentration
and A0 is the equivalent conductance at infinite dilution.
At low concentrations and for a 1:1 electrolyte the

Kd _
equilibrium AB 2: A+ + B led to the Ostwald dilution

equation (72),

2
A C
K = (1-17)
d AO(AO-A)

crfléi Ostwald dilution equation was rearranged by Kraus and

Bray (73) to give,

CA (1-18)

 

A afld {... CE.“
o
. l
010: c I age

found to be u.

electrolytes.

 

21

A0 and Kd can be obtained from the slope and intercept of a
plot of % against C . The Ostwald dilution equation was

found to be unsatisfactory for aqueous solutions of strong
electrolytes.

Kohlrausch (7H) found that for strong electrolytes the
equiValent conductance approaches A0 according to the em-

pirical equation,
A = A - sol/2 (1-19)

The square root law of Kohlrausch found its explanation in
the Debye—Hfickel-Onsager (DHO) theory.

Debye and Huckel obtained a good first approximation to
the solution of the conductance problem from the electro-
static theory of electrolytes. Debye showed that the
eaguivalent conductance at low concentrations should be a
liliear function of the square root of concentration.

The next important step in the electrostatic theory of
eslxectrolytes was taken by Onsager which resulted in the
Chiisager limiting law for completely ionized electrolytes
('7ES,76). In the case of 1:1 electrolytes the Onsager

lJirniting law is giVen by,

A = A0 - (a*AO + 8*)01/2 (1-20)

where

in union r; is

above theorgr a

22

where

 

* _ 8.2 X 105
a " /2
<DT>3
* = 82

in which n is the viscosity of the solvent in poise. The
above theory attributes the changes in the equivalent con-
ductance with concentration to two long range effects of
ion interactions known as the relaxation and electrophoretic
effects. The relaxation term (%§ = -a*Cl/2) results from
the perturbation of the applied field, X, by the asymmetry
of the ionic atmosphere. The electrophoretic term (AAe =

_B*Cl/2

) takes into account the decrease in the velocity of
an ion due to the counter flow of the solvent in the ionic
atmosphere. According to this theory the coefficients

a*, and 5* are independent of the model. A number of ex-
tensions of the Onsager limiting law have been made (77—
85). The behavior of weak electrolytes was described by

the Ostwald dilution equation while the limiting behavior
of strong electrolytes could be predicted by the DHO theory.
MacInnes and Shedlovsky (86) suggested that both the frac-
tion of the solute that contributes to conductance and the

mobility of the ions are concentration dependent. This

led Fuoss and Kraus to propose that, "for electrolytes in

 

general, equi
increases, ‘00
tribute to 0
tion, and bees
account of inc
They introduce
tance equatior

electric const

0? conductance
fluctance squat 4

an asSociated e

A : AO~S(CQ)1/

Where

LT]
I

7? L77
f\) A)
I l
R)
5:

23

general, equivalent conductance decreases as concentration
increases, both because the fraction of solute that con-
tributes to conductance decreases with increasing concentra-
tion, and because the mobility of the ions decreases on
account of increasing effects of interionic forces" (87).
They introduced the ion association constant to the conduc-
tance equation to account for the deviations in low di-

electric constant solvents,

 

A = d(AO - SVCd) (l-2l)
_ l-d
KA ‘ 2 2
Ca Y+

where S = a*AO + 8*, and a is the degree of dissociation of
the ion-pair. Fuoss and Onsager (81) extended the theory
of conductance by adding higher order terms to the con-
ductance equation. A revised Fuoss-Onsager equation for

an associated electrolyte is (83),

1/2

A = AO—S(Cd) +ECdlog(Cd)+JlCd-KAA(Cd)yE-J2(Cd)3/2 (1-22)

where
E = ElAO — E2
E1 = 2.3026K2a2b2/2uc
E2 = 2.3026K2abe*/I6Cl/2
K2 = nNe20/125 DkT
b = e2/DkT

and

‘5‘!

thecoezzicier

 

 

24

l—q
and KA = 2 2
Cd Yr

 

_ bK/2
9.1’1Yi _ _ 1+Ka

 

the coefficients J1 and J2 are functions of solvent prop—
erties and can be expressed as a function of the size
parameter a. There has been much debate on the necessity
of introducing the J2(Co¢)3/2 term in the conductance equa—
'tion. This term has been partially calculated by different
authors (83,84,88). The values for J2 and even for Jl
obtained by different workers are not in agreement. Only
accurate sets of data with internal precision better than
1% can be used with this method (89). The major limitation
of the method for determining association constants is that
the theory is valid only for symmetric electrolytes although
it has been used for unsymmetric electrolytes with fair
results (90). Equation (22) has been very successful in
fitting conductance data of 1:1 electrolytes with 10 < KA

< 1000 M.1 over a wide range of dielectric constants.

For KA < IO M-1 almost horizontal plots of equivalent con—
ductance versus 01/2 are obtained which makes the calcula—
tions difficult. For KA > 1000 Mil the slope of the con—
ductance plot becomes very high and insensitive to changes

OfAd Also the computed sum, ECdlog(Cd)+-chd becomes

 

neglected.
Karl and
conductance d
necessarily n
constant.

higher-order"

b

paramebb_s, xvi.

L«U
t .
WOPKEp

 

25

small with respect to KACayin, and therefore can be
neglected.

Karl and Dye (91) pointed out that a-good fit of the
conductance data to the theoretical equation does not
necessarily mean a good value for the ion-association
constant. The reason is that both association and the
higher—order terms involving ion size have the same concen-
tration dependence in the first approximation and the separa—
tion of the two effects depends upon second—order terms in
the association (92). Karl and Dye showed that the terms
which were dropped in the treatment of the electrophoretic
effect are not small for those cases requiring the intro—
duction of an association constant (91). In fact, simply
retaining these terms in many cases yields surprisingly
good fits of the data for reasonable and constant ion—size
parameters, without requiring consideration of ion—pair
formation (91).

Since the publication of the original Fuoss-Onsager
conduction equation (1957) various anomalies concerning the
physical meaning of the distance parameter have appeared
in the literature. The choice of ”a" used by Fuoss et a1.
as the distance parameter was criticized by Prue and co—
workers (93,9U). This criticism was supported by Justice
and colleagues (95,96). A reanalysis of available con—
ductance data by Justice (95) lead to a reconsideration

of the physical meaning of the distance parameter in

 

agreement Wit}
the Blerrum ic
the arbitrary
distance (1: a
Poisson equati
values for the
of q iS small.
gested that th
equation, 8, b
of an ion-pail"
Recently F
separated ion-t
tween unpaired
the electrostat
equation accorc
eter R was deff
beyond which cc
I‘et’ion a g r :
uncouples the F

short range eff

this model (aft

t is prema
c(inductance the
present time is
same value Of A

Size Daramet er ;

26

agreement with the Bjerrum ion-pair concept. Even though
the Bjerrum ion—pair model has been criticized because of
the arbitrary cut—off represented by the choice of the
distance q, a much more exact integration of the Boltzmann—
Poisson equation (97) indicates that the range of possible
values for the distance parameter around the Bjerrum value
of q is small. To avoid any ambiguity, Justice (96) sug—
gested that the distance parameter in the conductance
equation, R, be called the "furthest distance of separation
of an ion—pair".

Recently Fuoss (39) proposed a model in which the solvent
separated ion-pair is an intermediate transition state be—
tween unpaired ions and a contact ion pair. He calculated
the electrostatic and hydrodynamic terms of the conductance
equation according to the above model. A distance param-
eter R was defined as the distance from a reference ion
beyond which continuum theory may be applied. Ions in the
region a i r i B were considered as ion-pairs. This model
uncouples the R parameter of the conductance equation from
short range effects. The final conductance equation for
this model (after some correction) is given by Fuoss (98).

It is premature to assume that the difficulties of
conductance theory are resolved. What can be said at the
present time is that: (I) All equations yield nearly the

same value of A0- (2) Those equations which use an ion—

3

size parameter similar to the Bjerrum distance are favored,

 

.
Fae-G‘-
-y-s .‘Lu‘v'

‘
-:olvenr
-¥\..Av’

“G
4.1

'D‘

. t

. a
:Ht.
I
t

at:

27

(3) When association constants are to be compared, the
same equation should be used to analyze the data, (A)
when the association constant is large (>103) the choice
of the conductance equation is not very important, and (5)

Recent improvements in the statistical treatment of the

problem are encouraging.

(iii) Alkali Metal Nuclear Magnetic Resonance Spec-

troscoEy

(a) Introduction - Nuclear magnetic resonance

spectroscopy is a powerful technique for the study of
electrolytic solutions. Proton and 13C chemical shift

and relaxation studies have yielded much information about
ion—solvent, ion-ion and ion—ligand interactions in solutions.
Alkali metal nuclear magnetic resonance spectroscopy can
provide direct information about the interaction of alkali
cations in solution. All alkali metals have natural
isotopes with nonzero spin. Except for 7Li and 133Cs,

line widths are dominated by quadrupolar broadening which
means that deviations from a spherically symmetric environ—
ment around the nucleus considerably broaden the NMR

line. Lithium—7 and Cesium-133 show high sensitivity and
the lines are generally narrow due to the small quadrupole
moments of the nuclei. The chemical shift range of 7Li is
about 10 ppm, while that of 1330s is several hundred ppm.

Consequently resonance lines of dilute solutions (<lO_3M)

 

can be detect
are possible
chemical shif

;.v
general, they

u-gr-x..'.

w“; o :m
. ..g
iatv‘eho fiha ‘
I“.
lr
DASH '1 fable
\

 

28

can be detected and accurate chemical shift measurements
are possible for both nuclei. The sensitivities of the
chemical shift measurements vary with the nucleus, but in

general, they are adequate to detect resonance signals down

23 39 87

to 0.005 M for Na, K, and Rb nuclei especially when

the pulsed Fourier Transform technique is combined with

high field NMR instruments.

23Na, and l33CS NMR studies

39

A large number of 7Li,
appear in the literature, while K and especially 87Rb
NMR investigations are rather sparse due to the low sensi—
tivity of the former and the broad resonance lines of the

latter. The NMR parameters of the alkali metal nuclei are

given in Table l.

(b) Relaxation Studies — Alkali NMR relaxation
studies provide significant information on the structural
and dynamic aspects of ion-solvation. Lithium—7 and Cesium—
133 nuclei are characterized by small relaxation rates in
aqueous solutions, so that the contributionof‘nonquadrupolar
relaxation mechanisms must be considered for these nuclei.

0n the basis of the correlation times in H20 and D 0,

7

2

Hertz et 1. (99) have achieved, for Li, a separation of

the total relaxation rate into two contributions. At 25°C

one of these amounts to 0.031 sec"1

and is caused by
dipole—dipole interactions, while the other has a value

of 0.024 sec"1 and is due to quadrupolar interactions.

 

/ Ex 5 rCU C< rCL EC» C Had Hi. CHAMP. aNV QHWQB m0? . H W3®H03>~
QQfiEfi; CH ANIV

 

 

#:CEOE QCCQQCCO um I @UCTUCSQQ UT ANIEV
.UOOUQQ SaUaZGCfi; OHCLZLCESG Cu ®>MQQH0EH HTLSQTZ .OQLE $52
.XOLQL< .KCLLL< HTOfiLuOQHE >Jfi>fi¢HmC®W
-fiOHUZZ .nHQSH< -80 hhdctshflmuhns tHQeUHOJZ -H mofifldwru

29

 

 

 

 

 

.msso: wt: CH .mo93o oHQEmm EE OH cfi .pcoesppmcfl oml<o osp Qua: Uopoopoon
.zaampcoEHsodxo pocfiesopop npofizocfla umoHHmEmm
zlonH av 200.0: mloaxzs.: m\s 00H :mm.s mommH
mloaxm omH 2H.o sma.o m\m m.sm omw.mH nmsw
mlofixm m 50.0 zloaxmo.m m\m wo.mm oom.m xmm
mloaxfi m oa.o mloaxsm.m m\m OOH www.ma m2mm
mloaxm Hv H.01 :mm.o m\m mm.m: mam.mm HAN
sz e.Hom .e< Assamv names seem ARV eases mo:.H msefiosz
npfiefia :H Anmv newscz pcmpmcoo an m mocwocso< um Ammzv
.uoouoo nuofizocfiq oHOQSLUmSG on o>HpmHomH Handpmz .Uopm mzz
.xosdd< .xosdd¢ Hmofisuooam mufi>fiufimcom
.Hofiozz «mea< no mofiusodosm pmofiosz .H manna

small relaxat
make an appre
hauser enhanc
conclusion.

mechanism is

 

 

 

30

For 133Cs similar studies (100) show that in spite of the
small relaxation rate, dipole-dipole relaxation does not
make an appreciable contribution. The recent nuclear Over—
hauser enhancement study by Wehrli (101) confirms this
conclusion. For the other alkali ions, the relaxation
mechanism is mainly quadrupolar which is mediated by molecu—
lar reorientation of the solvent.

A large number of relaxation investigations have been

7 133

carried out for Li, 23Na, and Cs nuclei. According to
the investigations of Hertz and coworkers (99,102,103),
the 7Li quadrupolar relaxation rate for lithium chloride in

aqueous solutions increases in the order I- < Br_ < Cl

23

<< F-. The concentration dependence of Na relaxation in

aqueous halide solutions (104) indicates that the relaxa—
tion rate follows the sequence Cl’ < Br- 2 I- < F—. In
the case of 133Cs the trend is Br” < I- 2 Cl- < F_ (102).
In summary, for alkali halides (except fluorides)
the concentration dependence of the relaxation rates is
quite small and the sequence of 01—, Br- and I- ions bears
no simple relationship to the ion size. Studies of the
temperature dependence of the relaxation rate have also
provided information on the potential barriers associated
with the relaxation process (105,106).
NMR relaxation studies of alkali ions were first re-

ported by Jardetzky and Wertz (107). A 7Li quantitative

relaxation study was performed by Craig and Richards (108)

 

 

 

 

who studied 3
nethylforrnami
been used in
Eta+ (110,111:
ions. These
tightly 9&0?-
ions in netha
other solvent

Since ion
portant in no
polar relaxer:
vents should 3
vestigation o:
relaxation net

L. d 0
study 0: ion~a

this subject (
equilibrium CO
Uuuerstand'

31

. .+ .
who studied L1 salts in methanol, formic acid, and di-
methylformamide solutions. A variety of solvents has
been used in the NMR relaxation studies of Li+ (106,109),

+ (112), Rb+ (110), and Cs+ (106,110)

Na+ (110,111), K
ions. These studies demonstrate the formation of a rather
tightly packed first solvation shell for all the alkali
ions in methanol, and for the lithium ion in a number of
other solvents (113).

Since ion-ion interactions are generally more im-
portant in nonaqueous solvents than in water, the quadru-
polar relaxation rates of these ions in nonaqueous sol-
vents should provide very sensitive probes for the in-
vestigation of such interactions. Although the quadrupolar
relaxation method should be a very useful approach for the
study of ion-association, the theoretical treatment of the
ion-ion contribution to relaxation is very complicated.
Therefore only a few investigations have been reported on
this subject (106,109-111,11A). The reliable evaluation of
equilibrium constants requires further development of the

understanding of different contributions to ion-ion ef-

fects (115).

(0) Chemical Shift Studies - The shielding of a

 

nucleus varies as a function of time due to ion-solvent,
ion-ion, and ion-ligand interactions and therefore the

observed chemical shift is an average over the different

possible conff
the chemical 5

both the probe

'5
:3
O-
(D
F‘-
2:5
09
(I)
(t
s;
C)

distances. Th
is expressed b

developed a

to
0v

 

32

possible configurations around the ion. To rationalize

the chemical shift it is therefore essential to consider
both the probability of various configurations around the
ion being studied and the magnitude of the shielding con-
tributions exerted by other species when situated at various
distances. The total shielding that the nucleus receives
is expressed by the screening constant 0. Ramsey (116)
developed a general equation for the screening constant.
Although his treatment can be applied quantitatively only
to the simplest molecules, it provides an understanding of
the origin of screening effects and a framework for further
calculations. Saika and Slichter (117) have put the cal—
culation of the screening constant on a practical basis by

dividing it into three independent contributions,
0 = Gd + op + 0 (1—23)

The diamagnetic contribution, 0d, arises from the local

diamagnetic current in the molecule and is expressed by,

 

k k|w0>l (1—2u)

in which e and m are the charge and mass of the electron,

c is the velocity of light, Ek is the angular momentum of

the k'th ele
k'th electro:
magnetic terr

. D .3
have cancticz

3 L A '-
Oi Uhcse VTI‘JC’
protons is ‘4

usually the d

approxinat e‘. V
....L)
o = -

D

 

— #w-.a.~--eu.-ae ~~~ ~

33

the k'th electron, and ‘rk is the radial distance of the
k'th electron from the origin at the nucleus. The dia—
magnetic term Gd depends only on the ground state electronic
wave function To and is a function of the symmetry of

the electronic distribution and the density of circulating
electrons. Contributions to the shielding from the elec—

trons of the other atoms are contained in GO. The effect

 

and 0 on nuclei other than

3

of these two contributions, 0d

protons if; usually minor. The paramagnetic term op is

usually the dominant shielding term and can be expressed

approximately as,

A

. A 3
p m C2 (wolk§,(£klk'/Fk)l¢o> (1‘25)

 

Q
II
I
l>|l-—’

where A is the average excitation energy. This term arises
from the interaction of the ground state with excited states

in the presence of a magnetic field.

 

Several models (118,119) have been proposed in order
to rationalize the large paramagnetic shifts of ionic
crystals. It is not an easy problem to unambiguously choose
the correct model, but quantitative estimates on the basis
of different models have led most workers in the field
(120—122) to prefer the overlap model proposed by Kondo
and Yamashita (118). According to this theory the para-

magnetic shift of cations and anions of alkali halides is

   

 

 

s and p orbli

Tons.

'_1
.23
0Q
' .1

The GXtEI

chemical Shi:

Anions showed

The order of '

 

3“

due to the short—range repulsive forces between the outer
s and p orbitals of the central ion and those of neighbor-
ing ions.

The extension of the theory of Kondo and Yamashita to
chemical shifts in solutions is more complex due to random
variation of the environment of the magnetic nucleus with
time. In solutions an exact expression for the chemical
shift would require knowledge of the radial distribution
function of the solvent molecules and other ions around
the central ion. Deverell and Richards (121) investigated
the concentration dependence of the chemical shifts of
aqueous alkali halides and nitrates by alkali metal NMR.
Anions showed a definite pattern of shielding effects.

The order of increasing shielding for all cations was

I < Br < Cl < F‘ < H20 < N03 The magnitude of the
shifts increased considerably with increasing atomic number
of the cation. The authors concluded that the chemical
shifts were caused by changes in interactions with both

the solvent molecules and the counter ions. Typical plots
of 133Cs chemical_shifts versus concentration for various
cesium salts in waterenwegiven in Figure 1. Similar plots
were obtained for other alkali salts. The concentration

dependence of the 133Cs chemical shift of cesium salts has

been examined by Halliday, Richards and Sharp (120). The

authors assumed that the concentration dependence of the

chemical shift is essentially determined by cation-anion

 

....

 

 

FiEUl‘e l. 0631
COnQ

 

 

 

 

./
133Cs Chemical Shift Csl/*
in c/s at 7-350Mc/s f
400 .'
/
/)(
Cs Br
‘ .//’
300 i
. / x
_ ,s/ / Cs Cl
/
/ ‘ 1‘ x/
200-— // ‘/
/ 1 {/i/ i/
/?f ,/{ .’//
/ F 1 /
/ / / M’
/ / t ,l
100 I ‘ ./ {I
/¢,t
/‘/,¢
" i ‘/
4/
f
0.
"“h—:., CsNO3
L Concentration (moles/kg H20)
1 g g _1
1 2 3 I.

Figure 1. Cesium—133 chemical shift as a function of
concentration. Taken from Reference 121.

 

 

hneractions

accordin So

0')
(I

Cis t

I$IIIIllIIIIIIIIIIIIIIIIIlIIIIIII----------_--==:____fl__“nb

36

interactions, and therefore, the concentration dependence

of the chemical shift should follow the probability of

cation-anion contact (HRS theory). By taking into account

the influence of the ionic atmosphere on the probability of

ion-ion contact through a Debye-Huckel type of treatment,

 

 

 

 

 

 

 

the 133Cs chemical shift data were accurately represented
from the lowest up to very high concentrations in H20,

according to the following equation (120,123),
I

2
ZaZ e expE-K(Re-a)]

 

_ B _ I
éobs — AC exp(— DkTRe 1+Ka ) — d + B (1—26)
and
A = 6(a) “—3'” (sfl — a3><N/io3>
Rm = a + RS

6(a) is a constant which depends only on the solvent

properties, a and RS are the radii of the ion and the sol-

vent molecule respectively, K is the inverse Debye length,

C is the molar concentration, Za and Z8 are the valences

éobs is the shift relative to the infinite

dilution shift as zero, 6'

of the ions,
is an experimental shift referred

to an arbitrary zero, B is the infinite dilution chemical

shift, and Re (a < Re < Rm) has little effect on the con—

centration dependence of the chemical shift. Later, Richards

and coworkers (123) tested the validity of the HRS theory

 

in low diele

.....

no COPPGlatio

l I ,
Shift

‘” 11“: Var

U28)s of the

37

in low dielectric solvents and found it much less satis-
factory. The experimental and calculated chemical shifts
for CsBr in acetic acid-water mixtures are compared in
Figure 2.

The first systematic investigation of the applicability
of alkali NMR in nonaqueous environments is due to Maciel

7

t 1. (12“) who determined the Li chemical shifts of

LiBr, LiClOu in eleven nonaqueous solvents. Popov and co-
workers (125,126) obtained the infinite dilution 7L1 chemi-
cal shifts in a number of solvents by a systematic variable
concentration study of various lithium salts. They found
evidence for the formation of contact ion-pairs in tetra-
hydrofuran, nitromethane, and tetramethylguanidine. Their
results are in agreement with the data of Maciel at al.
(12U) and of Akitt and Downs (127). In contrast to 23Na,

no correlation was found between the limiting chemical

shifts in various solvents and the Gutmann donor numbers

(128)* of the solvents.

 

The Gutmann donor number is an empirical scale of the
donor ability of solvents. It is based on the enthalpy
of formation of the 1:1 complex between a dilute solu-
tion of a given solvent S and antimony pentachloride in
1,2-dichloroethane solution,
1,2 DCE
s + Shel5 I S'SbClS

(kca1.mo1“l)

’AHS-SbC15 = Gutmann donor number

 

Figure 2.

“’CB shift (obs) [Hz

 

O 05 1.0
[CsBrJ/mol dm—a

Cesium—l33 shifts against concentration for
CsBr+HOAc-H20 systems (shifts referenced to
infinite dilution shifts). o, 0.2 mole fraction
HOAc, 0.8 mole fraction H20; 0, 0.4 mole fraction
HOAC, 0.6 mole fraction H20, 0, 0.7 mole fraction
HOAc, 0.3 mole fraction H20. Curves show the

best least squares fit of data to Equation (26)

by using solvent bulk dielectric constants:

(a) D=57.2; (b) D=h2.5; (c) D=23.8. (Re=0.435

nm, a=0.365 nm, T=298K.) Note: curves a and b
have the same origin but have been separated

for clarity. Taken from Reference 123.

 

 

The fir
twelve nona
Kidd (122).
shifts in d
the solvent

gated vario

DN-
‘vtass1u
solutions q

39

The first comprehensive study of sodium iodide in
twelve nonaqueous solvents was that of Bloor and
Kidd (122). They found a correlation between chemical
shifts in different solvents and the aqueous pKa values of
the solvents. Popov and coworkers (125,129-132) investi-
gated various sodium salts in a number of nonaqueous sol-
vents. The experimental results of Bloor and Kidd (122)
were confirmed. In addition, they indicated that the counter
ion also plays an important role in determining the behavior

23

of Na chemical shifts. A linear relationship between

23

Gutmann's donor number and Na infinite dilution chemical
shifts were obtained as indicated in Figure 3. This linear
relationship was used to estimate the donor number of a
number of solvents, which had. not been measured calorim-
etrically, from the 23Na infinite dilution chemical shifts.

Potassium-39 chemical shifts have been studied for KI
solutions in ethylendiamine and KOH solutions in methanol
(132). Recently Shih and Popov (133) presented a rather
extensive report on the concentration and counterion de-
pendence for a number of solvents.

The concentration and counterion dependence of the
87Rb chemical shift of rubidium salts in nonaqueous sol-
vents has not been studied extensively so far due to the
broad lines.

The solvent dependence of 1330s chemical shifts was

briefly considered by Halliday et al. (120). A more

F:
We 3.

Figure 3.

U0

 

 

B \
P"\
III- \
t. \
n \
n!- \
\
"l ~ .‘2
\
n \
9- \ 3'
fl \
§ -- .
a 7-- \\
1 ~ ..
5!- \
\
ot- \
\
3'- \
\
3b 7.\\
l)- \
Oh I! ..\
\
nII- \
-2. h\
,3 L 1 1 g 1 1 1 1 1 1
O 4 I I! 16 N 36 29 33 36 no
mm

Sodium-23 chemical shifts Xi Gutmann donor
numbers. Reference - aq. Na+ at infinite dilu-
tion. 1. nitromethane, 2. acetonitrile, 3.
acetone, A. ethyl acetate, 5. THE, 6. DMF, 7.

DMSO, 8. pyridine, 9. hexamethylphosphoramide,
10. water. Taken from Reference 129.

systematic
aqueous soI
The infinit
nonaqueous
dependent :
contact ior
exchange be
on the NMR

is obtained

where 5f art

and the ion

cr
[—1

V6 mole f

tained from

Where

he mean act
Debye‘HfiCke]
obtained fI‘C

Chemical

0f preferem

 

 

 

Ml

systematic approach to the 133Cs chemical shifts in non-

aqueous solvents was reported by DeWitte gt al. (13“,135).
The infinite dilution chemical shifts of alkali cations in
nonaqueous solvent are summarized in Table 2. Concentration

133

dependent Cs chemical shifts were used to calculate

contact ion-pair formation constants (135). Since the
exchange between the solvated cation and ion-pair is fast
on the NMR time scale, only one population averaged signal

is obtained,

5 = ofxf + a X (l—27)

obs ip ip

where of and 6 are the chemical shifts of the free ion

ip
and the ion-pair respectively, and Xf and Xip are the rela-

tive mole fractions of the two species which can be ob-

tained from the equilibrium,

 

Ki
+ - p + -
M + X I M ' X (1-28)
where
l-a
K =
ip G2CYE

The mean activity coefficient can be obtained from the

Debye-HUckel equation. The values of Kip and 61p can be

obtained from a nonlinear least squares iteration program.
Chemical shift studies are also suited for investigations

of preferential solvation phenomena in mixed solvent

. a ... v . . _
"U. n i .

1|. 1n“ W;

0 AU L IJ I—IV
ad AC a» .. a
3 n“

Cu AU Aw»
.I. w .. [TV
10 L .J 3v
ha ..- _ AL
ma. ... u . ,1.

fi

 

H2

Table 2. Chemical Shifts/ppm at Infinite Dilution for

7 .+, 23Na+’ 39K+ and 133

L1

Solvents. Taken From Reference 115.

+ . .
Cs Ions in Various

 

 

 

Solvent Lia Na KC CsC
Nitromethane —o.36' 45.6 —2l.lo —59.8
Acetonitrile —2.8O — 7 — 0.Hl +32.0
Dimethylsulphoxide —l.Ol — 0.11 + 7.77 +68.0
Propylene carbonate —0.6l - 9.U —ll.48 -35.2
Methanol —O.54 - 3.8 —l0.0S ~45.2
'Dimethylformamide 0.H5 — 5.0 - 2.77 — 0.5
Acetone 1.34 — 8.U —lO.H8 —26.8
Pyridine 2.5M 1.35 0.82 —3l

 

 

aReference: Aqueous 4.0 M LiClOu.

bReference: Aqueous 3.0 M NaClOu.
cReference: Infinitely dilute aqueous solutions.

systems.

in the stu:
2:
13{ )3 Jfla

preferentié
quantity ir
tion point'
chemical st
shifts of t
asmmed the
composition
ionic solva
of the two

method

<' I“

o p:
that ion-ca;

measuring t}

43

systems. Thus a variety of solvent mixtures have been used

in the study of the alkali salts by 7Li (65,124,127,136,

23 87Rb (136) and 13303 (120,123,136,

137), Na (138—143),
137) NMR. In most cases only qualitative deductions about
preferential solvation have been made. An illustrative
quantity in this type of investigation is the ”isosolva—
tion point" taken as the solvent composition where the
chemical shift is at the midpoint between the chemical
shifts of the ion in the two pure solvents (144). It is
assumed that the isosolvation point corresponds to that
composition of the binary mixture at which the inner cat—
ionic solvation shell contains an equal number of molecules
of the two solvents. One important point in using the above
method to predict preferential solvation phenomena is

that ion—pairing must be eliminated. This can be done by
measuring the chemical shifts at different salt concentra—
tions and, at each solvent composition extrapolating to
infinite dilution. Popov and coworkers (143,145) have
determined the isosolvation points of the sodium cation in

a number of mixed solvents and found solvation to increase

in the sequence,

nitromethane << acetonitrile < pyridine < tetramethyl—

urea 2 dimethyl sulfoxide z hexamethylphosphoramide

A systematic approach to the preferential solvation has

 

been made i
simplifying
alkali cati

the equilit

in which M
Recently Be
the chemica
solvent mix
bidentate a1
coordinatiol

authors alsc

of tetrahydl

 

been made by Covington et a1. (136,137). By introducing

simplifying assumptions the valuesof Kl/n

were obtained for
alkali cations in H202, H2O solvent mixtures, according to

the equilibrium,

n—X-lBX+1 + A (1—29)
in which M is the alkali cation and A and B are solvents.
Recently Delville gt al. (146) reported marked changes in
the chemical shifts of NaClOu with the composition of binary
solvent mixtures of tetrahydrofuran with unidentate and
bidentate amines. Their results are consistent with tetra-
coordination of the sodium cation by these solvents. The
authors also followed the successive steps of displacement

of tetrahydrofuran from sodium coordination by the amines.

 

2. Connie)

Cryptar

through the
her of othe
considered
in addition
ethers (fir;
(first synt}
DPOperties 1
tures of sor.
compounds ar
interesting
CyCles for a
in their use
Of actiVe io
The abil

also had pro
istry, which
anion Salt b‘

the 4031; int:

anionic, i e

 

45

2. Complexation of Alkali Cations by Crown Ethers and

Cryptands

A. Introduction

Since Moore and Pressman (147) reported that the anti—

biotic valinomycin induces the transport of potassium cations
through the mitochondrial membrane by complexation, a num-
ber of other naturally occurring macrocycles have also been
considered as potential ioncarriersthrough membranes (148).
In addition, a large number of synthetic macrocyclic crown
ethers (first synthesized by Pederson (1-4)) and cryptands
(first synthesized by Lehn and coworkers (4—7)) with similar
properties have been prepared and investigated. The struc-
tures of some naturally occurring antibiotics, crown
compounds and cryptands are given in Figure 4. Particularly
interesting is the strong and selective affinity by macro—
cycles for alkali and alkaline earth cations which results
in their use as models for carrier molecules in the study
of active ion—transport phenomena in biological systems.
The ability of crowns and cryptands to complex alkali
cations, and their resistance to chemical reduction have
also had profound effects on alkali metal solution chem—
istry, which resulted in the isolation of the first sodium
anion salt by Dye and coworkers in 1974 (149). Although
the most interesting species in alkali metal solutions are

anionic, i.e., solvated electrons and alkali metal anions,

 

 

 

 

46

O- ~hy¢uy
Keno“...

3:: IL?
Md

Valinomycin

redo (\o’} OF‘N’W
E: “’3 c; 3 Ci :3
W0 \_/° 'vuv'

l8-crown-6 lS-crown-S

1.10 diazo-lB-crown-6

c ° 7,
W: W3  §§°W°W “Q32

cryptand-22l

cryptand-222 CPYPtand—2ll

r"’\
:3- 0 g 0
("A p (— ‘ 7
wow Veg. OK’NVO-J
cylindrical macrocylic spheroidal macrocyclic
cryptand cryptand
Figure 4.

Naturally occurring and synthetic macrocycles

it is the
Cryptands
studies of
of simple
the behavi
Since :
they have 3
Some of the
the separat
partitionir
as catalyst
tion reacti
Crown e
stoichiomet
sium cation
a2:l compl
dihenzo~2u-.
30~crown-10

showed by IL
plexes Witll

in Which thE
T

.n this case

dependent of

""4.- ” "ng‘v <__

47

it is the complexation of alkali cations by crowns and
cryptands which enhances the solubility. Consequently,
studies of the thermodynamics and kinetics of complexation
of simple salts with macrocycles can be used to predict
the behavior of alkali metal solutions.

Since macrocyclic ligands are expensive to synthesize,
they have had limited commercial applications so far.

Some of their possible commercial applications are (150):
the separation of isotopes, separation of optical isomers,
partitioning of radiactive streams. They can also be used
as catalysts in electron transfer, and anionic polymeriza—
tion reactions.

Crown ethers are able to form complexes of different
stoichiometries with alkali cations. For example the potas—
sium cation can form a 1:1 (93%gfl) complex with l8-crown—6,

a 2:1 complex with benzo—lS—cggwn—5, a 1:2 complex with
dibenzo-24—crown—8, and a wraparound complex with dibenzo—
30—crown—1O as demonstrated in Figure 5 (151). Mei gt gt.
showed by 13305 NMR that cryptand—222 forms two kinds of com—
plexes with cesium salts (152). The inclusive complex is one
in which the cation is inside the cavity of the cryptand.

In this case the chemical shift of the complexed cation is in—
dependent of the counterion and the solvent. The other form
is an exclusive complex in which the cation is only par—
tially inside the cavity so that the chemical shift still

depends on the solvent and the anion (Figure 5).

 

’1.
“We 5.

48

 

 

51' (\O/fi /\
O O 0:0 °
C @ 0) of?
.0 OP'OVO
K/Od L/ovo
K+-18-crown-6
. (DB15-crown-5)
6‘0 0,8
Ofl 0 MO 0
. no gfia 0.169 .
W .
\ K§+'DB24-crown—8 + .
K -DB30-crown-10

%

Exclusive Cs+-C222

  
 

 

Figure 5. (a) Various stoichiometry of K+-crown ether
complexes. (b) Exclusive Cs+-C222 complex.

L.

The de
determinat
of the reS'
achieved b;
are potent:
spectroscoy
such studie
authors (15
general pri
dynamics of
in Section
copy to stu

ftrmation w

The mos
pounds is t:
inDPEferen<
tics of the
sible fOP t}
inflHence t}

Cycle ligarx

(1)
fish
0‘
Dena" a1 Crow

with those n1

 

 

49

The detection of the complexation reaction, and the
determination of the thermodynamic and kinetic parameters
of the resulting complex or complexes in solution can be
achieved by a variety of physicochemical techniques. These
are potentiometry, electrical conductance, calorimetry,
spectroscopy, and relaxation techniques. The results of
such studies have been reviewed extensively by several
authors (153—159) and will not be repeated here. Instead
general principles which govern the selectivity and thermo—
dynamics of the complexation reactions will be discussed
in Section (B). Then, the use of alkali metal NMR spectros-

copy to study the thermodynamics and kinetics of complex

 

formation will be described in Section (C).

B. Selectivity of Complexation

The most interesting characteristic of macrocyclic com—
pounds is their ability to selectively bind certain cations
in preference to others in solution. Various characteris-
tics of the ligand, cation, anion, and solvent are respon-
sible for this selectivity. The following parameters
influence the selectivity and binding properties of macro—

cycle ligands.
(i) Relative Sizes of Cation and Ligand Cavity — In

general crown compounds form the most stable complexes

with those metal cations whose ionic radius best matches

¥

the radius
tion (1,2:
constants
of cation
cation rad
Prewitt (l
as the K-r
stability

alkaline e

50

the radius of the cavity formed by the ring upon complexa—
tion (1,2). Figure 6 shows how the complex formation
constants in the case of 18—crown—6 vary with the ratio

of cation to cavity diameter (160). In this figure metal
cation radii have been taken from the data of Shannon and
Prewitt (161) and the cavity radii of complexes are taken

as the X—ray crystallographic values (144). The maximum
stability for complexes of l8—crown—6 with both alkali and
alkaline earth cations occurs at a cation~to—cavity diameter
ratio of unity. The increased stability of complexes of K+,
and Ba2+ ions in aqueous solutions over those of other ions
in the series is largely due to the enthalpy term (162) which
corresponds to the greater electrostatic bond energy for
those cations that fit the ligand cavity. For the smaller
crown ether 15—crown—5, almost no cation selectivity has
been seen since its cavity is too small even for the sodium
cation. For benzo—l5—crown-5 it is difficult to distinguish
the trends because of the formation of 2:1 complexes (Figure
7a). Larger crown ethers are not as selective as 18—crown—
6 because of the formation of complexes of variable stoi-
chiometry. When stability peaks occur, as in the case of
dibenzo-27—crown—9 and dibenzo—30—crown—10, the strongest
Complexes are formed with K+ and Rb+ ions which are con—
siderably smaller than the cavity of the two macrocycles
(Figure 7b).

In the case of cryptands, much better relationships

 

FiEUPe 6 ‘

_.C1_:<.‘£D(/)

51

  
  

 

 

4.0~
8.20

3.5-
3.04

I"°’W

bgK 25s I? f)

LOJ

2.0-4
Cavity Dianna-r Mom

1.5-<
1.0- c.»
0.5 If I 1 f 1 I I

0.7 1.0 1.3
Din. Mm/ Db. Cavity

Figure 6. Selectivity of lB-crown-b: log K values for the re-
action of 18-crown-6 with metal cations in H20
vs. ratio of cation diameter to 18-crown-6 cavity
diameter. Taken from Reference 160.

 

IogK

Ck

logK

Cg C P(D.LL

 

 

52

     
 
 
 
 

 

 

5-1
‘Z————21-Crown-7 in MoOH
Dibenzo - 30-Crown—10 in MoOH
(b)
‘.. Dibenzo- 21-Crown-7 in MeOH
24—Crown-8 in MeOH
IogK
3 " Dibenzoeznt -Crown-8
in 70% MeOH
2 " Dibenzo-27-Crown-9
in 70% MeOH
1 l 1 ‘1 I
0
Cyclohexo-15-Crown-5
3 d (a) In MeOH
O
Dicyclohexo-12-Crown-4 .
b9“ .\ inMoOH BmuoqumwnsinMeon
2 ' “(V o
\\ o
\ \‘
1 -
. ‘9‘ \i \15-Crown-5 in H,O

 

 

I I r I l T u
100 130 150 | 180
Na‘ K‘ Rb' Cs’

Ionic Radius (pm)

Figure 7. Selectivity of cyclic polyethers of various

sizes: log K values for reaction of several
crown ethers with alkali metal ions vs cation
radius. (a) Crowns smaller than 18-crown-6.

(b) Crowns larger than 18—crown—6. Data
points labeled 0 indicate 2:1 complex forma—
tion. Taken from Reference 155.

 

 

eXiSt bet'l
sizes of i
strated iI
bound to t

tivity bec

ably becat

(ii)
ethers, ev
respect to
of larger,
than one c2
reduces the

crown ethel

results in

 

———i_ 7 - _ WM“;

 

53

exist between the stability of the complexes and the relative
sizes of the cation and the cryptand cavity. As demon—
strated in Figure 8, each alkali cation is preferentially
bound to the cryptand with the proper size (162). Selec—
tivity becomes less pronounced for larger cryptands, prob—

ably because of ligand flexibility.

(ii) Arrangement of Ligand Binding Sites — Crown

 

ethers, even the small l5ecrown—5 are fairly flexible with
respect to their oxygen donor groups in space. -The ability
of larger, more flexible crown ethers to accommodate more
than one cation or to wrap around a metal cation greatly
reduces their selectivity. Cryptands are more rigid than
crown ethers over a broader range of cavity sizes, which

results in their higher selectivity.

(iii) Typg and Charge of Cation — The binding of

 

alkali and alkali earth cations by macrocycles can be
considered to be electrostatic in nature. Many variations
in coordination number and geometry are possible (Figure 5),
and there are no real stereochemical requirements. All that
is necessary is that the ligand provides an electron—rich en—
vironment to replace the cationic solvation shell. Smaller
cations, such as Li+ are more strongly solvated than the
larger cations. Thus considerably more energy is required

to replace the solvation shell of smaller cations. On

 

logK

g:
*igure 8

7/‘nn1r

 

 

54

10.0-4 [2211b

log K

 

 

 

K‘ Rb‘ Cs‘

Metal Ion Radius (pm)

Figure 8. Selectivity of cryptands: log K values for re—
action of several cryptands with alkali metal
cations vs cation radius. Data points: a —
value reported <2.0; b — in 95% MeOH; c — in
MeOH. Taken from Reference 162.

C

\
V
J

I
1‘ 7V 5
. d '

\ 4‘

I
9

'ani.
cause of

1

6 other
00th becau

. Y) L.
‘0; LEE
9994
‘4...“
I

0

V

th

«LO

e CO'

V)

0 no

t

 

—: ' ___

55

the other hand larger cations are not able to attract and ‘
organize the ligand molecules as well as smaller cations.
These two effects cause the selectivity peaks for cations of

2+ to be generally higher than

intermediate size, as K+, Ba
for the other cations. Complexes of large alkaline earth
cations often have higher formation constants than mono—
valent alkali cations of similar size, whereas the op—
posite is true when comparing small cations of different

charges (163). Again this results from the competition

between solvation and complexation.

(iv) Type of Donor Atom - Substitution of sulfur or

 

nitrogen for oxygen in the crown ether ring reduces the
affinity of the ligand for alkali and alkaline earth cations,
both because of the reduction of the cavity size, and be—
cause of the lower donor abilities of S and N. However,

this substitution increases the complexing ability of the
ligands for transition metal cations of similar sizes, due

to more covalent character in the binding (164).

(V) Number of Donor Atoms — Little quantitative work

 

has been done to investigate the result of varying the
number of donor atoms in the ring without changing the size
of the ring. Cram et al. showed that l8—crown—6 is a much
better host for tert—butylammonium cation than is l8—crown-
5 with one less donor atom (165). Cryptand—222.produces

much stronger complexes with alkali cations than its

 

analog,cr

chains ar

(vi)
and cowor

benzene r

of the ma:

H:

the ormai
smaller t}
to one of
the Na+ cc
ties of K+
benzene SU

Stability

 

 

56

analog,cryptand—2208,in-which the oxygens in one of the

chains are replaced by —CH2— groups (162).

(vi) Substitution on the Macrocyclic Ring — Dietrich

 

and coworkers (166) have shown that the addition of a
benzene ring to crowns and cryptands alters the Selectivity
of the macrocycles. For example, in methanol solutions,
the formation constant of dibenzo-l8C6 with Ba2+ is

smaller than with K+. The addition of one benzene ring

to one of the bridges of C222 increases the stability of
the Na+ complex in 95% methanol, but decreases the stabili—

2

ties of K+ and Ba+ complexes. The addition of another

benzene substituent into a second bridge further decreases the

2 complexes (166). These results

stability of the K+ and Ba+
may be explained in terms of ligand bulkiness, rigidity of
the ligand and the electron withdrawing ability of the
benzene ring.

Substitution of cyclohexano groups has a less dramatic
effect on the stability of the complexes and on the cation
selectivity. Schori and Jagur—Grodzinski (167) have shown
that in dimethylformamide solutions, the dinitro derivative
of dibenzo—lB—crown—6 has a lower affinity for Na+ ion
than the unsubstituted ligand. Conversely, substitution of
-NH2 groups on the benzene rings results in a slight increase
in the Na+ complex formation constant. These results are
consistent with the electron—withdrawimgcharacter of --NO2

groups and electron-donating ability of —NH2 substuents.

 

(Vii)
reaction,
the catio
can produ

constants

the nature

constants

complex

 

 

57

(vii) Solvent and Anion Effects — In the complexation
reaction, ligands must compete with solvent molecules for
the cation in solution. Therefore, changes in the solvent
can produce significant changes in the apparent formation
constants of the complexes. The selectivity of the macro—
cycles for certain cations over others may also change with
the nature of the solvent. Frensdorff noted that formation
constants of crown ethers with metal cations were three to
four orders of magnitude higher in methanol than in water
(16M). Kauffman et al. (168) found out that the enhance—
ment of the stability of complexes in methanol over water
is primarily of enthalpic origin which can be explained
by the expenditure of less energy in the desolvation of the
cation in a lower dielectric solvent. Cahen gt al. (169,
170) demonstrated that the dielectric constant is not the
only solvent parameter that influences the stability of
macrocyclic compounds. They showed that the solvating
power of the solvent has a great influence on the stability
of the complex.

The degree of ion—pair formation of the complex affects
the stability of the complex. In low dielectric media,
and where the complex cation is exposed to the anion, com—
plex formation competes with both the ion—pair formation
of the salt and the complex and alters the stability of the
complex. Smid and coworkers (171) found that in tetra-

hydrofuran solutions, the complexes of substituted

lB-crown-
those wit
the re‘SP
predomine:
undissocie
of substit
tetrahydrc

The cc
C221)+Pth

.7

been measu
(172). At
two comple
While the

are 2-3 x 1

small d‘

'90s"
.Lil

complexed a

unCOmplexec‘

VPOpy

‘ Complex

 

 

58

18—crown—6 polyethers with K+ are much less stable than
those with Na+ ion, while in water and methanol solutions
the reverse is true. In tetrahydrofuran, ion—pairs are
predominent while in water and methanol we are dealing with
undissociated cations. The order of stability of complexes
of substituted 18—crown-6 polyethers with alkali cations in
tetrahydrofuran is, Na+ >> K+ > Cs+ > Li+.
The conductances of solutions of the cryptates (Na-
C22l)+PhuB_ and (K C222)+PhuB— in tetrahydrofuran have
been measured at various temperatures by Boileu et al.
(172). At 20°C the ion-pair formation constants of the
two complexes are 1.22 x 10M and 1.11 x 10“, respectively,
while the ion—pair formation constants of uncomplexed salts
are 2.3 x 10Ll and 1.1 x 10“. Considering the relatively
small differences between ion—pair formation constants of

complexed and uncomplexed salt, one may conclude that the

uncomplexed salts form solvent separated ion—pairs (159).

C. Thermodynamics of Complexation

The thermodynamics of complexation of alkali cations
by cryptands shows a remarkable range of enthalpic and
entropic contributions. The contributions to enthalpy
and entropy are discussed by Kauffman et al. (168). Ac—
cording to these authors, the enthalpy of formation of

the complex is influenced by:

 

(i)

placer

moleCL

outsic

comple.
(V)

cation

Changi]
VGnt, eSDGC

is eXDGCtec‘
thalpy Of c

TL.

b 18 expec
independent
50f Refere
Kauffma

entropy 0f .

(i) I

the Catj

59

(i) The variation in the enthalpy due to the re-
placement of the first solvation shell of the cation
by the ligand.

(ii) The change in the interaction with solvent
molecules outside the complex as compared to those
outside the first solvation shell of the cation.
(iii) The change in inter-binding site (or intrasolva-
tion shell) repulsions, which depends on the size of
the solvent molecules and the degree of localization
of the solvent dipole moments.

(iv) The change in ligand solvation enthalpy upon
complexation.

(v) The steric deformation of the ligand by the

cation.

Changing the solvent from water to a poorer donor sol-
vent, especially if the dielectric constant also decreases,
is expected to yield negative contributions to the en-
thalpy of complex formation from effects (i), (ii), (iv).
It is expected that effect (v) will be relatively solvent
independent. Effect (iii) is difficult to assess (Chapter
5 of Reference 157).

Kauffman t 1. (168) attribute the changes of the

entropy of cryptate complex formation to:

(i) Entropy increase caused by the desolvation of

the cation.

by ori
change

(iv
format
amount
freedo

(V)

StPUCtl

The equilil
by 0222 in
(113), and
Studied as
Values of -
Vents, reSp
Of the 05+.
to ‘14.l e.
large negat
wOrkers (17
ion With 1a;
all c3368 t]
tPOpy deSta]
blentpopy t

cmnbpmatior

 

 

60

(ii) Entropy increase caused by release of solvent
bound to the ligand.

(iii) Changes in ligand internal entropy caused
by orientation, rigidification, and conformational
changes.

(iv) Decrease in translational entropy due to the
formation of a single complex from two species, which
amounts to -15 to —25 e.u., depending on the motional
freedom remaining in the complex.

(v) Decrease in solvent entropy caused by solvent

structure formation about the large cryptated complex.

The equilibrium constants for the complexation of Cs+

by C222 in acetone, propylene carbonate, dimethylformamide
(143), and 95 wt% methanol-water mixture (162) have been
studied as a function of temperature. The data yield AS°
values of —32, —21, —19, and —23.7 e.u. for the above sol—
vents, respectively. The value of A80 for the formation
of the Cs+-18—crown—6 complex changesfrom -8.l e.u. in water
to —14.l e.u. in methanol (173,17U). The origin of such
large negative AS° value is not known. Popov and co—
workers (175,176) have studied the complexation of the Cs+
ion with large crown ethers in nonaqueous solvents. In

all cases the complexes were enthalpy stabilized but en—
tropy destabilized. The authors assume that the decrease
in entropy upon complexation is related to a change in the

conformational entropy of the ligand, although it is not

 

the only

plexation
of comple.
action are

and the me

u)
H?

61

the only factor governing the change in entropy of com-
plexation. Many additional studies on the thermodynamics
of complexation, as well as on the ligand—solvent inter—
action are needed before the entropy of complexation

and the macrocyclic effect (177) can be understood.

D. The Use of Alkali Metal NMR to Study Thermodynamics

 

and Kinetics of the Complexation

 

Alkali metal NMR can provide unique information about
stability, structure and dynamics as well as about kinetics
of the complexation. Quantitative information on the
stability of a complex can be obtained by fitting chemical
shift, variable signal intensity or relaxation data to a
model of equilibria.

Upon complexation,the nucleus of the complexed cation
usually resonates at a different frequency than that
of the uncomplexed cation. When the exchange between
complexed and solvated cationsis slow on the NMR time
scale, two resonance lines are observed. The integrated
intensities of the signals are proportional to the concen;
trations of the two species, and thus the formation constant
of the complex can be determined. However, this technique
does not produce accurate results because of inaccuracies
associated with the determination of the area under the

peaks.

When the exchange is fast on the NMR time scale, only

one weigh
complexed
tion 01 ti
fixed cat:
formation
the comple

then the c

in the cal

\a

in which 6
are the re
Species. f
while

the (

Cationic SI

 

F::::_________________________________________‘F5

62

one weighted—average signal occurs. If the free and

complexed cations have different chemical shifts, the varia—

tion of the chemical shift with mole ratio (M) at a
cation

fixed cation concentration can be used to evaluate the

formation constant of the complex. If the cation and/or

the complex exist in appreciable amounts as ion—pairs,

then the contribution of these species should be included

in the calculation of the observed chemical shift as
i

= Z X.6. (1—30)
1

in which éobs is the observed chemical shift, and the Xi's
are the relative mole fractions of different cationic
species. The latter are related to equilibrium constants,
while the chemical shifts are characteristics of the various
cationic species in solution. When ion—pair formation is
important, the concentration dependence of the chemical
shifts of the salt and the complexes will provide ion—pair
formation constants. These data can then be used in mole
ratio studies to obtain the formation constantcfi‘the complex.
The variation of linewidth or relaxation times with

the mole ratio could also be used to evaluate the complex

 

formation constant. This method is particularly useful
when one of the two sites has a much larger linewidth than
the other (Chapter A of Reference (157)).

.Alkali metal NMR spectroscopy also provides valuable

informati
a quadrup
not have
because 0
nucleus.
function c
thien f
relatively
line shape
performed
the quadru
the linewi
case only
mate SOlut
tiers (1114
alescence .
the exChanE
When the re
DOSsible tc

time.

63

information about the kinetics of complexation. When

a quadrupolar nucleus is placed in an environment which does
not have cubic or higher symmetry, the NMR signal broadens
because of the asymmetry of the electric field at the
nucleus. An investigation of the line broadening as a
function of temperature yields kinetic parameters.

When the cation exchange is slow, and the signals are
relatively narrow, two resonance lines appear. A complete
line shape analysis using modified Bloch equations can be
performed to obtain kinetic parameters (178,179). When
the quadrupole coupling constant of the nucleus is large,
the linewidth of the complexed cation is broad. In this
case only one resonance line is detectable, and an approxi-
mate solution of the Bloch equations yields kinetic param-
eters (114). The linewidth of the NMR signal at the co-
alescence temperature also yields the approximate value of
the exchange rate at this particular temperature (180).
When the rate of the complexation is extremely slow, it is
possible to study the kinetics of the complexation from
the variation of the chemical shift or linewidth with

time.

 

CHAPTER II

EXPERIMENTAL

614

 

The 1:
times by f
(181). Tl
from a so]
an ice-ace
the crysta
Shown in 1:
hours at a
nitrile.
the meltin
coldfinge.
COOled nit]
this Vacuur
the cold fj
bottle with
611133 kept
(hiring Weig
Was 39i1°c
cryptand 22

cold finger

1. Purification of Materials

A. Ligands

The ligand 18-crown-6 (Parish) was purified several
times by the formation of the complex with acetonitrile
(181). The fine white crystalline adduct was precipitated
from a solution of l8-crown-6 in acetonitrile by cooling in
an ice-acetone bath. The solution was filtered rapidly,
the crystals were transferred to the sublimation apparatus
shown in Figure 9, and pumped under high vacuum for several
hours at ambient temperature to remove weakly bound aceto-
nitrile. Then the crystals were heated under vacuum through
the melting point to about 60°C in an oil bath, while the
cold finger of the sublimator was maintained at -50°C with
cooled nitrogen gas. The l8-crown-6 crystals produced by
this vacuum distillation were collected on the walls of
the cold finger, and were transferred in a dry box to a
bottle with a vacuum take off side arm. Purified 18-crown-
6 was kept under vacuum and in the dark at all times except
during weighing. The melting point of the purified product
was 39il°C in agreement with the literature value (181).
Cryptand 222 (E. M. Laboratories, Inc.) was distilled under
vacuum at 110°C and the crystals were collected on the

cold finger and stored following the same procedure as in

65

66

To Vacuum Manifold

   
 

Cold N2 Gas

.\

Trap to
protect

Vacuum
Manifold

 

 

 

 

 

 

K)

 

 

 

lmpure

 

Figure 9. Cryptand sublimation apparatus.

Taken from
Reference

CESE‘

,o
\d

h

L

b

.1 _
.1

Wm;
AG

owl.

i

,(\ . C L r .Wl‘
. . w . C. 0‘ 11 03 d e e 0 .t d 13 t
Arc .Q d e a S ab VJ P... hi 0 P b .l . . h.
«l c x...” e in. .n . v... ad .5. e an u Lt hi 3 n S l .U.
0 ... . a; e to 1an S .l a (\
We w . o. . w; W... a hi . e i t m. S e -Tv d d .W. d
_ a) no -. i e e a 3 . u e 71 S e ..i Va 6
. c .o .1 C. S «nu. n m...” nu P t t W U t 0 m
Hr.“ HQ . Wm...” mm L ,U hu 0 C “k Ale 8 O Q . n 71‘ Vols
.5 ..1 .1 t n . .1 a n. no . 0 Q h -1 m .nlu. 9
ac n? . 1.. LL. n1 ...uu w; 1. i ..V. la. 10 ill 8 «1‘ l: .

 

 

67

the case of 18—crown—6. The meltingpoint of the sublimed
cryptand 222 was 68il°C (reported 68°C (182)). Liquid
cryptand 211 was vacuum-distilled in an apparatus similar
to that shown in Figure 9 except that a cup was attached to
the cold finger (8). The cryptand was heated to about 65°C
in an oil bath and the cold finger temperature maintained
at —50°C in semidarkness. After distillation, the cold
finger was warmed up to 30-35°C. The cryptand 211 then
liquified and dripped into the cup. Upon cooling to room
temperature, the ligand solidified as a waxy solid. The
arms were broken and the cup was transferred to a bottle
with a vacuum take—off side arm and stored in the same

manner as other ligands.

B. Solvents

Methylamine (Matheson, anhydrous, 98%) was transferred
from the gas cylinder to a glass bottle maintained under
vacuum and containing Cal-l2 and a magnetic stirring bar.

A pressure indicator was connected to the top of the glass

bottle to check the H pressure build up as the solvent

2
was stirred over the CaHz. When the pressure indicator
showed about 2 atmospheres, the solution was frozen with
liquid nitrogen, and pumped out. After 2“ hours, the sol—
vent was distilled into a bottle containing sodium—potassium

alloy (1:3 w/w). Many freeze-pump-thaw cycles were per—

formed until the liquid remained blue for several hours.

 

 

 

If the so
into anot
The dry m
glass bot
Liqui<
with Na-K
over CaHQ
ammonia.
Methar
day over m
distilled.

sulfoxide

 

68

If the solvent was not dry enough, it was transferred
into another Na—K bottle and the procedure was repeated.
The dry methylamine was then distilled into a heavy wall
glass bottle for storage (183).

Liquid ammonia (Matheson, anhydrous 99.99%) was dried
with Na-K alloy in a similar way. The preliminary drying step
over CaH2 was omitted because of the good quality of the
ammonia.

Methanol (Mallinckrodt or Fisher) was refluxed for a
day over magnesium turnings and iodine and then fractionally
distilled. Propylene carbonate (Aldrich) and dimethyl—
sulfoxide (Fisher) were refluxed over calcium hydride under
reduced pressure for 12 to 24 hours and then fractionally
distilled. Methanol, propylene carbonate, and dimethyl—
sulfoxide were further dried for 4-12 hours over freshly
activated 4A molecular sieves. These solvents showed a
water content of less than 100 ppm by Karl Fisher titra—
tion. Deuterium oxide (KOR isotopes, 99.75 Atom %D) was
used as received. The distilled water which was used for
the calibration of the conductance cell was deionized by
a "Milli—Q" water—purification system (Millipore Corporation).
The specific conductance of the deionized water was found

to be 9 x 10‘7 ohm—1 cm'l. The specific conductance of

methylamine was 1.1 x 10'8 ohm"1 cm—l.

u (\ Q a .C a .1 i 3:
LI _ A... I. HA1. my. . ..H,H S “I“
Qv Ow . VIA e .a .

AC ..nu mu \ e no a .c
WV .1 mm n. .Q 7,. at.

m. m nu DC a... n1 ..n1. .1-
Flu AU .HA ..I. .nl. ... a S
W; 9% n: w . O -H _ AC
.nd 7: :1. said who .mu. m .

ylborat

S

v
I
v
L'

Sl’llthesized
Dhen

S 73601“

Y?
.3.

69

C. Salts

Cesium iodide (Ventron Alpha Products), and cesium
bromide (Polyresearch Corp.) were dried at 60°C under
vacuum for several days. Cesium thiocyanate (Pfaltz and
Bauer) was recrystallized from reagent grade methanol and
dried under vacuum at 50°C for 2 days. Cesium tetraphenyl-
borate was prepared by reacting sodium tetraphenylborate
with cesium chloride in tetrahydrofuran solution. The
resulting precipitate was washed thoroughly with distilled
water and dried under vacuum at 70°C for 2 days (152).
Cesium triiodide solutions were made by adding equimolar
amounts of cesium iodide and iodine. Cesium nitrate and
cesium perchlorate (Ventron Alpha Products) were dried at
120°C for several hours. Potassium chloride (Mallinckrodt)
was recrystallized from Milli-Q water and dried in vacuum
at 70°C, then ground and dried once more for two days at
200°C in the presence of P205. Rubidium bromide and ru-
bidium iodide (Ventron Alpha Products) were dried at about
110°C for several days. Lithium perchlorate (Fisher)
and lithium bromide (Matheson Coleman and Bell) were dried
at 190°C for a few days. Tetraphenylphosphonium iodide
(Ventron Alpha Products) was recrystallized from water and
dried at 100°C. Tetraphenylarsonium tetraphenylborate was
synthesized by mixing equal proportions of aqueous solutions
of tetraphenylarsonium chloride (Aldrich) and sodium tetra-

‘phenylborate (Ventron Alpha Products), and dried at 100°C

L2.)

‘..'v ..‘_

 

IIIII::::j——————————————————————————————————————————=‘-———————-————————————t===::

70

for 2H hours. Tetraphenylphosphonium thiocyanate was
synthesized by mixing equal proportions of aqueous solutions
of sodium thiocyanate and tetraphenylphosphonium chloride,

and dried at 50°C for 2H hours.

2. Glassware Cleaning

The glassware for methylamine and ammonia solutions was
first washed with an HF cleaner which consists of 33%
HNO3, 5% HF, 2% acid—stable detergent, and 60% H20 by
volume. After thoroughly rinsing with distilled water,
the glassware was filled with aqua regia and kept under the
hood overnight. The glassware was then rinsed thoroughly
with deionized water and oven dried for several hours.
Other glassware was soaked in sulfochromic cleaning solu-
tion overnight, then rinsed with distilled water and oven

dried.

3. NMR Techniques

A. NMR Instruments

All 133Cs and 7Li NMR data were obtained on a home—
bUilt, single coil, pulsed spectrometer, at 1.A09 Tesla
which employed a Varian DA—6O magnet and console, and was
equipped with a wide band, variable temperature probe
Capable of multinuclear operation (18A). A small external

probe was placed 1.5 to 2.5 cm from the sample to serve

,- z.‘ .4
Width 01
.'_ 1

01°0th 1.0

71

as the lock. This probe contained water doped with a
small amount of a paramagnetic species (185). The line—

1H lock signal was about A Hz. The Varian

width of the
proton lock circuitry was used to lock the magnetic field.
A Nicolet 1080 computer which was coupled to a Diablo
magnetic disk system was used to carry out the averaging

of spectra and the Fourier-Transformation of the data.
Cesium-133 and Lithium-7 NMR were performed at 7.87 MHz

and 23.32 MHz, respectively. All 133CS NMR data were ob-
tained with 5000 Hz sweepwidth and 8 K memory.. In all
cases the linewidth at half-height was less than 2 Hz.

The temperature was controlled within :0.5°C as measured
with a calibrated thermocouple. The errors in chemical
shifts were 30.15 ppm. In 7Li NMR measurements a sweep—
width of 1000 Hz with 8 K memory was used, and the chemical
shifts obtained were accurate to within i0.l ppm.

A11 87Rb NMR and one set of 133Cs NMR (for a comparison
with DA-6O results) measurements were performed on a
Brucker WH-180 superconducting multinuclear spectrometer
which consists of a superconducting solenoid, a Nicolet
1180 computer disk system, a quadrature detection system,
and a temperature control unit. Most of the spectra were
obtained with a sweepwidth of 5000 Hz and used 8 K of

87Rb chemical shifts depend

memory size. The errors in the
on the linewidth and the signal to noise (S/N) ratio of the

:resonance line. The broader the line, the smaller is the

 

 

72

S/N ratio, and less well—defined is the maximum of the

peak.

B. Data Handling

Cesium—133, lithium-7, and rubidium—87 chemical shifts
were first referred to; a 0.7 M aqueous solution of CsBr,
a 4.0 M aqueous solution of LiClOu, and a 1.0 M solution of
RbBr in D20. The chemical shifts were then corrected to
refer to infinitely dilute aqueous solutions. The values
of such correctionsforl33Cs, and 87Rb reference solution
are, +9.89 ppm, and +5.89 ppm, respectively. The reference

solution for 133Cs measurements was sealed in. a 5 mm NMR

 

tube which was coaxially sealed into a 10 mm tube. The
space between the two tubes was evacuated and vacuum—sealed.
In this way, the ambient temperature shift of the reference
could be obtained even when the probe was cold (186). Two
kinds of reference samples were used for 7Li measurements.
Both of them contained 4.0 M aqueous LiClOu solutions but

one of them was placed in a 10 mm NMR tube and the other

in a 5 mm tube which was coaxially sealed into a 10 mm

tube. The chemical shift of aqueous LiClOu is concentra-
tion independent; but because of the homogeneity differences,
the chemical shiftscfi‘these two reference samples are not
0.23 ppm). All 7Li chemical shift

the same (a a

10mm— 5mm =
data were corrected to the infinite dilution with respect

 

netic sus:
reference

Transform

(1})

 

 

73

to the reference sample in the 10 mm NMR tube. Chemical
shifts are corrected for the differences in bulk diamag—
netic susceptibility of the solvent (nonaqueous) and the
reference (aqueous) (l87a) as appropriate for Fourier

Transform NMR (l87b),

2 sam 1e ref
5 — + 3710“) p - xv ereme) (1—31a)

corr _ 6obs

41 ( sample _ reference)
3 XV Xv

6corr = éobs (1'31b)

where Xsample Xreference

v , u are the volume susceptibility
(31b) of the sample and reference solutions, respectively,
6corr and éobs are the corrected and observed chemical
shifts, respectively. Equation (l—31a) applies to the DA—6O
instrument where the applied magnetic field is transverse
to the long axis of the cylindrical sample tube, while
Equation (1-31b) applies to the WH—l80 spectrometer where
the polarizing magnetic field is along the long axis of
the sample tube. The values of volume susceptibility of
the solvents and the corresponding corrections on each
instrument are given in Table 3. The contribution of the
salt to the magnetic susceptibility of the solution was
ignored since all measurements were done at low concen-

trations.

 

 

 

.WDQGESCHQWCH
Omwfllzz UCQ OWI<Q CO mucmxxfiom. m30fic:w> L0 COflUOTLLOU EQHHfiQHHQanmwumw OfiQQEMwWEWufiQ -m @HQMRH

 

74

 

 

mx m>+<>\m> + >x m> + <>\<> n >x

 

 

 

 

 

< oLprHE "509% oopmHSonQm
ems.o hopes
se.o- mmm.o+ Aev woe.o omzoxteaseaseeesxoa
w:.o| :m.o+ mom.o Aomzmv oUHKOMHSmfikcooEHQ
mm.o: wH.o+ :mm.o, Aomv ouwcoohmo oCoH%Q0hm
mm.OI m:.o+ mam.o AmOoEV Hocmflpoz
fim.o+ moa.ou mm.o masoEE<
s:.o| mmm.o+ wow.o AooHHIV ocflEmamnpoz
AEQQV AEQQV OH x zpflafloflpdoomsm pco>aom
owfllmz go om|<m :o w capocwmsmflo
cowpooppoo Coepoonsoo oESHo> xasm

 

 

 

.mpgoszspmcH
owalmz ocm ow|<m Co muco>flom mSOHsm> mo SOHpoohhoo hpflafipflpgoomsm OHrommEaHQ .m oHomE

lllIllIlIIlIIIIIIIIIIIIIIIIIII-IlI---------

 

The i
were obta

equations

gram (188

Two k
were used
Solutions
wall this:
solvents 1
Of 0.5 mm
0°C a8 Sh<

measuremel

75

The ion-association and complex formation constants
were obtained by fitting the NMR data with the appropriate
equations using the nonlinear least squares KINFIT4 pro-

gram (188) on a CDC-6500 or a CDC-7501 computer.

C. NMR Sample Preparation

Two kinds of 10 mm 0.D. precision NMR tubes (Wilmad)
were used for measurements on the DA-60 NMR instrument.
Solutions in liquid ammonia were prepared in tubes with
wall thickness of 1.0 mm; those in methylamine and other
solvents were prepared in tubes with the wall thickness
of 0.5 mm. These two kinds of tubes were calibrated at
0°C as shown in Figure 10. The samplesftm°Brucker WH—l80
measurements were prepared in l5-mm spinning NMR tubes
(Wilmad) and coaxially mounted in 20 mm tubes which con-
tained D20 as the lock.

All NMR samples in methylamine and liquid ammonia were

prepared under high vacuum (<10.5 torr) in extended NMR

 

tubes of the type shown in Figure 11. In the case of

salt solutions, solutions used for the mole ratio studies,

 

and solutions used for the concentration study of the 2:1
1806
(“T
Cs

ligand were placed into the NMR tube. The Kontes valve

) complexes, weighed amounts of the salt and/or the

was then closed and the tube was connected to the vacuum
manifold with 9 mm Fisher-porter ”Solv—Seal" joints. The

NMR tube was flamed and pumped out for an hour. Then the

   

Au.—

6.0 '

3.0 -

L n

0 0.
9.. I

SEE» @E3.0\/

figure 10

 

 

76

a)

 

E _ ..
g4o- -
2 _ -
§

 

 

l 1 l

 

l I l I
6.0 8.0 l0.0
Height (cm)

 

I l l I I 1

3.0 *-

N
O
l

Volume (ml)

'6
I

 

 

 

0 [0 2.0 3.0 40 5.0 6.0
Height (cm)

jFigure 10. Calibration curve for 10 mm NMR tubes at 0°C.

(a) wall thickness = 0.5 mm, (b) wall thick—
ness = 1.0 mm.

Figure 11.

77

T0 VACUUM
g

 

 

Figure 11. Extended NMR tube for high vacuum.

solvent

:msimw

l—cJ
i“:

’..'
|__.l

thorough

the sclu

78

solvent was distilled very slowly into the NMR tube, which
was immersed in an isopropanol—dry ice bath at -78°C,

and filled to the mark. The walls of the tube were washed
thoroughly by the solvent to bring all the reagents into

the salution. The solution was then frozen completely in
liquid nitrogen, pumped out, and vacuum sealed. The frozen'
solution was thawed in an isoprOpanol-dry ice bath. The
height of the solution in the tube was measured carefully

at 0°C, and finally the volume of the solution was obtained
from the calibration curve (Figure 10). In the case of the
concentration studies of the 1:1 and 2:1 complexes, stock so-
lutions were made in methanol. Known volumes of the solution
were transferred to the NMR tube, frozen, and pumped out.
Methanol was then removed by distillation under high vacuum,
and the residue was pumped out for 1 hour, before transfer
'of the solvent into the NMR tube. Salt solutions in sol-
vents other than methylamine and liquid ammonia were pre—
pared from stock solutions by using volumetric flasks. The
volumetric flask was weighed before and after the addition
of the ligand, then the flask was filled to the mark with
the stock solution of the salt. The sample for the kinetics
study of complexation of lithium bromide by cryptand-211 was
prepared in the apparatus shown in Figure 12. Weighed
amounts of lithium bromide and the ligand were placed in

the NMR tube and the side-arm respectively via the exten-

sion tubes. The extension tubes were sealed and the

Figure 12 .

79

 

TO VACUUM _
+-

 

 

 

 

 

 

Figure 12. Extended NMR tube for the kinetic experiment.

apparatu
into the
the vacul
side-arm

both the

(‘1‘

the sal
apparatus
salt and
tions we:
ratus was
The time
data was
data were
data vau

0V er a tW

' Com

RGSiS'
HZ with a
by ThOmDS<

minor mm

the Cell I

was shunts

80

apparatus was connected to vacuum. Methylamine was distilled
into the NMR tube and the apparatus was disconnected from
the vacuum. Some of the solvent was distilled into the
side-arm and the apparatus was shaken at -50°C to dissolve
both the salt and the ligand. Care was taken to ensure

the salt and the ligand solutions were not mixed. The
apparatus was kept at -50°C overnight to make sure that the
salt and the ligand were completely dissolved. The solu-
tions were mixed at -50°C in the NMR tube, and the appa- e
ratus was placed in the precooled (-50°C) probe immediately.
The time lag between mixing and the acquisition of the first
data was about 15 seconds. After a few pulses (1-5) the
data were stored on the disk for later processing. The
data acquisition and storage process was repeated 98 times

over a two hour period.

4. Conductance Method

 

A. Conductance Equipment

Resistances were measured at 400, 600, 1 K, 2l<and 4 K
Hz with a bridge assembly originally designed and described
by Thompson and Rogers (190) which was duplicated with
minor improvements by Smith (191). The complete con—
ductance circuit is described elsewhere (191,192). When
the cell resistance was greater than 90,000 ohms, the cell

was shunted in parallel with a 90,000 ohm standard precision

 

resistor, a1
measured re
point detec
with a side
salt, was Ll

i0.04°C in

 

The cel
in the samp
chloride so

of Barthel

81

resistor, and the cell resistances were computed from the
measured resistances. An oscilloscope was used as a null-
point detector. An Erlenmyer-type cell shown in Figure 13,
with a side arm for the introduction of the solvent and
salt, was used. The cell was thermostatted to within

i0.04°C in a constant temperature ethylene glycol bath.

B. Data Handling

 

l was determined

The cell constant of 1.0213i0.0004 cm-
in the sample resistance range at 25°C. Aqueous potassium
chloride solutions were used and the conductance equation

of Barthel g2 El. (193) was applied as follows:

1/ 3/2

A=l49.873-95.01 c 2+38.u8 c logC+l83.l C-176.4 G (1-32)
Changes in the cell constant with temperature are
negligible. If we consider a conductance cell which is
made of Pyrex (coefficient of linear expansion = 3.5 x 10"6
1)

°K- , and its electrodes are 10 cm apart from each other,

and have radii of 1 cm, the change in the cell constant

for a 40°C change in temperature is about i0.00045 cm"-1

which is about the accuracy of the measurements.
Measured resistances were corrected for irreversibility

at the electrodes, and the capacitance by-pass effect by

using Equation (32),

 

Figllre 13‘

 

82

 

The conductance cell.

lgure l3.

in which

resistanc
able pare
tion was

KINFIT pr
calculate
ion assoc:
were dete

conductan

Potas
Cessive p
(1810le ed

CCSiu
proCedure
w:"blaok

hours: lln

Obtained,
age bottl
Side drnl.

the Cell,

83

2 b
R = R + af + —: (1-33)
meas o /f
in which Rmeas and R0 are the measured and corrected

resistances, f is the frequency, and a and b are adjust-

able parameters. The best value of R0 for each concentra—
tion was obtained by using the nonlinear least squares

KINFIT program (188). This value of R0 was then used to
calculate the equivalent conductance of the solution. The
ion association constant and limiting equivalent conductance
were determined by fitting the conductance data to the prOper

conductance equation with the KINFIT program.

C. Sample Prgparation for Conductance Measurements

Potassium chloride solutions were made by weighing suc-
cessive portions of the salt into a weighed amount of
deionized water in the conductance cell.

Cesium iodide solutions were prepared by the following
procedure: The lid of the cell was sealed with Apiezon
W, "black wax", (Figure 13). Then the whole cell assembly
was connected to high vacuum and pumped out for several
hours, until a pressure of less than 1 x 10-5 torr was
obtained. Methylamine was transferred from a weighed stor-
age bottle into the cooled (-40°C) cell under vacuum. The
side arm was flamed out to transfer all the solvent into

‘the cell. Valve B was closed and the cell assembly and

W.
08.
EC.

0

4.
t

he on
e be

.0

the s
'T1
Th

QC
an
4 . .

«D
Q.
0,.

mu,“

84

the storage bottle were disconnected from the vacuum line.
The outside of the storage bottle was cleaned and dried.
The bottle was weighed again to calculate the amount of the
solvent transferred. Weighed amounts of cesium iodide were
added into the side arm, and the cell assembly was con-
nected to the vacuum line again in order to evacuate the
side arm. Valve A was then closed and the cell was dis-
connected from the vacuum. [The salt was washed into the
cell by repeatedly distilling some solvent into the side
arm, dissolving the salt, and transferring the solution
back into the cell. After complete transfer of the salt,
the side arm was warmed up to ensure the complete transfer
of the solvent into the cell. Valve B was closed, and the
cell was disconnected from the vacuum line, and kept in the

' glycol bath for 30 minutes before making resistance measure—

ments.

 

CHAPTER III

THERMODYNAMICS OF ION—ASSOCIATION OF

CESIUM SALTS IN METHYLAMINE

 

85

 

The
complexe
tands ir
and liqu
formatio
the pres

The
shifts o
l8-crown
US to st
that a C
investlg.
SOlvent,

The <
Blerrum ;
of ion-pa
or medium

iOn‘dSSoc

than 15.

 

 

1. Introduction

The main purpose of this dissertation is to study the
complexation of alkali cations by crown ethers and cryp-
tands in nonaqueous solvents, especially in methylamine
and liquid ammonia. Such studies produce valuable in—
formation about the behavior of alkali metal solutions in
the presence of macrocyclic ligands.

The unusual concentration dependence of the chemical
shifts of 1:1 and 2:1 complexes of cesium salts by
l8—crown—6 in methylamine solutions (Chapter IV) motivated
us to study this system extensively. It became clear
that a complete understanding of the system required the
‘nvestigation of ion—association of cesium salts in this

olvent. .

The concept of ion—pair formation was introduced by
jerrum in 1926 (19). Since that time, various properties

f ion—pairs have been studied, mostly in solvents of high
r medium dielectric constant, but little is known about
cn—association in solvents with dielectric constants lower
han 15. The existence of triple ions in low dielectric
edia was proposed by Fuoss and Kraus (24) many years ago,
ut until recently the presence of such species has merely

een inferred on the basis of deviations from classical

aws .

In

of cesi
be pres
high as
-ines a:
tions (<
and the
hethylar

boiling
on the t
In a

iodide

[—1.

05 two m
Constant

in this

 

 

87

In this chapter, an extensive study of ion—association

of cesium salts in methylamine by 133Cs NMR Spectroscopy will

be presented. The sensitivity of 1330s NMR is relatively

high as compared to other alkali nuclei, and the resonance

lines are very narrow. Therefore, signals from dilute solu—

tions (down to 0.0005M) of cesium salts have been detected

and the chemical shifts have been measured accurately.
Methylamine has a dielectric constant of only ll at its
boiling point (~6.3°C) so we rationalized the chemical shifts
on the basis of the formation of ion—pairs and triple—ions.
In addition to NMR studies, the conductance of cesium
iodide in methylamine was measured to permit comparison

of two methods for the determination of ion-pair formation

constants. The results of such studies will be discussed

in this chapter; and will be used in the next chapter to
ermit calculatiOn of the complexation constants for cesium

alts with l8—crown—6 in methylamine solutions.

Cesium-133 NMR Studies of Cesium Salts in Methyl—
amine

A. Concentration Dependence of 133CS Chemical Shifts

of Cesium Salts in Methylamine

The concentration dependence of the 133Cs chemical
ifts of cesium iodide in methylamine at various tempera—

res was examined. The results are given in Table 4

om.

 

 

 

 

 

 

 

 

 

 

 

 

OCfiEdn%£;®E

5. WV

\Vpg .h;\~nh

H 3 U. H, got 3 U

 

.QQLSQQLQQEQ WSOJLQ
t N

Q .J «A .0 U «K O 079 AH

206:3 3L. 3:00:00

Q

my N. fi~ SMLw

1!!
I!

 

 

 

 

 

 

 

em :ma om.:mH mw.:ma om.mmH em.mmH em.mmH no.5mfl Hozmo.o
em ems oo.:ma 50.:NH mfl.mma mm.mma am.owfi eo.sma . ssmmo.o
. HH.:NH ms.ema msomo.o
mw.mma HH.:NH sm.:ma wm.sma mo.mma s©.mmfl mm.oma mwwfio o
s mma mm.mmfl mm.mma sm.:mfi ©©.:NH mm.mma om.mma swwflo o
. .em.mmfi Hm.mmfi momae.e
Wm.mmfi mm.mmfl om.mma sm.mmfi ww.mmfl 35.:NH mm.mma smmflo o
w mmfi sw.mmfi sm.mmfi om.mma m:.mmfl m:.:ma mm.:ma meoao o
ms.mma mm.:ma osmoo.o
. H:.mmH mm.mmfl mosoo.o
% we Hma sw.HmH OH.NNH mm.mmH H:.mma HH.mmH :m.mmfl :Hmoo.o
m . os.omfi mm.mmfl oomoo.o
H omH em.ONH 0:.omfl mm.oma :m.oma o:.HmH ms.ama ssmoo.o
mo.HmH osaoo.o
om.wHH mm.oma maaoo.o
Hm.sHH m:.mHH msooo.o
ma.mHH oo.maa moooo.o

mm: s.mH| m.m: m: m.m o.ma o.mm sz

_ .ocoo
oo noszpmpoQEoB

 

Asoov whee

 

 

 

 

 

 

 

 

.mothwLoQEoB mSOHho>
Pm wflflEwfihflpmz CH HmO .HO P.HHQD HQOHEBC) D) aD|.|SIL|)1 Ill

 

 

 

and shc
in the
magneti
interac
solvent
phenylb

illustr

sible t!
The 8011
was fine;
Solutior
lil Com;
chemica;
practice
fOre> Ct
COUCentr
mole rat
Table 6

iHCPeasi
at Vario
CGSium 0
than Wit
CeSium t:
independ.
the ChEm;

aPe giVeI

89

and shown in Figure 1“. At all temperatures an increase
in the concentration of cesium iodide results in a para-
magnetic (downfield) shift indicating that the cesium cation
interacts more strongly with the iodide ion than with the
solvent. The data for a similar study with cesium tetra-
phenylborate in methylamine are given in Table 5 and are
illustrated in Figure 15. Since the solubility of cesium
tetraphenylborate in methylamine is low, it was not pos-
sible to study this system at temperatures below -3°C.

The solubility of cesium tetraphenylborate in methylamine
was increased by the addition of lB-crown-6 to the salt
solutions. Since the formation constant of the resulting
lzl complex is larger than 10“ (Chapter IV), a plot of the
chemical shift versus (l8-crown-6)/(Cs+) mole ratio is
practically linear in the range 0 < mole ratio < 1. There-
fore, the chemical shift of the uncomplexed Salt at each
concentration could be obtained by extrapolating to zero
mole ratio. The results of such studies are shown in
Table 6 and Figure 16. A diamagnetic shift occurs upon
increasing the concentration of cesium tetraphenylborate
at various temperatures (Figure 15) which means that the
cesium cation interaction with the solvent is stronger
than with the tetraphenylborate anion. In the case of
cesium thiocyanate, the chemical shift is concentration
independent in the concentration range studied. However,
the chemical shift is temperature dependent. The results

are given in Table 7 and illustrated in Figure 17. In

 

)
hobsflppm

 

"4 X
"6*
"8-
.\
120-
|22~
|24~
126-
6‘
)3.
.28 . ’2)
63% 4‘
’3’5
wok

Fi‘a’ul‘e lu

 

ppm)

 

__’___________ ___.._L.

90

  

 

.gure l“.

“4

..Il6

-||8

l20

|22

|24

l26

l28

 

I30

Concentration and temperature dependence of the
Cs chemical shift of cesium iodide in methyl-

amine.

E / E), u. . v? a l
5 / \ 0C 9. MU- «3 7i ii 0 5 7 0 5 9 mi a v1 C 0
II. _,{ 7 1!. 2 7a 7. 6 .l. 9 0 0 WI. dd 33 4|. m

e . .Hv O 0 .Il qli l 2 2 «3 3 C). PW; r0 7! O m
.l. C O «No AU 0 0 AU 0 flu O 0 AU filo 0 0 TL 6 e
b n 0 0 Av flu fl filo AU AU AU 0 O 0 AU 0 0 h h
a O . . . . . . . - . . - C at

T nb flu flu ml; 0 Wu flu O 0 0 O O 0 AU 0 dd 2“

 

 

 

91

133

 

 

 

 

Table 5. Concentration Dependence of the Cs Chemical
Shift of CsBPhu in Methylamine at Various Tem—
peratures.

éobs (ppm)
Temperature, 0C

Sonc. (M) 25.0 13.2 5.8 -2.9

0.00048 17.72 24.70 27.96 31.37

0.00072 13.30 19.35 22.69 25.71

0.00074 l3.07,l3.07 22.53 26.02

0.00113 9.19 14.62 17.80 20.82

0.001275 7.72 13.38 16.25 19.27

0.00171 6.56 14.70 17.26

0.00210 4.85 9.97 12.84 15.55

0.00265 2.83 7.88 10.36 12.68

0.003175 1.75 6.48 8.65 10.90

0.00390 0.04 6.79 9.27

3.00505* 2.0:0.5 3.8t0.5

1.00509' —2.44

3.00612 —4.07,-3.91 2.45

).00727* —5.0i0.5 -O.95i0.5 l.OiO.5

).0103* —7.u:o.5 -3.4 :0.5 1.65:0.5

 

 

 

3Chemical shifts were obtained from the extrapolation of
the mole ratio curves to 0.0 mole ratio.

.1gure 15

«EQQV anon

 

 

Sobs (ppm )

Figure 15.

92

 

 

 

 

 

3O -.
1 l 1 l 1 1 1 1 l 1 l
0.0 0.2 0.4 0.6 0.8 l0 l2
[Cs’] x lo"- (M)
Concentration and temperature dependence of the

133Cs chemical shift of cesium tetraphenylborate
in methylamine.

U

able

4‘

e
w I n
AC 1.) .l
w I! AU a
U 4|. #0
O O b
. Q - AU
DIV 0 a

 

 

 

93

Table 6. Variation of the 133Cs Chemical Shift with the
Mole Ratio (18C6)/(CsBPhu) in Methylamine Solu—
tions at Different (Cs+) Concentrations and
Various Temperatures.

 

 

 

 

 

 

 

Gobs (ppm)
(Cs+) Mole Ratio Temperature, °C
(M) +
(1806)/(CS ) 25.0 13.2 5.8
0.00505 0.0a 2.0e0.5 3.8:0.5
0.404 8.03 10.12
8.11
0.519 9.50 11.75
0.648 11.75 13.92
0.760 13.61 15 55
0.00727 0.0a _5.0:0.5 —0.95:0.5 1.0:0.5
0.396 2.76 6.48 8.57
as 0.456 4.00 7.49 9.81
0.668 8.11 11.52 13.85
0.822 10.28 13.69 15.78
0.0103 0.0a -7.4:0.5 —3.4:0.5 —1.65:0.5
0.209 —3.06 0.74 2.60
0.495 3.07 6.79. 8.73
0.644 6.01 9.43 11.52
0.857 9.89 13.54 15.71

 

 

aObtained by the extrapolation to 0.0 mole ratio.

4.1

I
t

igure 1(

 

94

a) [Cs’] . 00051 M b) [cg - 00072 M

 

 

 

 

 

 

 

 

v I 1 l
at of
g 5 - E 5 -
5 §
10 - ‘° IO - aw c
are 102- c
'5 P- 5“ '5 '- 5'. C
1 1 . 1 J . 1 1 1
00 04 08 00 04 on
[mm/[cc] [necsmcr]

c) [(23] - 00103 M

' I ' I

 

-5-

o—

 

(I

 

Figure 16. Cesium-133 chemical shift versus (18-crown-

6)/(CsBPh ) mole ratio at different concen-
trations of CsBPhu and various temperatures.

0.001.

314

u].
0

0.01803

 

 

 

 

 

 

L4_4, rrrrr‘———————————————-——————————__‘=‘=“‘_“’_____:flllillv
95
Table 7. Concentration Dependence of the 133Cs Chemical
Shift of CsSCN in Methylamine at Various Tem—
peratures.
aobs (ppm)
m Temperature, °C
conc.

(M) 25.00 9.4 6.0 -2.5 —10.3 —16.2
0.00094 60.68 64.33 65.26 67.51 68.82 69.76
0.00148 60 68 64.17 65.34 67.04 68.82 69.91
0.00428 60.76 64.25 65.34 67.12 69.06 69.76
0 0054 60.65 —————————— 67.15 68.89 —————
0.00823 60.53 64.48 65.34 67.27 68.75 69.99
3.01314 60.76 64.56 65.41 67 04 68.59 69.99
3.01803 61.07 64.40 65.41 67.58 68.82 69.99

 

 

 

a a. a. K ..r.

A ELQQV «new

3 .
.1gure l

...a 8.8.

 

 

96

 

58.

 

 

 

 

 

 

 

 

 

I f I I I I l I T
60-
5°C 7’5 5‘5 WA 0 25.0°C
627
A 6 t- a
g- 4 30 T o 9.4oc
0- 3
"’ 4 v .. tr 6.0°C
3 66- '
O
00
" O o o J 0
O ‘2-5OC
68‘
-wr o 4 ° -|03°c
7O -°L 1* c # -l6.2°c
72 1 #14 L 1 4 1 l 1
0.0 0.4 0.8 IE 1.6 2.0
[w] x 102 (M)
‘igure 17. Concentration dependence of the 133Cs chemical

shift of cesium thiocyanate in methylamine at
various temperatures.

 

 

addit101
shift 0:
S.6°C wz
shown in
ical shi
nitrate
of these
of the 5
results
bilities
To c
data for
19. T}
should,
fore, tr
is ObVic
occurs 6
cumulati
Conseque
Solution
Chemical
bOPate a
thiOCYah
determin
The P980
The

made hum

 

97

addition, the concentration dependence of the 1330s chemical
shift of cesium triiodide in methylamine at 25.0°C and
5.6°C was studied briefly. The data are given in Table 8 and
shown in Figure 18. The concentration dependence of the chem—
ical shift of cesium bromide, cesium perchlorate, and cesium
nitrate could not be studied due to the low solubilities
of these salts in methylamine. Therefore the chemical shifts
of the saturated solutions were measured at 25.0°C. The
results are given in Table 9 along with approximate solu—
bilities of the salts in methylamine.

To compare the results, the concentration dependence
data for various salts at 25.0°C are illustrated in Figure
19. The chemical shift of the free solvated cesium cation

should, of course, be independent of the counterion; there-

 

fore, the curves should converge at infinite dilution. It
is obvious from Figure 19 that substantial ion—association
accurs even at the lowest concentration studied, where ac-
:umulation times of 8—10 hours per sample was required.
Ionsequently, it was not feasible to study even more dilute
1olutions. From the concentration dependence of the 133Cs
.hemical shift of cesium iodide and cesium tetraphenyl-
crate and the requirement that these salts and cesium
hiocyanate have a common intercept, it was possible to
etermine the ion—pair formation constants of these salts.
he results will be presented in Section C.

The long extrapolation of the data to infinite dilution

1de numerical calculations very difficult, so that attempts

 

98

Table 8. Concentration Dependence of the

133

4444V______________—___________—==fi‘__________:illll’

Cs Chemical

Shift of CsI3 in Methylamine at 25.0° and 5.6°C.

 

 

 

 

6(ppm)
Temperature, °C
Conc. (M) 25.0 5.6
0.00131 123.88 123.57
0.00348 125.59 125.36
0.01177 128.46 127.37
0.01991 131.64 130.93

 

 

 

 

|22

l24

l26

|28

7801.. (ppm)

l30

I32

 

1.

 

56°C:
250°C

 

1 l 1 l

l

 

'3‘004 0? 08 1.2

.gure 18.

T6 20
[or] x 102 (M)

Concentration dependence of the 13305 chemical
shift of cesium triiodide in methylamine at
25.0 and 5.6°C.

 

100

Table 9. Cesium—133 Chemical Shifts of Saturated Solu-
tions of CsBr, C8010“, CsNO3 in Methylamine

 

 

 

at 25.0°C.
Salt Conc. (M) . dobs(ppm)
CSBP <0.001 103.80
103.87
CscloLI 50.0007 49.52
CSNO3 <0.0007 46.72

46.34

 

 

 

 

 

 

 

 

 

 

 

 

CsBph4 ‘
.1 40 ‘_ sat. CsNO3 - ,
g " sat. CsClO4 _
3 60 -- : : : fl.- CsSCN "
egg" — _
80 - —
'00 2 $01. CsBr '
14K) 1 1 1 I 1 1 1 1 I 1 1
0.0 04 0.8 12 LG 20 2.4

ire 19. Concentration dependence of the

[Cs*]x102 (M)

133

Cs chemical

shifts of some cesium salts in methylamine at

25.0°C.

102

were made to obtain the chemical shift of the solvated
cesium cation experimentally. Although such attempts.failed
to give the chemical shift of the free cation directly, the
data contain some information about ion-association which
will be discussed in Section C.

Cesium thiocyanate data do not appear to give much in-
formation because of the concentration independent chemical
shift. In the case of cesium thiocyanate three possibilities

exist:

(1) Cesium thiocyanate is not ion-paired even at the
highest concentration. From the behavior of the other salts
in this low dielectric constant solvent this possibility is
highly unlikely. The linewidths of the signals are larger
for this salt than for the other salts which is also an in-
dication of ion-ion interactions;

(ii) It is possible that cesium thiocyanate is com-
pletely ion-paired even at very low concentrations. If
this is true then the chemical shift might suddenly change
at lower concentrations which are beyond the detectability
limit of the method. The direction of the change is not
known even though in all the solvents which were studied by
Popov and coworkers (129-135) a diamagnetic shift has been
observed for alkali thiocyanates; and

(iii) It is probable that the chemical shifts of the
free solvated cesium cation and cesium thiocyanate ion pairs

are the same. This would not be surprising since both

 

103

:hiocyanate and methylamine are nitrogen donors. Actually,
;his assumption formed the basis for our choice of the
:hemical shift for the free solvated cesium cation as

rill be discussed later in this chapter.

B. Ion Association of Cesium Salts in Methylamine

 

Various models were used in an attempt to analyze the
:oncentration dependence of the 133Cs chemical shifts of
:esium iodide and cesium tetraphenylborate in methylamine
Lolutions. Among them, a model which involves the forma—
1ion of ion—pairs and two kinds of triple—ions is the most
11ausible and will be discussed in detail in Section ii—b.
lhort reviews of two other models will be given in sections

and ii-a for the sake of completeness.

(1) Simple Ion—Pair Model — We first tried to fit the
hemical shift data for cesium iodide and cesium tetra—
henylborate with a simple model in which only ion—pairs
orm. The following equations were fit to the data by

sing the weighted nonlinear least squares program KINFIT:

K.
1p
Cs + X Z CS-X (3-1a)

(CS.X) = l—CX (3-lb)
1p (Cs)(X)vi d2Cy2

i"

 

 

104

6 1/2
Y1 = exp _(__£1121§fl£19_£921_____I7?_) (3—1c)
‘——_‘—__————1

3/2 50.298100)
(DT) [1 +
(DT)1/2

6 X +

obs = CsaCs XCS°X605.X = 06CS + (1— )GCs.X (3—10)
in which Cs and X are the solvated cation and solvated

anion, respectively; Cs-X is the ion—pair (charges are omitted

for simplicity), the terms in parenthesis in Equation (3—lb)

are the molar concentrations of various species, Kip is the
Lon-pair association constant, a is the degree of dissocia—
;ion of the ion—pair, Y: is the mean activity coefficient of
:he salt in solution, C is the analytical concentration of
1he salt, D is the dielectric constant of methylamine, T is
he temperature in , 8 is the distance of the closest ap—
roach (8 = 5.3 h)*, sobs is the measured chemical shift,
Cs and 6Cs-X are the chemical shifts of the free solvated
ation and ion—paired cation, respectively, and X03 and
05.x are the relative mole fractions of the free and ion—
aired cation respectively. Values of the dielectric

onstant at different temperatures were obtained from the

quation in Reference 194,

D = DO - 0.09195 (3—2)

 

The distance of the closest approach was chosen as the av—
’age of (rCS+ + r1-) and ¢Cs+ + PI' + rs) in which rCs+ =
‘67 8 and r _ = 2.20 8 are the crystal ionic radii of the
ésium cation and the iodide anion respectively, and rs =

7 is the Vander Waals radius of methylamine molecule.

1wever, the exact choice of "a” does not affect the results
.gnificantly.

 

 

105

where DO — 11.3 is the dielectric constant of methylamine
at 0°C and t is the temperature in oC. Cesium iodide and
cesium tetraphenylborate data at 25.0°C were fit simul—
taneously by equations (3-1) with five adjustable param—
eters. These are: two ion—pair association constants,

two chemical shifts of the ion—pairs, and the chemical
shift of the free cesium cation in methylamine (see Ap—
pendix 1A for details). The results of this type of curve
fitting are illustrated in Figure 20, where the experimental
and calculated chemical shifts are compared. The adjust—
able parameters are given in Table 10. The simple ion—pair
model requires a sharp change in the chemical shift at low
concentrations with a flat portion at high concentrations.
Even the "best fit" of the data is very poor at all tempera-
tures. A closer look at the chemical shift—concentration
plots (Figures 14 and 15) shows the existence of rapid
Changes with concentration at low concentrations and slower
continuing changes at higher concentrations. This indi—
cates that other interactions are important in the solu—
tion. Table 10 shows that none of the adjustable param—
eters are well—determined by this model. The average
standard deviation of the residuals is about 1.0 ppm

vhich is much higher than the experimental errors in the
zhemical shift determination. Therefore it is clear that

1 simple ion-pair model cannot describe the behavior of

lesium salts in methylamine, and that other effects are

 

106

 

 

 

 

 

1 I r l . I I l I I . T I
CsBPh4
4O -
E 60 '-
CL -
£-
3 80-
o
m -
IOO~
120K. '
_ C51
140 -
l I l I l l l I 1 I 1 I 1
0.4 0.8 l2 |.6 2.0 2.4

[C§]x l02(M)

Figure 20. Concentration dependence of 133Cs chemical
shiftscfiszI and CsBPhh in methylamine at
25.0°C. o experimental points, x calculated
from the simple ion pair model.

107

Table 10. Calculated Thermodynamic Parameters of Ion-
Association of Cesium Salts in Methylamine at
25.0°C According to a Simple Ion—Fair Model.

 

 

 

CsI CsBPhu
.9 ..
6Cs+ ppm ~0115
K' M-l (“i )x10“ (14:1)x10Ll
1p
5- ppm 130:: _33i25

1p

 

 

108

also responsible for the chemical shift changes as a func-
tion of concentration. It must, however, be realized that

most of the changes in chemical shift with concentration

 

can be accounted on the basis of ion-pair formation so that
the remaining information needed to improve the model is
relatively minor. It would seem that the logical next step

would be to invoke triple-ion formation.

(ii) Formation of Triple—Ions - According to theory

 

(89), the maximum concentration, Cmax’ for which triple-
ion formation of a univalent electrolyte in a solvent of
dielectric constant D may be neglected is given by:

Cmax z 1.19 x lO-lu(DT)3. In methylamine, even at the
lowest temperature, and concentration which we studied,
the formation of triple-ions cannot be ignored according

to this equation. Therefore, we tried to analyze our data

according to models in which triple-ions form.

(a) One Type of Triple-Ion - In this model it

 

was assumed that only ion pairs and anionic triple—ions
will form in the solution. Even though the formation of
cationic triple—ions cannot be neglected, this model was
used as a starting point and is worth describing briefly.
The equilibria and subroutine equations required for the
analysis of multiple data sets according to this model are

given in Appendix 18.

109

To analyze the data completely (neglecting the tempera-
ture dependence of the chemical shifts), it is necessary
to evaluate at least seven parameters for each salt. Four
of these are ion—pair and triple-ion formation constants
together with the enthalpies of the formation of the two
species. The other three are the chemical shifts of the
free solvated cation, the ion-pair, and the triple-ion.
Although we found out that our data could be fit well by
this model, the determination of all seven parameters is
not possible. In general, it becomes apparent in all model-
fitting that those parameters which are highly correlated
with each other, and/or are characteristics of minor species
in the solution cannot be determined simultaneously. For
example, high correlation coefficients exist between the

formation constant of the anionic ion-triple, K and its

ta
chemical shift. Since the anionic triple-ion, X.Cs.X,

is a minor species in the solution, we cannot determine

both the chemical shift and its formation constant simul—
taneously. Because of the existence of only small relative
amounts of Cs+ in solution, even at the lowest concentra-
tions, and the consequent long extrapolation of the chemical
shift to infinite dilution, the accurate determination of
the chemical shift of the solvated cation was not possible.
If we try to adjust 6Cs+’ high marginal standard deviations

in the other parameters result. Although we would prefer

to determine the chemical shift of the free cation by data

110

fitting, it was necessary to fix it at a reasonable value.
In order to maketflmeproblem tractable, we assumed that
the chemical shift of the ion-pair of cesium thiocyanate
and that of the free cesium cation are equal (see section
iii for more explanation of this choice). In addition,
the association constant of the triple—ion was calculated
from the Fuoss equation (24) and used as a constant (more
eXplanation is given in section iii). With these assump-
tions, the data at various temperaturesnmawsfit well by
this model and the average standard deviation of the re-
siduals was reduced to 0.45 ppm. The calculated thermo-
dynamic parameters obtained from 11 data sets are given
in Table 11. Even though all parameters, except the chemi-
cal shift of the triple-ion, are well-determined by this
model, we feel that the formation of the cationic triple-
ion cannot be ignored. Therefore,we refined our model by
introducing the formation of the cationic triple—ion in the

equilibria.

(b) Two Types of Triple-Ions - The most reasonable

 

model for the analysis of the NMR chemical shifts of cesium
salts in methylamine is a model in which the ion-pair
Cs+'X-, and both kinds of triple-ions (anionic and cationic)
exist in the solution. The equilibria involved in this

model are,

111

Table 11. Calculated Thermodynamic Parameters for Ion-
Association of Cesium Salts in Methylamine at

25.0°C According to the Ion-Pair and Anionic
Triple-Ion Model.

 

 

 

Assumptions:
1. 6C5 = 60.73 ppm from CsSCN data at 25.0°C.
2. Kta = 32.5 M_l from the Fuoss equation
at 25°C.
CsI CsBPhu
Kip M‘l (4.3+1.0)x105 (1.510.51x10“
Ahgp kcal. mole-l (2.0:0.3) (4.710.5)
écs-X ppm 121.7i0.4 -2l:5

SX-CS°X ppm 784ill9 -337:58

 

 

112

Kip
Cs + X z Cs-X

C
+ CS°X°CS (3-3)

where X-Cs-X and Cs-X'Cs are anionic and cationic triple-
ions (charges are omitted for simplicity), and Kta and KtC
are formation constants for the anionic and cationic triple-
ions, respectively. The equilibrium constants, mass balance
equations, charge balance equation, and activity coefficient
equation were used to solve for the concentration of the
different species in solution. The numerical calculation
was based on an iterative method with convergence on the
major species (Cs+-X‘) in the solution. The detailed
algebra and the subroutine EQN for the KINFIT program are
given in Appendix 10. The calculated concentrations of

the various species were then used in the chemical shift

equation,

2 X. = 1 (3—4)
1

113

where Xi's and 51's are the mole fractions and chemical
shifts of the species containing the cesium cation. A
complete solution to the above equations for each salt at
various temperatures would require the adjustment of

three association constants, three enthalpies of formation
(for the ion-pair and two kinds of triple-ions), and four
chemical shifts even if the temperature dependence of the
chemical shifts is ignored. Since the chemical shift of
the free cesium cation is a common parameter for both salts,
19 parameters would have to be adjusted for a complete.
solution to the problem. As mentioned in Section ii, the
high correlation among some of the parameters would clearly
prevent solution of the complete problem. Assumptions must
therefore be made in order to obtain any quantitative in-
formation about the system. As we shall see, certain
parameters are very insensitive to these assumptions and
can therefore be well-determined. The final set of assump-

tions was:

1. The chemical shift of the free solvated cation was

taken as the chemical shift of cesium thiocyanate in methyl-

 

amine. The concentration independent chemical shift of
cesium thiocyanate suggests that the chemical shift of the
free solvated cation and the ion-paired cation are the
same. It seems that the chemical shift of the triple-

ions and the ion-pair are also the same, since there is

114

no concentration dependence. The chemical shift of
a 0.02M cesium thiocyanate solution in methylamine which
is saturated with tetraphenylphosphonium thiocyanate is
60.84 ppm at 25.0°C Which is equal to that of cesium thio-
cyanate in methylamine. The addition of tetraphenylphos-
phonium thiocyanate to the solution should increase
triple-ion formation. Only if the chemical shift of the
ion-pair and the anionic triple—ion are the same would we
expect the same chemical shift upon addition of tetraphenyl-
arsonium thiocyanate. This experiment suggests that the
chemical shift of the triple-ion and the ion-pair are equal,
so that the chemical shift of the ion-pair and the free
cesium cation would also be expected to be the same. A
similar experiment was carried out for a cesium iodide
solution in methylamine. The chemical shift of a 0.024M
solution of cesium iodide in methylamine which is also
saturated with tetraphenylphosphonium iodide is 129.38
ppm at room temperature while the chemical shift of pure
cesium iodide at this concentration is 127.06 ppm. A down-
field shift (2.2 ppm) as a result of the addition of tetra-
phenylphosphonium iodide indicates an increase in the forma—
tion of the triple—ion. The addition of tetraphenylarsonium
tetraphenylborate to a 0.0032M cesium tetraphenylborate in
methylamine, results in a 0.38 ppm upfield shift at 25°C,
also indicating the formation of more triple-ions.

As mentioned above, the chemical shift of the free

solvated cation, 5 could not be obtained from the data

Cs’

115

since a very long extrapolation is required (Figure 19) and
the concentration of the free cation is very small (less than
10% at the lowest concentration used). However, the choice
of 6Cs+ is critical, since ion—pair association constants

are affected significantly by a change in the chemical

shift of the free cation. For example, if we change 60s
from 80 ppm to 40 ppm, the ion—pair formation constant of
cesium iodide decreases by a factor of 4 while the ion—pair
formation constant of cesium tetraphenylborate increases by
the same factor (compare Tables 12—14). The residual surface
is not very dependent upon the choice of one of these values,

provided the other parameters are adjustable,and both choices

of 008 give nearly equally good fits to the data.

In summary, our choice of the chemical shift of the

free solvated cesium cation is
(003+)t = 60.73 - 0.224 (t — 25.0) (3-5)

where (0CS+)tis the chemical shift of the free cesium cation

at a given temperature. The temperature dependence was ob-

tained from a plot of the chemical shift of cesium thio—

cyanate versus temperature which yielded a straight line

with a slope of -0.224 as shown in Figure 21.

2. Equal probabilities for the formation of two

kinds of triple—ions. The determination of the formation

 

116

 

60

70-

 

 

 

72 l l l I
~20 -10 0 1o '20

Figure 21.
cyanate solutions versus temperature.

Cesium—133 chemical shifts of cesium thio—

117

Table 12. Thermodynamic Parameters for Ion-Association
of Cesium Salts in Methylamine at 25.0°C; Ob—
tained with the Assumptions that Ion-Pairs and
Two Kinds of Triple Ions are Present, and That
6Cs = 60.73 ppm at 25.0°C.

Assumptions: 6Cs = 60.73 ppm (from CsSCN data
' at 25.0°C).
_ _ —1
Kta — Ktc — 32.5 M (from Fuoss

equation at 25.0°C).

6Cs.x.0s = 60s.x

 

 

Adjustable Parameters at 25.0°C

 

CsI CsBPhu
K. M‘1 (2.54i0.31)x105 (1.41:0.30)x10”
1p
Ahgp kcal. mole‘l (3.86:0.28) (4.71i0.40)

= . i . 1 -1 .1:4.2

SCS-X-CS 6CS-X ppm 124 19 0 3 3

4 8:24 — 2 8:42
GX'CS‘X ppm 5 9

 

 

 

IIIIIIIIZZ::44r———————————————————————————__________lll .11,

118

Table 13. Thermodynamic Parameters for Ion—Association of
Cesium Salts in Methylamine at 25.0°C; Obtained
with the Assumptions that Ion—Pairs and Two
Kinds of Triple Ions are Present, and That

6C5 = 40 ppm.
Assumptions: 605 = 40 ppm.
Kta = KtC = 32.5 M"1 (from Fuoss
equation at 25.0°C).
6Cs.x.Cs = 6Cs.X

 

 

Adjustable Parameters at 25.0°C

 

CsI CsBPhu
Kip M—l (4.3:0.6)x105 (7.6:0.7)x103
AHEp _ kcal. mole"l (3.40:0.3) (4.66:0.3)
écs-x-Cs=5cs.x ppm 124.05i0.33 -9.8i2.3
GX'Cs-X ppm 545i4o —336i21

 

 

 

119

 

 

 

Table 14. Thermodynamic Parameters for Ion—Association of
Cesium Salts in Methylamine at 25.0°C; Obtained
With the Assumptions that Ion—Pairs and Two Kinds
of Triple Ions are Present, and That 6Cs = 80 ppm.
Assumptions: 0C5 = 80 ppm.
Kta = Kto = 32.5 M‘1 (from Fuoss
equation at 25.0°C).
60s.X.Cs = 50s.x
Adjustable Parameters at 25.0°C 1
CsI CSBPhu
-1 5 4
Kip M (1.10:0.13)x10 (2.97io.67)xlo
AHEp kcal. mole‘l <4.8510.27> (5.38:0.57)
6Cs-X-Cs=SCs-X ppm 125.07iO.3 —8.4i3.4
_. +
6X-Cs-X ppm 359:11 391—77

 

 

120

constants of the triple—ions .isnot possible along with

the determination of the ion—pair formation constants, since
these two constants are highly correlated to each other and
only a small fraction of the cesium cation is in the form
of the ion—triple (less than 10% at the highest concentra—
tion). The values of the ion—pair formation constant,
enthalpy of the formation, and chemical shift of the ion—
pair do not change significantly with a change in the forma—
tion constant of the triple-ion. Therefore the assumption
of equal values of the two triple—ion formation constants

is acceptable even though the degree of the solvation of

the cation and the anion are different.

3. Fixed value for the formation constant of
tgiplg:ign§. Since triple ions are minor species and
the ion—pair parameters do not change much with a Change

in the formation constant of the triple ion, we can fix the
formation constants of the triple—ions at ”reasonable"
values with the understanding that the resulting chemical
shift parameters for the triple—ions will depend upon this
choice. Two procedures were used:

(a) The formation constants of the triple—ions at

different temperatures were calculated from the Fuoss equa—
tion

2WNa3

3 = W I933) “-8)

121

Values of I(b3) for integral values of b are tabulated (24)
so that values of I(b3) for nonintegral valueswereobtained
from a plot of log 1(b3) versus b.

(b) Independent of the model which we used, the value
of the formation constants of the ion—pairs at 25.0°C ob—
tained from our NMR data for cesium iodide is almost 5 times
larger than the Fuoss value, and almost 5 times smaller than
the Fuoss value for cesium tetraphenylborate in methylamine.
If we assume that the ratio of the ion—pair and triple—ion
formation constants calculated from the Fuoss equation is

the same as the corresponding ratio obtained from NMR data,

we can write,
K = A x K. (3—6)

where A = (Kt/Kip)Fuoss' This assumption suggests that if

any effect is missing in the calculation of the ion—pair
formation constant according to the Fuoss theory, it is
also missing in the calculation of the triple-ion

formation constant. Again, it must be emphasized that

some such assumption is forced upon us by the inability
of the chemical shift data to define all the unknown
parameters.

The analysis of data according to either assumption
0 or b yields the same thermodynamic parameters for ion—

pair formation (compare Tables 12 and 15). If we adjust

122

Thermodynamic Parameters for Ion—Association of

 

 

 

Table 15.
Cesium Salts in Methylamine at 25.0°C; Obtained
with the Assumptions that Ion—Pairs and Two Kinds
of Triple Ions are Present, and That Kt/Ki is
a Known Constant. p
Assumptions: 60s = 60.73 ppm (from CsSCN data
at 25.0°C).
= _ -3
A Kt/Kip — 6.8 x 10 (from
Fuoss equations at 25.0°C).
CSCs.X.Cs = 6Cs.X
Adjustable Parameters at 25.0°C
CsI CsBPhu
—1 5 4
Kip M (2.68:0.19)X10 (l.l6:0.l5)x10
AHEp kcal. mole_l (3.75i0-ll) (4.0910.l5)
0 = 0
Cs x-Cs Cs.X ppm 124.05iO.20 —17.8i3.2
5 ppm 299il.2 —906i51

X'Cs-X

 

 

123

"A" for the best fit, the standard deviations become too
high but the best-fit value of this parameter is equal to
the corresponding value calculated from the Fuoss equations
within the standard deviation (Table 16). Even if we use

a value for the triple-ion formation constant which is 3
times larger than the Fuoss value, no change in the ion—
pair formation parameters occurs. This confirms the idea
that the choice of the triple-ion formation constant is not

important as long as its value is within a reasonable range.

4. Chemical shifts of anionic and cationic triple-
ions. The high correlation between the chemical shifts of
the two kinds of triple-ions prevents their determination
simultaneously. For example, since they are formed in
equal concentrations, the chemical shift of one could go
down an arbitrary amount provided that it is balanced
by a corresponding increase in the chemical shift of the
other triple-ion. Therefore we were once again forced to
make some assumptions about the values of their chemical
shifts.

It is important to point out that the choice of the
chemical shifts of triple ions does not influence the ion-
pair formation parameters significantly. Essentially the
same values (within standard deviations) for the ion-pair
formation parameters result regardless of the choice of the

chemical shifts of the triple-ions. The reason is that the

124

Table 16. Thermodynamic Parameters for Ion—Association of
Cesium Salts in Methylamine at 25.0°C; Obtained
with the Assumptions that Ion—Pairs and Two Kinds
of Triple—Ions are Present, and that Kt/Ki
is an Adjustable Parameter. p

Assumptions: 5C8 = 60.73 ppm (from CsSCN data

 

 

 

at 25.0°C).
A = Kt/Kip (Adjustable)
50s.x.0s = CSCs.x
(6Cs.X>t = (6Cs.X)25.O + b(t‘25'0)
Adjustable Parameters at 25.0°C
CsI CsBPhu
—l 5 4
Kip M (2.85i1.0)x10 (1.05i0.35)X10
Apr kcal. mole_l (3.65il.4) (2.56i3-2)
acs-X-Cs=6CS-X ppm l23.73:1.19 —19.9i8.8
b ppm-deg‘l —0.0067:0.0029 -0.25iO.53
6X-Cs-X ppm 283ill ~608i273
A 0.0011110.00055

 

 

 

 

125

ion-pair formation parameters are almost completely
characterized by the low concentration region of the chemi-
cal shift—concentration plots, and in this region less than
1% of the cesium cation is present in the form of triple-
ions.

Most workers in the field agree that alkali metal NMR
chemical shifts are only sensitive to nearest neighbor
interactions. Reasonable assumptions about the chemical
shifts of the triple-ions can be made by considering the
nearest neighbor effect.

a. If we assume that the degree of overlap of the
outer p-orbitals of the cation and anion are the same in
the ion-pair and the cationic ion-triplet, Cs.X.Cs, then
the chemical shift of the two species should be equal.

With this assumption the chemical shift of the cationic
species could be fixed at the ion-pair chemical shift and
5 the chemical shift of the anionic triple-ion could be
adjusted.

b. If the degree of overlap is not the same for ion—pair
and ion-triplets, then we can assume that a change in the
degree of overlap results in a change in the chemical
shift. Thus the chemical shift of the cationic triple-

ion can be expressed as

CS°X°CS ‘ 60s x

126

where A is the chemical shift characteristic of the dif-
ference in the degree of overlap between the cation and
anion in the ion-pair and ion-triple. Since the cesium
cation is surrounded by two anions in the anionic triple-
ion, the chemical shift of the anionic triple ion can be

written as

GX-Cs-X = 2((SCS.X - 5C3) + 6C5 - A (3_7b)
assuming that the same effect-causes corresponding changes
in the chemical shifts of both triple—ions with respect to
the chemical shift of the ion-pair.

We used both assumptions a and b in the analysis of the
NMR data. Both assumptions lead to the same values for the
ion-pair formation parameters, again showing that the choice
of the chemical shift of triple—ions is not critical (com-

pare Tables 12 and 17).

5. Temperature dependence of the chemical shifts. Since

 

the degree of interaction between cation, anion, and the
solvent is temperature dependent, the chemical shift of
various species should also be temperature dependent. Un-
fortunately there is no theory for the temperature depen-
dence of the chemical shift. The CsSCN data show a linear
dependence of the chemical shift on temperature (Figure 21).

In general, it can be assumed that the chemical shifts of

 

 

   

127

n—Association of

 

 

 

 

 

Table 17. Thermodynamic Parameters for To
Cesium Salts in Methylamine at 25.0°C; Obtained
with the Assumptions that Ion—Pairs and Two
Kinds of Triple Ions are Present, with Equi—
partition of the Chemical Shifts.

Assumptions: 50st: 60.73 ppm (from CsSCN data
at 25.0°C).
Kta = Kto = 32.5 M‘1 (from Fuoss
equation at 25.0°C).
50s.x.Cs = 5Cs.x ‘ A
5x.0s.x = 2(50s.x ' 50s) + Cs ‘ A
Adjustable Parameters at 25.0°C
CsI CsBPhu
—1 5 4

Kip M (2.49i0.28)x10 (1.49i0.31)x10

AHEp kcal. mole‘l (3.89i0.26) (4.89:0.41)

écs-X ppm 124.28i0.29 —11.8i3.8

A ppm -l33i11 114125

7__—4.

,1. r ..raerQ - _. 1,,

128

 

 

 

X-Cs-X

Table 18. Thermodynamic Parameters for Ion-Association of
Cesium Salts in Methylamine at 25.0°C; Obtained
with the Assumptions that Ion-Pairs and Two Kinds
of Triple Ions are Present, and that SOS X is
Temperature Dependent. °
Assumptions: 6C = 60.73 ppm (from CsSCN data

5 at 25.0°C).
Kta = KtC = 32.5 M.1 (from Fuoss
equation at 25.0°C).
6Cs.X.Cs = 5Cs.X
(SCS.X)t = (50s.x)25.0° + b(t'25'0)
Adjustable Parameters at 25.000
081 CsBPhu
-1 5 4
K10 M (2.50:0.22)x10 (l.21:0.2l)x10
AHEP kcal. mole”l (3.15:0.21) (3.3lt0.79)
= 4. i . - . t .

GCs-Xocs 6Cs-X 12 47 0 23 16 1 3 7

b 0.020i0.002 -O.l6i0.09

0 469il9 -280i27

 

 

129

various species is linearly dependent on temperature. The
chemical shifts of triple ions are not well determined by
any of the models. Therefore it is obvious that the intro—
duction of temperature dependence of the triple-ion chemi—
cal shifts is not warranted. A comparison of Tables 14

and 18 also indicates that the ion-pair formation parameters
are the same whether the chemical shifts of the ion-pairs
are temperature dependent or not.

Lest the reader feel that any collection of parameters
can fit the model, it should be emphasized that the model
chosen must fit not only the concentration dependence of
the chemical shifts of CsI and CsBPhu at a given temperature
but at EL; temperatures studied. While the data do not per-
mit unambiguous choice of all possible parameters, the model
used is a reasonable one - theory predicts that ion—pairs
and triple-ions should form in this solvent. We expect
different chemical shifts for free ions, ion-pairs, and
triple-ions and reasonable choices of the corresponding

chemical shifts suffice to describe the data very well.

C. Complementary Experiments

Since the determination of the chemical shift of the
free solvated cation in methylamine requires a long ex-
trapolation of the data, we tried various ways to determine
it experimentally. All such attempts failed, but the data

provide some information about ion—association of cesium

 

 

 

 

 

130

salts in methylamine. Therefore, the results will be given

in this section.

i. Cesium Tetraphenylborate in 90% v/v Methylamine in
_____________________________________________
Dimethylsulfoxide Solutions — It was thought that if we could

extrapolate the chemical shift-concentration data of cesium
salts in mixed solvents, where one of the solvents is methyl—
amine, then the chemical shifts of the free cesium cation

in various solvent compositions could be obtained. Extrapo—
lation of these chemical shifts to 100% methylamine would
then give the chemical shift of the free cesium cation in
methylamine. Exploring this idea, we measured the 13303
chemical shift of cesium tetraphenylborate in 90% v/v methyl-
amine in dimethylsulfoxide solutions as a function of the
salt concentration. The data at 25.09C are given in Table

19 and shown in Figure 22. It had been found previously

that cesium tetraphenylborate does not form ion-pairs in

DMSO and that the chemical shift of the cesium cation in

this solvent is 68 ppm (135). From the data of Table 19,

it is obvious that cesium tetraphenylborate remains highly
associated in this mixed solvent, probably because of the
high percentage of methylamine. The chemical shifts at

all concentrations are about 40 ppm downfield from the cor—
responding values in pure methylamine solutions. Even
though the solvent contains only 10% DMSO, the chemical shift

is determined largely by the chemical shift of the cesium

131

 

 

 

Table 19. Concentration Dependence of the 13305 Chemical
ggiggcof CSBPhh in 90% V/V Methylamine-DMSO at
[08+] (M) obs (ppm)
0.00056 57.04
0.00075 54.17
0.00105 50.83
0.00135 47.58
0.00174 47.11
0.00221 45.25
0.00255 44.48
0.00352 42.30
0.00428 41.30
0.00527 39.44
0.00615 39-59
0.00674 38.70

 

 

132

 

s -.
0.50-
m ..
.0

0

00

60 r-
r .
.4 l I 1 .I l
0.0 0.2 0.4 0.6 0.8
[Cs *] x IOZ (M)

 

 

 

Figure 22. Concentration dependence of the 13303 chemical

shift of cesium tetraphenylborate in 90%
v/v methylamine in dimethylsulfoxide at
25.0°C.

133

cation in DMSO indicating preferential solvation by DMSO.

It is clear that the extrapolation of the data to infinite
dilution cannot be easily done. Therefore, this experiment
did not help us to obtain the chemical shift of the cesium

cation in methylamine solutions.

(ii) Mixtures of Cesium Iodide and Cesium Thiocyanate

in Methylamine - Early in the study of cesium salts in

 

methylamine, when we had examined only the concentration
dependence of the chemical shift of cesium iodide and cesium
thiocyanate, it seemed plausible that cesium iodide forms
contact ion—pairs in methylamine while cesium thiocyanate
does not (see Figure 19). To test this hypothesis, mixtures
of these two salts at a constant total concentration of the
cesium cation but various mole ratios of the two salts in
methylamine were prepared and the chemical shifts measured.
The results are given in Table 20 and are compared with the
results for the pure salts at 25.0°C in Figure 23. Extrapo-
lation of the cesium iodide data to high concentrations
gives a chemical shift of 127 ppm or larger. If the limit—

ing shift were due to ion-pairing only, a plot of(6 -127)/

obs
(GCSSCN-127)versus the mole fraction of iodide should be a
straight line with unit negative slope, provided the pres-
ence of CsSCN shifted the CsI ion-pairing equilibrium to

completion. The fact that the plot is curved (Figure 24a)

shows that this simple interpretation is invalid. If,on

 

 

 

 

 

 

134
Table 20. 133Cs Chemical Shifts of Different Mole Ratios
of (I‘)/(SCN‘) +(I') in Mixtures of CsI and
CsSCN in Methylamine at Various Temperatures;
(Cs+) = 0.0054 n.
_ éobs (ppm)
(_I ) _ Temperature, 0C
(SCN )+(I )
25.0 —2.5 -10.3
0.00 60.65 67.15 68.85
0.26 77.67 81.85 83.02
0.52 92.40 95.04 95.73
0.76 107.75 108.61 ' 108.92
1.00 122.10 122.33 123.26

 

 

 

 

135

 

_ [1-]/ [scw-]+ [1']

 

 

 

 

 

‘Eg (SC)-o.-——-o—o-———o—-—4L ’rOChfiscwi
g ‘000
§ ' a 026
,0 80-
b A 0.52
ICO-
_ ' 0.76
'20“ .11“: lg CSI
”4() 1 1 .1 1 I J .1 1 .1 I 1 1
00 0.4 0.8 l2 LG 20 24
[05*] x 102 (M)
Figure 23. A comparison of 13305 chemical shiftscfi‘pure

cesium salts and the mixture of cesium salts
in methylamine at 25.0°C.

 

80b5— 8CsI
Sosscw- 8CsI

Figure 24.

.0
(I)
1

~ (0) -
0.6r / 4
L _

(b)
4 1' -
1- _
0.2 - -

136

 

 

 

 

I I I I I 1
O 0.2 0.4 0.6 0.8 1.0
XI‘

Plot of (éobs—SCslj/(acsSCN _6CsI) versus

mole fraction of iodide. (a) 6CSI = 127.0,

(b) écsl = chemical shift of CST at the con-

centration of CsI in the mixture.

137

the other hand, cesium thiocyanate is more strongly ion-
paired than cesium iodide, a plot of <SObS-SCSI)/(6CSSCN-6CSI/
should be a straight line when the value used for écsl is

the observed value at the cesium iodide concentration in

 

the mixture. This plot which is shown in Figure 24b is
indeed a straight line with unit negative slope. Therefore,
it can be concluded from this experiment that cesium
thiocyanate forms ion—pairs which are at least as stable

as cesium iodide ion-pairs. Of course, complications are
introduced by the formation of triple—ions which could in-
validate this conclusion. Evidence to be presented later
confirms the existence of substantial ion-pair formation

in cesium thiocyanate solutions (Chapter IV).

(iii) Mixtures of Cesium Iodide and Cesium Tetraphenyl-

borate in Methylamine - The chemical shifts of mixtures of

 

cesium iodide and cesium tetraphenylborate in methylamine

at fixed total concentrations of the cesium cation and
varied proportions of the anions were measured at 25°C.

The results are given in Table 21 and are compared in
Figure 25 with the data for pure salts. The chemical shifts
at each concentration and all ratios favor the chemical
shift of cesium iodide which indicates that cesium iodide

is more associated than cesium tetraphenylborate in methyl-
amine. At first glance, one might think that the chemical

+
shift of Cs at infinite dilution is greater than 105 ppm.

138

Table 21. Cesium—133 Chemical Shifts of Different Mole
Ratios of (I )/(BPhE ) + (I ) for 0.0007 and
O. 003 M Cs+ in Methylamine Solutions at 24. 6°C

 

 

 

 

 

 

(1‘) (Cs+) = 0.0007 M Cs+= 0.003 M
CBPh4)+(I-) 5obs 6calc* Sobs 6calc

0.00 13.07 2.00

0.40 63.55 60.3 55.25 55.0

73.94

0.50 74.18 71.2 68.67 66.8

0.60 86.97 81.5 81.15 78.0

0.80 104.96 101.5 102.71 100.6

1.00 119.46 122.33

 

 

*
Chemical shifts were calculated by considering only ion-

pzir formation and using ion-pair parameters from Table
l

139

 

 

 

 

 

CsBph4
A 40"
g -
a. 0.40
2 ...,»
‘0 _(,A 0.50
80:,» 0.60
'00 ”rm, 0.80
'20 . 1.0 631’
1 1 1 1 l 1 1 1 1 l 1 1
'4000 0.4 0.8 1.2 LG 20 2.4

[Cs’] x IO2 (M)

Figure 25. A comparison of 13305 chemical shifts of pure

cesium salts and mixtures of cesium salts in
methylamine at 25.0°C.

140

However, this is not the case. Instead,the concentration
dependence in the mixture has its origin in the differences
in the degree of association of these two salts in methyl-

amine. A plot of (do ӎcsl) versus the mole

bs'5Cs1)/(50ssehu
ratio of CSI is curved as shown in Figure 26. In this plot
6031 and écsBPhu are the chemical shifts of CsI and

CsBPhu at their concentrations in the mixture. The non-
linearity of the plot results from differences in the

degree of ion-association of CsI and CsBPhu in methylamine.
In fact, we used the chemical shifts of mixtures of cesium
iodide and cesium tetraphenylborate to check the calculated
ion-pair parameters derived for the two pure salts. The
chemical shifts of mixtures were calculated by using ion-
pair parameters and neglecting triple-ion formation.

These calculated chemical shifts are also given in Table

21 for comparison. The trend of the calculated shifts as

a function of concentration,follows the same trend as the
experimental chemical shift. We extended the calculation to
lower concentrations by using the ion-pair parameters from
Table 12. The results at a mole fraction of 0.5 are shown
on a semilog plot in Figure 27, which indicates that the
chemical shift reverses its direction at lower concentra—
tions and approaches the chemical shift of the free cation.
The calculated chemical shifts are a few ppm different from
the experimental values. The reason for this discrepancy is

probably that in the calculations welumnaneglected triple-ion

80 - 86:!

 

Figure 26.

141

 

 

s
\
- ‘
s
s
O 1 L 1 1 1 l 1 1 1 ‘
O 02 0.4 0.6 0.8 1.0
X
I -
Plot of (dobS-dcslVNCSBPh -6051) versus mole
fraction of iodide. 0 “6 are the

C81’ CsBPhu
chemical shifts of CsI and CsBPhu at their

concentrations in the mixture.

 

142

 

IOCSFH .m mm @9me ECG HmO .HO wmhspvmflE ..wO mprwflflm HGOHEmflo wOMMH UmpflHSOHMO

~-o_xo._

.Uo>gomho o .QOHpoELoa somloadflap mcfluooawo: Ugo ANH oHDoBV
whopososog pHoQIQOH Sosa oopoHSoHoo x .m.o u IHX

e.o_xo._
q

A2108
m-o_xo._

.QOHpoAQCoocoo go comp

0.0. 5..
_

To. x O._

 

 

n.o_xo._
_

 

 

 

Om
wk

wk.
Vb
Nu.
ON
mm
mm
vm

Nm

 

.sm opsmflm

(011111me

143

formation (the solution to the equilibrium equations become
very difficult when all possible types of triple ions are
considered). The differences in the calculated and experi—
mental chemical shifts can be accounted for by the forma—
tion of triple ions. For example at a total concentration
of 0.003 M, and the mole ratio (I-)/(BPhu-)=l, according to
our model, almost 3.7% and 0.7% of the cesium cation is in
the form of iodide and tetraphenylborate triple-anions
respectively. Since the chemical shifts of ion-pairs and
anionic triple—ions are different, the existence of triple-
ions results in a chemical shift. The value of this chemi-
cal shift is about +1.8 ppm which accounts for the dif-

ferences in the calculated and experimental chemical shifts.

D. Conclusion

 

Cesium iodide and cesium tetraphenylborate are highly
associated in methylamine. According to theory triple—
ions form in methylamine as well as ion—pairs. A model in
which ion-pairs and two kinds of ion-triples are formed, fits
well to our NMR data. To obtain the ion—association param-
eters of these systems, it is necessary to make certain assump—
tions. Among the various assumptions mentioned in this chap—
ter only the one concerned with the choice of the chemical
shift of the free solvated cesium cation is critical. The
assumption that the chemical shift of the free solvated

cation is equal to that of ion-paired cesium thiocyanate

 

144

is consistent with all of the data. The other assumptions
have only minor effects on the values of the ion—pair for—

. O
matlon parameters (Kip, AHip’ 61p

12 and 15—18 reveals that the parameters for the formation

). An inspection of Tables

of ion—pairs are well determined and they are the same
within their standard deviations, regardless of the model
used.

One obvious deficiency of the less critical assumption
is that the chemical shifts obtained for the triple ions

are very different from the values one expects on the basis

 

of the overlap model. The origin of such behavior is not
known to us. If the effect is real, and not merely a

consequence of inadequacy of the model, the discrepancy

 

must be caused by some kind of interaction between the two
sets of overlapping orbitals in the triple ions, which will
affect the average excitation energy in the Ramsey equa—
tion (Equation 25). Another reason for such behavior may
be due to changes in the short range ion—solvent interactions.
When the anion or the cation interacts with the ion—pair,
the solvent molecules may be rearranged in such a way that
it causes a large chemical shift. In solvents such as
methanol where ion-triple formation is not expected, the
plots of 133Cs and 87Rh chemical shifts of 051 and RbI

are not simple (Chapter V and Reference 211). The chemical
shift changes rapidly at lower concentrations, but changes

more slowly at high concentrations.

145

According to our model, at the lowest concentrations we
studied,90% and 55% respectively of the cesium cations in
cesium iodide and cesium tetraphenylborate are ion-paired
at room temperature. At the highest salt concentrations
(where the complexation by l8-crown-6 is usually studied)
only 3% and 25% of the cesium cations in cesium iodide and
cesium tetraphenylborate respectively are free. Therefore,
in methylamine solutions,ion-association of cesium salts can-
not be ignored in the study of the thermodynamicscfi‘the com-
plexation of these salts by 18-crown-6. We have used the
results of the ion-association of cesium salts in methyl-
amine described in this chapter to obtain thermodynamic
formation constants for complexation of cesium salts by
18-crown-6 in methylamine as discussed in Chapter IV. The
conductance of cesium iodide in methylamine as a function
of concentration was also measured in order to permit a
comparison with the NMR results. This study will be des-

cribed in Section 3 of this chapter.

3. Electrical Conductance Measurements of Cesium Iodide

In Methylamine

 

A. Introduction

 

The thermodynamics of ion-association of cesium salts
in methylamine has been investigated by 133Cs NMR tech-

niques as described in the previous section. It was

 

146

pointed out that the thermodynamic parameters of the minor
species cannot be well-determined from the NMR data. If
we could independently determine the ion—pair formation
constants of cesium salts in methylamine by another tech—
nique, and use them as fixed values in treating the NMR
data, we could obtain more information about further ion—
association from our NMR data. Ion—pair association
constants of cesium salts (Picrate, tetraphenylborate, and
iodide) cannot be studied by UV spectroscopy, since the
anion absorption band is either weak or insensitive to

ion—pairing with the cesium cation (196). A common

 

approach is to measure the electrical conductivity as

a function of concentration, even though conductance theory

 

faces difficulties in determining ion-association constants,

as described in the Historical chapter.

B. Results

(i) Calibration of the Conductance Cell — The

cell constant of 1.02l3i0.0004 cm-1 was determined by
using dilute aqueous potassium chloride solutions and Equa—
tion 1—32. Measured resistances of water and of potassium
chloride solutions at 25.0°C are given in Table 22 at
various frequencies.

The following procedure was used for the calculation of
the equivalent conductance. First, the resistance of the

solvent at each frequency was computed from the parallel

 

 

 

 

147

 

 

 

 

 

 

 

 

 

 

 

 

 

moamo.fi mommo.fl Afilsovg
O
sso.o sam.o ss.o a me
mowam ososm eoaxmomma.fi Awesov om
maamm smmsm oofixmsmos.a oaomm oases comm
omaam smmsm ooagaaoom.a weasw swsom . omom
wawam mammm eoasmmoaa.a oammw oases mom
mmwflm mzwmm woflxfimmmfi.fl mmsmm omsom sam
mflwflm mmwmm moaxawmafl.a mmmmm omsom mam
mamo.m mamm.fi Lopez popes + powwflmom AonV
a soehsmom esseseom hostesses
o m as OH x sz Hog eseesspm esm.oa
exm.om

 

 

 

 

 

AmEQOV oocopmflmom

 

 

 

 

 

 

 

 

 

 

 

Spawmopom m50050< pct

.ooao.oao.hm he hsoflosflom oeasoaso
.soosz .soomamom eseespsm esm.om one so hoosssmahom .mm oases

148

resistance according to the equation

 

l _ l. _ 1 (1 H,
R ‘ "R 4‘
solv solv+SR SR
where Rsolv’ RSR’ and Rsolv+SR are the resistances of the

solvent, the standard resistor, and the solvent shunted by
the standard resistor, respectively. Then the resistances
of water and potassium chloride solutions were corrected
Ifor the polarization effect at the electrodes and for the

capacitance by-pass effect according to the equation,

R = R + af2 +

b
meas 0 ;EE (1-33)

The corrected resistances, R0, together with their marginal
percent standard deviations are given in Table 22. The
cell constant at each salt concentration was then computed

from the corrected resistance according to the equation,

 

 

ACRO
_ x01
K _ R0 (3-9)
1000(1 - R KCl)
0
H2O

Another set of calibrations was carried out at three dif-

ferent concentrations of potassium chloride. The computed

149

cell constants were 1.02114, 1.02127, and 1.02125 cm'l.

The average value of the cell constant from these five

1

determinations is 1.021310.0004 cm—. Cince the cell constant

does not change over a concentration range of potassium

4 — 3.15 x 10‘”

chloride (1.07 x 10- M), the procedure for
the correction of resistances for the frequency dependence
can also be used with confidence for the conductance measure-

ments of cesium iodide in methylamine.

(ii) Conductance of Cesium Iodide in Methylamine

 

at -l5.7°C. - Resistances of cesium iodide solutions in

 

methylamine were measured at -l5.7°C. The measured
resistances at 617, 962, 2020, 3960 Ph: were corrected with
the same procedure which was used for the calibration of
the conductance cell. Equivalent conductances were then

calculated from the following equation,

 

= 1000K ( l _ l
C Rosin Rosolv

) (3-10)

and are given in Table 23. The plot of the equivalent con-
ductance versus the square root of the concentration is shown
in Figure 28. Since the specific conductance of methyl-

8

amine is very 1ow (1.1 x 10— ohm.1 cm—l), precise deter-
mination of this quantity was not possible. The main

problem in our experiment resulted from the use of a

150

Table 23. Equivalent Conductances of Cesium Iodide Solu—
tions in Methylamine at -15.7°C.

 

 

 

Conc. x 105 —1 A_l —l- .
(M) (ohm cm eq ) 0A Weight
3.522 99.2 1.7 0.0015
9.022 70.7 1.4 0.0023

15.42 59.2 0.97 0.0047
22.87 52.3 0.65 0.011
31.02 47.3 0.38 0.031
49.28 39.23 0.18 0.13
73.34 33.48 0.10 , 0.42
103.3 29.137 0.058 1.25
142.0 25.715 0.041 2.5

200.5 22.189 ‘ 0.027 5.6

 

 

 

151

 

100 '

l
D
I

70

50 ~ -
40 - ~
sot -
20 . ~-

A(.0."cm2 eq”)

 

 

 

1 I l
1.0 2.0 3.0' 4.0 5.0

. C’2 x 102(M’2)

Figure 28. Plot of equivalent conductance versus the
square root of the molar concentration of
cesium iodide in methylamine at —l5.7°C.

152

glycol bath for the temperature maintenance. An oil bath
would be preferable for such an experiment but was not
available to us. An error analysis of the data was per-
formed and the errors in the equivalent conductances were
calculated and are also given in Table 23. The analysis
shows that at low concentrations where the resistance of

the solvent is not negligible compared to the resistance of

the solution and also the relative error in the concentration
is large, high standard deviations are associated with the
calculated equivalent conductance. To take account of this
error, appropriate standard deviations for equivalent conduc-
tances and concentrations were used in the fitting of the
data; i.e., each point was used with a weight proportional

to the reciprocal of the variance for that point. The
associated weights for each point according to the Onsager

limiting law are also given in Table 23.

C. Discussion

 

Electrical conductance data of cesium iodide at -15.7°C
were analyzed according to various conductance equations.
The Onsager limiting law (LL) for weak electrolytes is

expressed as,
A = 01(AO - 3763) (1-21)

and K = *

 

 

The extended conductance equation which adds higher order
terms to the conductance equation has the general linearized

form (83),

A=AO—S(Cd)l/2+EC log(Cd)+JlCd—KAA(Cd)yi—J2(Ca)3/2 (1—22)

where S is the coefficient of the limiting law, and E de—
pends only on the properties of the solvent and the charge

on the ions, while J and J2 depend on the same parameters

1
and also on the distance of closest approach of ions. The
coefficients E, J1 and J2 have different values according to
the partiCular theory employed. Among the conductance equa—
tions are: Pitt's equation (F) (77), the Fuoss—Hsia equa-
tion (FH) (83) (both linearized by Fernandez—Prini (78,84)),
the Fuoss-Hsia equation corrected by Chen (FHC) (197),

and the Justice equation (J) (95,96). The Justice equa—

tion consists essentially of setting the distance parameter
equal to q (Bjerrum distance) in the FHC equation. The
results of the analysis of data according to the above equa—
tions are given in Table 24 and the values of the coef-
ficients along with the subroutine EQN for the KINFIT pro—
gram are given in Appendix 2. For all calculations a value
of 5.3 A was selected as the distance parameter (Section 2B1)
except for the Justice method in which the Bjerrum distance
Of 33.0 A was used. Also the formation of the triple-ions

was ignored since the mobilities of triple—ions are not

known.

 

 

_. _. .......__ . __.

 

 

 

 

 

 

 

zoaxw.m Ama canoe
Eogavmzz
om.o mm.o omwammm moaxg:.mha.flv m
03.0 sm.fi H.mae.sm moaxflm:.ohos.mv ems
1.4 .
my mm.o s.m ashamfi seasxa.aao.mv as
mm.o o.H mmsmafi soasxo.flaa.mv a
ese.o eso.o m.sho.aea soasxem.ohms.mv on
<. Cm mHmSUHmom do A 1oo Eo 1E£ov A 12v compozom
compofl>om mogosom do Ezm H mo H .M
poopcmpm popnmfloz < m
owopo><
.mcowpmsom

cocopoSpcoo mSOHLm> an ooCfiopno Dow.mfl1 pm oQHEoncpoz CH opHUOH Esflmoo
mo oocwpospcoo pcoflm>HSUm mCHpHEHq Ugo pcopmcoo compofloomm< map 00 monao> .qm magma

 

155

It is clear from 24, that both the ion-association
constant and the limiting equivalent conductance depend
strongly on the conductance equation used. The same
behavior was observed by Gilkerson (198) for ion-
association of cesium tetraphenylborate in acetonitrile,
and of silver nitrate and lithium picrate in 2-butanone.

As was mentioned in Chapter I, the apparent reason for such
behavior is that both the higher order terms in the con—
ductivity equation and the terms caused by association have
the same concentration dependence in the first approximation.
An increase in the sum ECdlog(C0) + J100 can be compensated
for by a decrease in the ion-association constant. Our data
clearly show that the most recent equations, which intro-
duce higher order terms into the conductance equation,
produce smaller ion-association constants as long as the
distance parameter is the'same. On the other hand, changes
in the distance parameter cause changes in the J1 and J2
coefficients. An increase in the distance parameter

(Fuoss 1977 (199) and Justice (95)) causes J1 to decrease
and J2 to increase. Both such changes in the J1 and J2

coefficients would be compensated for by an increase in the

ion-association constant.

D. Conclusion

 

The ion-association constants obtained from conductance

measurements depend on the conductance equation used for the

156

calculation of this parameter. The Onsager limiting law

fits the data best as indicated by the smallest sum of

the residual squares. The Justice method produces an ion-
pair formation constant which is larger than that obtained
from the NMR data. In this case, the fit is poor and the
ion—pair formation constant and the infinite dilution equiva-
lent conductance are not well-determined. Because the ion-
association and the higher order terms in the conductance
equation have the same concentration dependence, the separa-
tion of these two effects does not appear to be possible with
the available theory, at least at the level of precision of
our measurements. Therefore the ion-association constants
obtained from conductance measurements cannot be trusted
until the separation of these two effects can be made or

until an independent determination of A0 is made.

4. Comparison of NMR and Electrical Conductance Measurements

The only value obtained for ion-pair association con-
stant from the conductance measurement which is larger
than the NMR value is that obtained by the Justice method.
The ion—association constant obtained from other conduc-
tance equations are smaller than the NMR values (Table 24).

Electrical conductance measures the fraction of un-

charged species. The equilibria in the solution are,

K K
+ 1 2

M + x‘ z [M+.s.x‘] 2 M+.X- (3-11)

157

+ _
where M and X are the solvated cation and anion respec-
* + _ + _
tively, and M -S-X and M -X are solvent separated and
contact ion-pairs. According to the above equilibria, the

conductance ion—pair constant can be written as

K = (MSX)+(MX)‘ <,_.2)

cond (M)(X)Yi

 

in which the charges are omitted for simplicity. Sub—
stitution of the equilibrium constants into Equation 3-12

gives,

Kcond = Kl<l + K2) (3-13)
With respect to NMR, the second equilibrium in Equation (3-11)
is independent of concentration. Therefore, it is the first
equilibrium which determines the concentration dependence

of the chemical shift. Thus, the observed chemical shift

can be written as

6 = 6

obs M + X

X +

M 6MX[XMSX (i‘lu)

IVIX:J

in which MX=(6MSX+K26MX)/(K2+l) is the population averaged
chemical shift of contact and solvent separated ion-pairs.
Since the exchange between the two types of ion-pairs is fast

on the NMR time scale,the formation constants of these two

158

species cannot be separated by the NMR method. Again,as
in the case of conductance,the calculated association con-

stant from NMR measurements would be

_ (MX)+(MSX) _ - ’ D .
KNMR - _ Kl(l+K2) (J‘LS)

<M><X>Y§

 

It should be emphasized again that the limiting chemical

shift at high concentration, 5MX’ is not the chemical shift
of the contact ion-pair but is the population averaged
chemical shift of the two types of ion-pairs.

From the above discussion, it is clear that the ion-
associations obtained from conductance and NMR measurement
should be the same. The discrepancy between the calculated

values (Table 2“) is probably due to the inadequacy of the

conductance equations.

 

 

 

 

OCHAPTER IV

COMPLEXATION OF CESIUM SALTS BY l8-CROWN-6

IN METHYLAMINE AND LIQUID AMMONIA

159

 

 

 

 

I. Introduction

 

The complexation of the cesium cation by lB-crown-o (18C6)
in aqueous and methanolic solutions as well as in mixtures
of these solvents has been studied by potentiometric (160)
and calorimetric (173,17A) techniques. Mei et al. (200,
201) used 13305 NMR to study complexation of cesium tetra-
phenylborate by 18—crown—6 in six nonaqueous solvents. In
all solvents studied, the formation of the 1:1 complex was
followed by the addition of a second molecule of the ligand
to form a "sandwich" 2:1 complex.

The use of high donor solvents such as liquid ammonia
and methylamine to study alkali metal solutions in the pres-
ence of macrocyclic ligands (183) motivated us to investi-
gate the complexation of cesium salts by lS-crown-6 in
these solvents. In the course of such studies with methyl-
amine, it became clear that many equilibria are involved
in the complexation process. Therefore an extensive study
of the system was required to obtain the thermodynamic.
formation constants of the 1:1 and 2:1 complexes. The
results of these studies are presented in this chapter and
compared with the results in liquid ammonia and in other

solvents.

160

161

2. Complexation of Cesium Salts by 18-crown-6 in Methyl-

 

amine

A. Mole Ratio Dependence of l33Cs‘Chemical Shift in

 

Methylamine

 

(1) Results - Cesium-133 chemical shifts of cesium
iodide and cesium tetraphenylborate in the presence of
18-crown-6 were measured as a function of (18-crown—6)/
(Cs+) mole ratio (R) at a fixed concentration of the salt
in methylamine solutions. The results for cesium iodide
at various temperatures are given in Table 25 and shown
in Figure 29. At all temperatures, an upfield shift
resu1ts as the mole ratio increases. This means that
the cesium cation interacts more strongly with the iodide
ion than with lB-crown-6. A plot of the chemical shift
versus mole ratio is practically linear in the range of
O < R < l. The linearity of the plots below R = l indi-
cates the formation of a strong lzl complex (Kf Z 10“).
The formation of the strong l:l complex is followed by the
formation of a weaker 2:1 complex as indicated by a
change in the slope of the mole ratio plot above R = 1.
Similar results for cesium tetraphenylborate are

given in Table 26 and illustrated in Figure 30. A

162

Table 25. Mole Ratio Study of 18C6, CsI Complexes in Methyl—

 

 

 

 

amine at Various Temperatures; (Cs+) = 0.0206
1 0.0008 M-
60bS(ppm)

(¥8ég)§?0:$) +25.1°C +13.2°C +9.5°C +6.0°C
0.0 127.10 127.10 126.36 126.13
0.205 117.91 118.22 117.52 117.37
0.365 109.85 110.08 109.69 109.30
0.070 100.30 . 100.73 100.26 100.26
0.576 100.85 101.16 100.62 100.50
0.810 89.05 89.10 88.52 88.37
0.885 87.13 86.58 86.35 85.88
0.958 80.02 83.87 83.02 82.63
1.012 82.70 80.92 80.38 79.99
1.197 79.99 78.13 . 77.u3 76.73
1.569 75.57 72.63. 71.15 69.83
2.050 70.80 66.50 60.25 62.39
2.295 69.00 60.60 61.39 59.91
2.668 65.80 59.29 56.81 50.17
3.170 63.32 50.95 51.92 08.82
0.531 50.30 03.55 39.59 35.87
6.096 07.58 35.09 30.29 26.25

.11.109 28.57 13.27 8.30 0.23

73.66* 17.72 2.37 ____________

 

163

 

 

 

 

Table 25. Continued.
obs<ppm)

Mole Ratio ‘

(1806)/(0s+) +2.2°c —2.5°c -10.3° —16.3°c
0.0 125.67 125.20 ------ 12u.66
0.205 117.u5 116.52 —————— 116.uu
0.365 109.u6 108.8u —————— 108.80
0.470 10u.26 103.80 ------ 103.95
0.576 100.39 99.92 —————— 100.23
0.810 88.60 87.75 ------ 88.13
0.885 85.96 85.27 —————— 85.57
0.958 82.u7 81.70 ------ 82.01
1.012 79.76 79.53 81.23 78.60
1.197 76.19 75.149 711.10 72.86
1.569 68.83 66.65 .63.32 60.30
2.050 59.91 56.81 51.69 u6.08
2.295 58.28 5u.32 97.97 A3.08
2.668 50.83 £17.35 39.82 33.146
3.170 A5.6u 01.61 32.07 25.01
u.531 32.38 26.01 16.95 8.36
6.096 22.111 15.86 6.17 -3.80

11.109 0.u3 —5.32 -1u A6 —21.21
73.66* ------ —1u.5u -21 36 -29.50

 

160

 

 

 

 

 

 

Table 25. Continued.
60bS(ppm)

Mole Ratio -

(18c6)/(0s+) -32.1°0 —uu.0°c —u8.0°c
0.0 125.36 129.66 12u.19
0.205 116.67 116.83 116.98
0.365 110.00 110.15 109.08
0.u70 10u.96 105.89 105.19
0.576 101.39 101.78 102.17
0 810 89.92 90.62 91.16
0.885 87.05 89.08 88.53
0.958 83.33 8A.56 8A.87
1.012 78.83 ------ 79.1u
1.197. 69.99 68.83 67.82
1.569 51.8u uu.u8 01.76
2.050 32.22 21.83 18.56
2.295 27.07 16.87 12.53
2.668 16.17 u.15 1.05
3.170 5.78 -7.87 -12.29
n.531 —10.ou -20.07 -25.00
6.096 -19.89 -28.u9 -32.06

11.109 -3u.u6 -39.12 _u0.82
73.66* ———————————— —u3.u6
(08+) = 0 002 M

165

 

 

 

 

 

:2 341867619:be
Mole Ratio( 8-crown-6)/(CsI)->

Figure 29. Cesium-133 chemical shift versus (l8-crown-6)/
(CsI) mole ratio and temperature in methylamine;
(CsI) = 0.02 g.

 

 

 

 

 

 

 

   

166

Table 26. Mole Ratio Study of 1806, CsBPhu Complexes in
Methylamine at Various Temperatures; (Cs+) =
0.0108 0.0005 g.

 

 

 

 

60bS(ppm)
Mole Ratio Temperature, °C
(1806)/(Cs+) 25.0 13.2 5.8 —3.0
0.000a -7.05 -3.35 —1.65 0.25
0.209 -3.06 0.90 2.60 0.50
0.095 3.07 6.97 8.73 10.82
0.600 6.01 9.03 11.52 13.50
0.857 9.89 13.50 15.71 17.80
0.875 11.29 10.78 16.33 18.30
0.901 11.68 10.78 16.08 18.50
0.922 11.68 10.78 16.79 18.89
0.999 12.05 15.78 17.57 19.08
1.089 11.68 10.39 16.02 17.72
1.365 10.28 11.21 11-00 11.36
1.511 8.57 8.81 8.02 7.11
1.516 7.33 6.90 6.25 0.39
1.639 6.63 6.03 0.85 2.21
2.013 3.30 1.00 -0.73 —0 30
2.377 -0.65 -0.10 -6.90 -ll.59
2.720 -2.98 -7.00 -10.35 -15.63
3.100 —6.07 -11.51 —15.23 -20.66
3.331 —8.02 -13.29 -17.02 —22.99
3.797 -10.97 -17.09 —20.66 -26.55
6.005 —19.96 -26.00 -29.81 -30.85
11.076 -28.96 —33.92 -36.79 —00.51

 

167

 

 

 

 

Table 26. Continued.
60bS(ppm)
Mole Ratio Temperature, °C
(18C6)/(Cs+) —16.2 —32.1 _ -07.7
0.000a 1.65
0.209 6.25 b b
0.095 12.91 b b
0.600 15.86 b b
0.857 20.36 23.77 b
0.875 20.82 23.85 b
0.901 21.06 20.39 b
0.922 21.60 25.17 b
0.999 22.57 25.36 b
1.089 19.82 22.38 b
1.365 9.97 8.65 7.95
1.511 3.80 0.28 —2.50
1.516 0.51 -3.68 -7.17
1.639 -2.83 -8.56 -10.57
2.013 -1l.28 -19.19 -27.60
2.377 -20.58 -29.19 -38.19
2.720 -25.00 -33.77 -0O.9O
3.100 -31.13 -38.11 —00.02
3.331 -32.68 -39.82 -05.08
3.797 -35.90 -01.83 —06.60
6.005 -0l.75 —05.79 -08.50
11.076 -05.50 -07.09 -09.16

 

 

aObtained from extrapolation.

b

Precipitation in solution.

 

 

 

 

1 1 l 1 1 1 1 1 1
| 2 3 44 5 6 7’ 8 9 K) H
Mole Ratio (I8-crown-6)/(CsBph4)
_——,

Figure 30. Cesium-133 chemical shift versus (18-crown—6)/
(CsBPhu) mole ratio and temperature in methyl—
amine; (CsBPhu) = 0.01 M.

169

linear downfield shift followed by an upfield shift which
gradually approaches a limiting value can be explained by
the formation of a relatively strong 1:1 complex followed
by the addition of a second molecule of the ligand to

form a 2:1 sandwich complex.

133

(ii) Discussion — The variation of the Cs chemical
shift as a function of (18-crown—6)/(Cs+) mole ratio in
methylamine can be explained by the formation of a strong
1:1 complex followed by the formation of a 2:1 complex.

If we were able to neglect ion—pair formation for the salt,
the 1:1 complex, and the 2:1 complex, the data could be

analyzed according to the equilibria,
M+c (0—1)

M+C <0—2>

in which M+, C, M+C, M+C2 are the cesium cation, the ligand,
the 1:1 complex, and the 2:1 complex, respectively. Since
the mole ratio plot is linear below mole ratio of unity,

the formation constant of the 1:1 complex cannot be ob-
tained from the data and only a lower limit of this value
can be estimated (Kl : 100). Then the variation of the
chemical shift above R = 1 could be used to obtain the

formation constant and the limiting chemical shift of the

170

2:1 complex by assuming that the formation of the 1:1 com-
plex is complete at a mole ratio of unity. The solution to
these equations and the subroutine EQN for use with KINFIT
Euwagivenelsewhere (186). The results,according to this
simple scheme,are given in Table 27 for cesium iodide and
in Table 28 for cesium tetraphenylborate. The enthalpies
and entropies of complex formation were obtained by
using the KINFIT program. The van't Hoff plots are shown
in Figures 31 and 32.

In the 2:1 sandwich complex, the cesium cation is ex-
pected to be effectively isolated from the solvent and
the counter-ion. However, at least for the iodide salt,
the limiting shift is strongly temperature dependent. In
addition,comparison of Tables 27 and 28 shows that the
formation constant of the 2:1 complex at a given temperature
is strongly anion dependent. Both of these effects suggest
that other equilibria are important in the solution. We
have seen in Chapter III that cesium salts are highly
associated in methylamine. Therefore it is reasonable to
assume that the 1:1 complex,in which the cesium cation sits
above the 18-crown-6 cavity,can also form ion-pairs with the
anion. Since the ion-association constant of cesium iodide
is stronger than that of cesium tetraphenylborate (Chapter
III), the calculated complexation formation constant accord-
ing to equilibrium (0-2) should be smaller for cesium

iodide than for cesium tetraphenylborate, because the

 

171

Table 27. Thermodynamic Parameters for the Formation of
the 2:1 Complex of l8—Crown—6 and CsI in Methyl—

amine. K i 100.

 

 

 

 

t°:O.5 1:21 (611m)2:l
(0C) - (M ) (ppm)
25.1 5.0010.20 —25.8:2.0
13.2 6.93:0.13 -36.8:1.0
9.5 7.87i0.19 -39.9i1.3
6.0 8.82i0.17 d01.2i1.0
.2 10.30i0.15 -00.5i0.7
-2.5 12.68i0.29 —01.3iO.9
-10.3 17.29:0.00 —00.2i0.8
-16.3 22.71:0.95 -05.5i1.2
-32.1 00.12i0.98 —50.2iO.5
-00.0 65.3:2.2 -09.3i0.0
—08.0 75.5 11.9 —50.0:0.3
AG398°= —0.9610.02 kcal.mo1e-l.
AHO = —5.210.1 kca1.mole_l.

A80 = -l0.2i0.0 e.u.

 

 

 

172

Table 28. Thermodynamic Parameters for the Formation of
the 2:1 Complex of l8—Crown-6 and CsBPhu in

 

 

 

 

Methylamine. K1 1 10 .
t°i0.5 "¥_" 1 (611m)2:1
(00) (M ) (ppm)
25.0 23.1:1.0 -07. i .9
13.2 03.6:1.5 -05.8iO.5
5.8 58.9:1.0 -06.0:0.3
-3.0 89.7il.9 -07.6iO.2
-16.2 186.9i0.1 -09.3i0.1
-32.1 007 i12 -09.5i0.1
-07.7 893 i09 -50.1i0.1
6039800=-1.86:0.03 kca1.m61e‘l.
AH° = -6.8310.25 kca1.mole .

880 = -16.35i0.96 e.u.

 

 

 

 

 

 

 

173

 

4.2 P

3.8 -

3.4 *-

3.0-

an2

2.6 "
2.2 "

l.8-

 

 

lg; l I l I l l
' 3.2 3.4 3.6 3.8 4.0 4.2 4.4

l/T x lo3 (°K"')

 

Figure 31. Ln"K2" vs 1/T for the 2:1 complex of 18-crown-

6 and CsI in methylamine. K1 1 10“, (Cs+)=0.02M.

170

20

 

£55"

5£P'

In K2

‘45-

135-

 

I

 

 

I I I I L
303.2 34 3.6 3.8 40 4.2 44

 

l/T x 10’ PK")

Figure 32. Ln "Ké'zs l/T for the 2:1 complex of l8-crown-6

+
and CsBPhu in methylamine. K1 1 10“, (Cs )=0.01M.

“-5.

 

ligand and the anion are competing for the cesium cation.
Thus, although the simple picture given above can be used
to fit the data,it is obvious that ion—association of the
1:1 complex cannot be ignored in the treatment of data.

It will be shown later in this chapter that even the 2:1
complex forms ion—pairs in methylamine (which are probably

not contact ion—pairs). The complete scheme for this system

can be written as,

K
_ ta _ _
K + x z x .M+.X
+ — ip —
M + x 2 M x K
t _
+ M+ : M+ x .M+
+ +
c 0
6C ++ ++ KX
K
_ A _
MC + x : MC+.X (0-3)
+ +
c c
KC2 ++ ++KX2
K

MG; + x' gf2 MG;.X_

in which MC+, M05, Mc+.x‘, and MCZ.X‘ are the 1:1 complex,
2:1 complex, ion—paired 1:1 complex and ion—paired 2:1

complex, respectively. Other symbols have the same mean—
ings as in Chapter III. It is important to note that the

1:1 complex might form both contact and solvent—separated

176

ion-pairs but the separation of the formation constants of
these two kinds of ion-pairs is not possible from the NMR
data (see Chapter III). It should also be obvious from the
complexity of the complete scheme that the evaluation of all
the equilibrium constants as functions of temperature and
the chemical shifts of all the species is an impossible
task. Clearly it will be necessary to make some assumptions
and approximations in evaluating the parameters.

The concentration dependence of the chemical shift of
the 1:1 complex could, in principle, be used to evaluate

K

c’ KA’ and Ki as functions of temperature. Then the com-

plexation formation constant and the ion-pair formation
constant of the 2:1 complex might be obtained from the
mole ratio studies by using proper equilibria. The results

of studies of this type are given in the next sections.

133

B. Concentration Dependence of the Cs Chemical Shift

of the 1:1 Complex in Methylamine

(1) Results — The concentration dependence of the 133CS

chemical shift of the 1:1 complexes of 18-crown-6 with cesium
salts was examined. The results at various temperatures

for cesium iodide, cesium tetraphenylborate, and cesium
thiocyanate are given in Tables 29, 30, and 31, respectively.
Plots of the 133Cs chemical shift versus the concentration

of the 1:1 complex are shown in Figures 33, 30 and 35 for

each salt.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 29. Concentration Dependence of the l‘33Cs Chemical
Shift of the 1:1 Complex of CsI and 1806 in
Methylamine at Various Temperatures.

 

 

6obs (ppm)

0
Cone. Temperature C

 

(M) 25.2 12.3 6.0 —2.1 —10.0 -15.9
0.00005 95.81 ————— 79.53 76.35 70.72
0.00092 91.00 {85.50 83.95 80.85 79.37 78.29

90.85 85.73 78.21
91.16
0.00202 89.30 85.11 83.97 82.09 80.77 79.68
79.99
0.00377 87.98 80.60 83.08 82.09 81.39 80.69
87.98
0.00070 87.36 ————— 83.08 81.93 81.39 80.85
0.00606 86.66 80.02 83.00 82.20 81.78 81.15
86.76 83.09
0.00755 86.03 .83'95 83.09 82.32 81.93 81.07
0.00960 85.73 83.79 83.17 82.32 81.93 81.62
0.01198 85.02 83.00 82.86 82.16 81.93 81.62
85.19
0.01793 80.57 83.02 82.71 82.20 82.09 81.72

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

178

Table 30. Concentration Dependence of the 133Cs Chemical
Shift of the 1:1 Complex of CsBPhu and 18C6 in
Methylamine at Various Temperatures.

 

 

6

 

 

obs

Conc. Temperature

(M) 25.0 6.0 -2.5 —16.1
0.00020 20.90a ---------- 30.36a
0.00051 17.18a 23.38a 25.00a 28.25a
0.00100 15.63 21.60 23.62a 26.80a
0.00158 10.50 20.00 22.38 26.02a
0.00206 10.00 19.82 21.60 25.55
0.00272 13.85 19.51 21.75 20.07
0.00002 13.30 18.73 21.06 23.85
0.00090 12.91 18.30 20.20 23.62
0.00750 12.60 18.03 19.70 23.07

12.30

0.01129 {12.05 17.65 19.12 23.07

 

 

aThese points were omitted in the analysis of the data (see
text for explanation).

179

 

 

 

 

Table 31. Concentration Dependence of the 133Cs Chemical
Shift of the 1:1 Complex of CsSCN and 18C6 in
Methylamine at Various Temperatures.

dobs (ppm)
Conc.
(M) Temperature
25.0 6.0 -16.0 -30.8 -50.0
0.00099 03.23 01.10 00.21 00.37 01.99
0.00198 {00.52 39.28 39.36 00.29 02.23
00.21
0.00503 37.88 37.73 {38.82 00.37 02.31
39.13

0.00760 36.09 37.30 38.50 00.00 02.55

0.00993 36.02 36.80 38.58 00.52 02.38

0.01273 35.71 36.01 38.55 ----- 02.69

0.02010 35.09 36.01 38.01 00.68 02.15

 

 

 

180

72.......

 

76

80

 

 

84

80bs (ppm)

88

92

 

96‘

 

 

 

1 I I I
l000.0 0.4 0.8 l2 L6 2.0

' [65*] x lo2 (M)

Figure 33. Concentration dependence of the 133Cs chemical
shift of the 1:1 complex of 18—crown—6 and
CsI in methylamine at various temperatures.

 

181

 

 

 

 

l2- 25.0°C
'6.—
A ' ‘ aco"
g o “25°C
3 20-
U) 7. CI‘O
.0
o -l6l°c
0° 243° ,
0 V
"
V
28"
32 I J
0.0 0.4 0.8 l.2
[Cs’] x IO2 (M)
Figure 30. Concentration dependence of the 133Cs chemical

shift of the 1:1 complex of 18—crown—6 and
CsBPhu in methylamine at various temperatures.

182

34 j 7 l

 

 

 

 

 

 

 

r I l
250°C
60°C

’7 462°C

6
6C? 5'308°C
v ‘504°C

44 ‘ 4 ' l g 1
0.0 0.4 0.8 l2 l6 2.0 2.2
[65*] x lo2 (M)
Figure 35.

Concentration dependence of the 133Cs chemical
shift of the 1:1 complex of 18—crown—6 and
CsSCN in methylamine at various temperatures.

183

(ii) Discussion — (a) General Discussion - In all

 

 

cases the variation of the chemical shift as a function of
concentration and temperature reflects the competition
between ion-pair formation and complex formation. This
behavior is most pronounced in the cesium iodide case. The
cesium iodide data (Figure 33) show that at low concentra-
tions and high temperatures the chemical shift approaches
that of the Cs+.I- ion-pair (120 ppm), while at low concen-
trations and low temperatures an upfield shift occurs as
concentration decreases. It seems reasonable to believe

that this upfield shift is due to the formation of the MC+
complex. At high concentrations all curves converge to the
same chemical shift whichijsbelieved to be the chemical shift
of the ion-paired complex (MC+.I-). The concentration and
temperature dependence of the chemical shifts of the 1:1
complexes of 18—crown-6 with cesium tetraphenylborate (Figure
30) and cesium thiocyanate (Figure 35) can also be explained
in the same way. However, the cesium iodide data are more
illustrative since the chemical shift of the ion-paired

complex, 6 lies between the chemical shift of the

MC+.X"

ion—paired salt, 6 and the Chemical Shift of the

M+.x-’
complex, 6MC+°

According to the above discussion, the equilibria
responsible for the chemical shift changes of the 1:1

complexes as a function of concentration and temperature

can be written as,

+ _
M .x M+
7 +
Kt
M+
+

c c - (0-0)

The formation constants and the chemical shifts of the ion-
pairs and triple ions as well as the chemical shift of the
free cation are known (Chapter III) and can be used as con-
stants in the above equilibria in order to obtain other param-
eters. The solution to the above equilibria is given in Ap-
pendix 3A together with the subroutine EQN for use with
KINFIT. To completely analyze the data for each salt at

least six parameters would have to be adjusted. These are

0 and 6 +

O O o .
KX, AHX, KA’ AHA, MC+’ MC .X” Since KC is a depen—

dent variable (KC = K Kx/KA) it need not be independently

1p
adjusted. Again, as in the case of cesium salts in methyl-

amine (Chapter III), the determination of all parameters

 

 

 

is not possible since some of the parameters are highly
correlated with each other and/or correspond to minor
species. For example, the chemical shift of the com—
plex, 6MC+’ is difficult to determine from the data.
Since ion-pair formation of both the salt and the 1:1

complex are competing with simple complex formation, so that

the concentration of MC+ in solution is small at all con—

centrations and temperatures. Although this species has its

highest mole fraction at the lowest concentration and the

lowest temperature, even under these favorable circum—

stances, it amounts to less than 15% of the total cesium

concentration. The ion—pair formation constant of the 1:1
complex, KA, and its enthalpy of formation, AHE are strongly
coupled and the simultaneous determination of these param—

eters is not possible. Consequently, we were forced to fix

6MC+ and AHE (or KA) at "reasonable" values in order to
obtain the other parameters. The rationale behind our choice

Of 6MC+ and AHK will be described in the next two sections.

(6) The chemical shift of the 1:1 complex, 6MC+°

As described in Chapter III, the chemical shift of cesium

thiocyanate in methylamine is independent of concentration
so that we were unable to determine the ion—association

parameters for this salt. Therefore, it might seem that

the concentration dependence of the chemical shift of the

1:1 complex of 18—crown-6 with CsSCN would not provide

186

much information about the complexation reaction. On the
contrary, however, the most valuable information about the
chemical shift of the 1:1 complex, can be obtained directly
from the cesium thiocyanate data (Figure 35).

Since the chemical shift of cesium thiocyanate is in-
dependent of concentration and is presumably the same as
the chemical shift of the free cesium cation (see Chapter
III), the chemical shifts of the 1:1 complex, 6MC+’ and

of the ion-paired complex, 5 should also be the

Mc+.x-’
same. A closer look at Figure 35 shows that only the
chemical shift of the 1:1 complex (and the ion-paired com—
plex) can be responsible for the upfield shift at high
temperatures, because the chemical shiftscfl‘other species,
igeg, the free cation and the ion-pair, are both larger
than all of the observed chemical shifts. Therefore,
extrapolation of the curves to high concentration at each
temperature should provide the chemical shift of the 1:1
complex (and the ion-paired complex). Fortunately, the
curves at low temperatures level off at high concentrations
and 5MC+ can be obtained directly. If we assume that the
chemical shift of MC+ is linearly dependent on temperature,
(as is the case for ion—pairs and the free ions), then

6 + at high temperatures can be determined from the ex-

MC
trapolation of the low temperature data. In fact a plot
of the chemical shift versus temperature is almost linear

at low temperatures (Figure 36). By complete analysis of

187

 

 

 

 

 

Figure 36. Limiting 133Cs chemical shift of the 1:1 com-
plex of 1806 and CsSCN vs temperature in methyl-
amine. A experimental values at the highest
concentration studied (Figure 35), 0 calculated
values obtained from the parameters of Table

36.

 

 

 

 

 

188

the data (section iiic) we found that the chemical shift

of the complex at a given temperature can be expressed as,

(61%.)t = 32.5 —o.13 (t - 25°C) (0—5>

where the chemical shift of the complex at 25°C is taken as
the reference chemical shift.

Now let us see if the above conclusion about the chemical
shift of the 1:1 complex is consistent with the other results.
The cesium iodide data (Figure 33) suggest that the chemi-

cal shift of the complex at 25°C should be smaller than the

limiting chemical shift, 6MC+ I‘ z 80 ppm, since the cesium

cation interacts more strongly with the iodide ion than

with the solvent. The same data give an upper limit of 72

ppm for 6MC+ at —l6°C. The cesium tetraphenylborate data
(Figure 30) indicate that the chemical shift of the complex
is greater than 12 ppm at 25°C and greater than 23 ppm
at —16°C, because the cesium cation interacts more strongly
with the solvent than with the tetraphenylborate anion.
Therefore, the chemical shift of the complex is limited to,

80 > 6 > 12 ppm at 25°C

Mc+

_ O
72 > 6MC+ > 23 ppm at 16 C

which is consistent with the above conclusion.

189

(c) Enthalpy of formation of the ion-paired complex

 

As stated earlier, the ion-pair formation constant of the 1:1
complex, KA’ and the enthalpy of the formation of the ion-

paired complex, AH:
simultaneous determination of these two parameters is not

, are highly correlated and therefore

possible. This is evident from attempts to obtain these

two parameters simultaneously from the cesium iodide data.
The results are given in Table 32. The standard deviation
associated with AHO

A
is even greater than the parameter itself.

is very large and the standard devia-
tion of KA
This indicates that the information content of the data is
insufficient to determine both parameters and we must fix
one of those at a reasonable value.

+ -
The free energies of formation of the ion—pair, M .X ,

+ _
and the ion—paired complex, MC .X can be written as,

AGip RTanip AHip IASip (0 6)
and
0 = - = 0 _ 0 _
AGA RTanA AHA TASA (0 7)

If we assume that the difference in the free energies of

 

ion-association of the free cesium cation and the complexed

cation is entirely of enthalpic nature, then we can write,

0 _ o _ o = _
6AS — ASA ASip 0 (0 8)

 

 

 

 

190

Table 32. Thermodynamic Parameters forthe Formation of the
1:1 Complex of l8-Crown-6 and CsI in Methylamine
at 25.0°C; with Adjustment of AHO.

 

 

A
xx (8.53il.65)x103 ' M'l

AH; —20.0:3.1 kcal.mole-l
KA (0.3:3.6)x105 M-l

6H3 7.1:3.1 kca1.mole-l
6MC+.X- 83.08:0.20 ppm

-1

bMC+ X‘ -0.002:0.011 _ ppm.deg
56(3) 0.30 ppm

 

 

aAverage standard deviation of chemical shifts (the symbol
has the same meaning in subsequent tables).

191

Subtracting Equations 0—6 and 0—7 and introducing 5AS°

from Equation 0—8 gives,

K.
0= 0 1p
AH AHip + RTln (KA ) (0-9)
With this assumption it is only necessary to adjust one of
the parameters (KA or ARK) since Kip and Ang are known from

the salt results (Chapter III).

iii. Analysis of the Data

The concentration dependences of the chemical shifts
of the 1:1 complexes of l8—crown—6 with cesium salts were
analyzed according to equilibria (0-0). Since the data
for each salt do not provide equal amounts of information,
the treatment of the data for each salt will be discussed
separately. The solution to the equilibria and the general

subroutine EQN are given in Appendix 3A.

(a) Cesium iodide — The concentration and tempera-
ture dependence of the chemical shift of Cs+l8C6.I_ was
analyzed according to equilibria (0-0). The ion—association
parameters of the salt were taken from Table 12. Since
the values of these parameters are internally consistent,
the choice of the model for ion-association should not have
an appreciable effect on the complexation parameters. The

chemical shift of the complex at various temperatures was

192

computed from Equation 0-5. The enthalpy of formation
of the complex was obtained from Equation 0.9. In addi-
tion it was considered that the chemical shift of the ion-

paired complex, 6 is linearly dependent on tempera-

MC.X’

ture according to,

(6 ) = (6

MC.X t + b(t - 25°) (0-10)

MC.X)25°
The calculated parameters are given in Table 33. It should
be noted particularly that the ion—pair formation constant
of the 1:1 complex is similar to that of the uncomplexed
salt. If the cesium cation were forming primarily contact
ion-pairs in the salt solution, then one would expect

that the ion-pairs would dissociate upon the addition of
the ligand and the ion-pair formation constant of the
complexed cation would be significantly smaller than that
of the salt. Therefore it is reasonable to conclude that
even the uncomplexed salts form largely solvent separated
ion-pairs. Shchori et al. (167) also found that the dis-
sociation constants of NaBPhu (Kd = 5.02 x 10'5 M at 20°C)
and Na+DBl8-crown-6.BPhu- (Kd = 6.00 x 10'5 M at 20°C)

in dimethoxyethane are of the same order of magnitude,
which is an indication of "loose" ion—pair formation.

In addition Boileau et al. (172) investigated the ion—
association of Na+BPhu_ and K+BPhu- and their complexes

with cryptands in tetrahydrofuran conductometrically.

Table 33.

193

Thermodynamic Parameters for the Formation of
the 1:1 Complex of 1806 and CsI in Methylamine
at 25.0°C; with Calculation of AHX from Other

Adjustable Parameters.

 

 

Fixed Parameters

 

 

= _ _ O
(6MC)t 32.5 0.13 (t 25 )
O = O T
AHA AHip + RTln(Kip/KA)
Adjustable Parameters
KA (1.51:0.06)x105
xx (6.33:0.00)x103
AH§ -16.00:0.53
SMC.X , 82.69i0.2l
bMC.X -0.006:0.007
5 0.30
5 K K 0
Kc 1; X (1.07:0. l5)x10
A
0 - TO 0
AHC — Ahip + AHX

.. AHO

A -16.72:0.80

(From Equation 0—5)

(From Equation 0-9)

kca1.mole-l

ppm
ppm.deg-l
ppm

M-1

kcal.mole-l

 

 

 

 

 

 

The authors found that the dissociation constants of Na+—
BPhu‘ (Kd = 9.33 x 10"5 M at 20°C) and Na+22l.BPh4_ (Kd =
8.97 x 10_5 M at 20°C) are almost equal. Similarly the dis—
sociation constants of K+.BPhu~ (Kd = 0.39 x 10_5 M at 20°C)
and K+222.BPh4_ (Kd = 8.16 x 10‘5 M at 20°C) are of the

same order of magnitude. The authors concluded that the un—
complexed salts form solvent separated ion pairs in tetra—
hydrofuran.

In summary, our results are consistent with a model in
which both salt and complex form largely "loose" ion—pairs
in methylamine and are in accord with the results of two sets
of authors for similar systems. However, the effect of the

anion on the chemical shift shows that some contact ion—

pairs must be formed.

(b) Cesium tetraphenylborate — The concentration and
temperature dependence of the 1:1 complex of l8—crown—6 and
cesium tetraphenylborate in methylamine was analyzed ac—
cording to equilibria (0—0). The ion—association param—
eters from Table 12 were used as constants. The chemical
shift of MC+ was obtained from the limiting chemical shift
of the CsSCN data as described above (Equation 0—5) and a
linear temperature dependence was assumed for the chemical
shift of the ion-paired complex (Equation 0—10). The value of

AH: was fixed at the value of Ang. The results obtained

in this way are given in Table 30. In the analysis of the

 

 

 

 

 

Table 30. Thermodynamic Parameters for the Formation of
the 1:1 Complex of 1806 and CsBPhu in Methyl-

- o.- 0= 0
amine at 25.0 C, With AHA AHip.

 

 

Fixed Parameters

(6M0)t = 32.5-0.13 (t—25°) (FrOm Equation 0—5 )
AHX = Ang

Adjustable Parameters

 

 

KA (l.30:0.20)xlou M“l
KX (1.08:0.63)x100 M‘l
AH; —8:25 kca1.mole_l
6M0.X 8.08:1.10 ppm
bMC X —0.l2i0.02 ppm.deg'l
66 0.22 ppm
, _..—_—__L

 

 

 

 

196

data we had to omit some of the points at low concentra—
tion, since it was not possible to achieve convergence on
the concentration of species.

The solution to the equilibrium equations were compli-
cated (Appendix 3A), therefore, the iteration procedure for
the calculation of the concentrations was based on the major
equilibria in the solution and successive corrections for
the concentration of the minor species, M+, X_.M+.X—, and
M+.X—.M+. At low concentrations and especially at low
temperatures the fraction of M+ is not small (3 10%) and
therefore the above procedure would not work for these points.
However, neglecting these points should not have signifi—
cant effect on the calculated parameters since it is only a
result of the convergence failure when these concentrations
are included and does not depend on the adjustable parameters.
The only effect of neglecting these points is on the cal—
culated standard deviations of the parameters. Table
30 shows that the standard deviation in AH; is huge. The
reason is that this parameter is largely determined by
points at low concentrations and temperatures, some of
which had to be discarded. To improve the standard devia—
tion in AH; we can use the parameters obtained for CsI.
The formation constant of the unassociated complex, Kc’
is independent of the counter ion,

+

K
M +0 :PMC+

 

 

 

 

 

197

The value of KC can be calculated from cesium iodide data
(KC = Kipr/KA) and then used as a constant in the tetra-
phenylborate data. The enthalpy of the formation of the

unassociated complex can also be expressed in terms of the

enthalpies of formation of other species (AH: = AH; +

p
AH; - AHX). Thus only four parameters must be adjusted.
O 0
These are Kx’ AHX, 6MC.X’ and bMC.X' Then KA and AHA

can be expressed in terms of the other parameters. The
calculated parameters are given in Table 35. These results
are more meaningful than the results in Table 30 since KC
(which is also strongly dependent on the low concentration
points) has been used as a constant. The use of K0 and

AH: from the cesium iodide data to fit the cesium tetra—
phenylborate data has another advantage in that it provides
a check on the consistency of the two data sets. The ion—
pair formation constant of the complex for cesium tetrae
phenylborate is the same order of magnitude as the ion-

pair formation constant of the salt and the enthalpies of
formation of these Species are almost equal. This sug-
gests again that "loose" ion-pairs are important as was the
case with cesium iodide. The value of KX is somewhat smaller
for CsI than for CsBPhu which reflects the different degrees

of ion-pair formation of the two salts.

(c) Cesium thiocyanate - Since the chemical shift of

 

the free cesium cation and ion-paired cesium thiocyanate

 

 

 

198

Table 35. Thermodynamic Parameters for the Formation of
the 1:1 Complex of 1806 and CsBPhu in Methyl-
amine at 25.0°C; K0 was used as a Constant.

 

 

Fixed Parameters

(6M0)t = 32 5—0.l3 (t—25°) From Equation 0—10
KC = 1.07x10“ M‘l From Table 30
AH: = —16 72 Kcal.mole‘l From Table 30

Adjustable Parameters

KX (8.00:1.0)x103 M"l
AH; —l8.80i0.95 kcalmole’l
—l
bMC.X —0.l9:0.03 ppm.deg
66 g 0.23 ppm
K. K
KA = —iE—§ (l.l6iO.35)XlOu M‘1
K
C
o __ o o_ o ‘1
AHA — AHip + AHX AHC 2.63:1.31 kca1.mole

 

 

 

 

 

 

199

are the same, the ion—pair formation constant of this salt
cannot be obtained from the concentration dependence of the
chemical shift. Similarly the ion—pair formation constant

of the complex, KA’ cannot be extracted from the concentra—
tion dependence of the chemical shift of the 1:1 complex, be—
cause the chemical shifts of the complex and ion—paired
complex are the same.

We have shown in Chapter III that in methylamine solu—
tions CsSCN is ion-paired. The value of KX can be approxi—
mated by considering that cesium thiocyanate is completely
ion—paired in methylamine. Then the only equilibrium which

causes changes in the chemical shift would be,

K

M+.X‘ + c 33‘ MC+.x‘
Four parameters were adjusted to analyze the data. These
are KanHE’ 6MC+.X" and bMC+.X"' The results are given
in Table 36.

The other extreme case is that cesium thiocyanate is com-
pletely dissociated in methylamine although this would be
extremely unlikely being given the low dielectric constant
Of the medium. In such case, the only equilibrium respon-

sible for the chemical shift would be,

The parameters obtained for this extreme case are the same as

the parameters of Table 36 except that KC==KX and AHg==AH;.

 

 

 

 

 

200

Table 36. Thermodynamic Parameters for the Formation of
the 1:1 Complex of 18C6 and CsSCN in Methylamine
at 25.0°C.

 

 

Assumption

 

a) CsSCN is completely ion-paired in methylamine

then the only equilibrium involved is

K
- X _
M+.X + c z MC+.X

b) CsSCN is completely dissociated in methylamine

K
C
M++C2MC+

Adjustable Parameters

 

Kx or KC = (0.87:0.53)x103 M‘l

AH; or AH% = —13.50t0.73 Kcal.mo1e‘l
— i

5MC.X or 6MC - 32.51 0.23 ppm

b or b = -0.130i0.000 ppm.cieg‘l

MC.X MC

 

 

 

 

 

 

The fact that Kg obtained by assuming complete dis—
sociation of the salt is different from the values ob—
tained from data for the other salts also confirms that
cesium thiocyanate is associated in methylamine. An at—
tempt was also made to calculate the parameters of Table.
36 by fixing KA and Kip at various values. The values for
K and AH; calculated in this way did not change appre—
ciably. Since KX for CsSCN is smaller than the correspond—
ing values for the other salts, it can be concluded that

CsSCN is more associated than either cesium tetraphenyl—

borate or cesium iodide. The ratio of the ion—pair forma—

+ _ + _
tion constants of Cs .SCN and Cs 18—crown-6.SCN can be ap—

proximated and has a value of 2.2 (Kip/KA = Kc/Kx z 1.07

U
x 10'/0.87 x 103). This ratio for cesium iodide and cesium

tetraphenylborate is 1.67 and 1.27 respectively.

(d) Summary — The thermodynamic parameters for the
formation of the 1:1 complex between 18—crown—6 and cesium

salts in methylamine at 25.0°C are summarized in Table 37.
c

AHg
It is interesting to note that

MC+) is enthalpy stabilized

747251

The complex formation (M+ + C
and entropy destabilized.
with very few exceptions, macrocyclic complexes in non—
aqueous solvents seem to be enthalpy stabilized but entropy
destabilized.

It would be very helpful to be able to describe the

solvent dependence of AHg and ASE of complexation, but the

 

202

Table 37. Thermodynamic Parameters of the Complexation of
Cesium Salts by l8—Crown—6 in Methylamine at

 

 

 

25.0°C.
. Salt (a)
Parameter CsI CsBPhu CsSCN
Kip (M'l)' 2.50 x 105 1.01xlOu >105
AH§p(Kcal.mole‘l) 3.86 0.7
ASS:p (e.u.) 37.7 30.8
KA (M‘l) 1.51 x 105 1.16x10” >105
AHZ<kca1.mo1e‘l)(b) 0.18 2.63
ASE (e.u.) 37.7 27.0
KC (M'l) 1.07 x 10” 1.07x10” 1.07x10Ll
AHg(kcal.mole_l) —16.72 -16.72 —16.72
Asg (e.u.) —37 6 ‘ -37.6 —37 6
KX (M‘l) 6.33 x 103 8.00x103 m0.87x103
AH;(kcal.mole‘l) —16.00 —18.80 ' m—13.50
-37.6 —05.1 m—28.0

O
ASX (e.u.)

 

a . . .
Assuming complete assoc1at1on.

b
A

AHO = 9
AHlp + RTRn (Kip/KA).

 

 

203

data presently available are limited. The value of AH:

for the above reaction changes from —3.97 kcal.mole_l in
water (173) to —8.09 kcal.mole_l in 70 wt % methanol-Water
mixture (170), and to —l6.7 kcal.mole—:L in methylamine (this
work). Values of ASE are —8.1 e.u., -l0.l e.u., and —37.6

e.u. in water, 70% methanol and methylamine solutions,
respectively.
The comparison of these data indicates the profound

effect of the solvent on the complexation. The stronger

solvation of the cation in aqueous solutions seems to be

responsible for the smaller negative enthalpy of formation

in aqueous solutions than in methylamine solutions. Of

course, other factors such as the Born term (arises from
changes in ion—solvent interaction beyond the first solva—
tion shell of the cation and/or the complex) and changes in
the ligand solvation enthalpy may be responsible for the
more negative AHg in methylamine solutions than in aqueous
solutions.

The origin of the large negative values of ASE is not
known. It seems reasonable to assume that the decrease. in
entropy upon complexation is related to changes in the con—
formational entropy of the ligand (176). Of course, other
factors such as translational entropy loss on formation of
a single complex from two species, the change in the solva-

tion of the free and complexed cation, as well as change in

the solvation of the free and complexed ligand are also

 

 

 

 

200

responsible for the changes in the entropy of formation of
the complex. The much larger negative value of ASS in
methylamine solutions than in aqueous solutions seems to
reflect the difference in the solvation of the cation and/
or the ligand in these two solvents.

More data in other nonaqueous solvents are needed before

the entropy of complexation is understood.

205

C. Thermodynamics of Formation of 2:1 Complexes of

l8-crown-6 With Cesium Salts in Methylamine

Cesium-133 chemical shifts caused by the complexation
of cesium salts by l8-crown-6 as a function of the mole
ratio and temperature are given in Tables 25 and 26. A
complete analysis of the data would require the solution to
the equilibria given by the equations in 0—3, which are
very complicated. By noting that the 1:1 complex is
nearly completely ion-paired at the cesium concentration at
which the mole ratio studies were carried out, the data

above mole ratio 1.0 should approximately follow the

equilibria,
+ - KX2 +
MC -x + C : M02.x‘ (0—11)
+ - KA2 + -
MC2 + x : MC2.X (0-12)

In the case of C31, for example, the 1:1 complex is almost
completely ion-paired. The concentration of the free com-
plex, (MC+), in 0.02 M solution is always less than 5% of the
total salt concentration and, therefore, can be ignored in
the initial calculations. Since KA2 and AHK2 are highly
correlated, these parameters cannot be obtained simultan-

eously and we must fix one of them. If we assume that the

difference in the ion-pair formation constants of the salt

 

and the 2:1 complex is entirely of enthalpic origin then

206

the enthalpy of ion—pair formation of the 2:1 complex can

be written as,

K.
AHO = AH? + RT2n(—lB) (0-13)
A2 1p KA2

This eliminates one of the adjustable parameters. In ad-
dition it was shown earlier that the salt and the 1:1
complex both form contact and "loose" ion-pairs in methyl-
amine. Since the cesium cation is sandwiched between the
two ligand molecules, it is reasonable to assume that the

2:1 complex only forms "loose" ion-pairs. If this is the

case, then we might expect that the chemical shifts of

MC2+ and MC +.x‘ would be the same.

2

The cesium iodide data were analyzed according to this
model and the results are given in Table 38.. The sub—
routine EQN for use with KINFIT is given in Appendix 3B.
All of the parameters in Table 38 are well—determined except
KA2' The inability to determine KA2 was expected since ion
pair formation by the 2:1 complex does not affect the chemical
shift. The standard deviation in the calculated chemical
shifts is 2.0 ppm accordingtx>this model which is more than
the experimental error. Since equilibrium (0-12) does not
contribute to the chemical shift changes, approximate
values for Kx’ AH; and 6MC X could be obtained from the

2
analysis of the data according to equilibrium (0-11) alone.

 

 

 

Table 38. Thermodynamic Parameters for the Formation of
the 2:1 Complex of CsI with 18—Crown-6 in
Methylamine at 25.0°C; Assuming Complete Ion-
Pair Formation of the MC+ Complex at (Cs+)=0.02M.

Assumptions:

1:1 complex is completely formed and completely ion—
paired at 0.02 M total cesium iodide concentration.

K.
AHO = AH° + RTtn<~lB)
A2 ip KA2

6 = 6
MC2 MC2X

Adjustable Parameters

(from Equation 0—11)

 

 

 

 

—1
KX2 = 0.52iO.20 M
AH§2 = —5.03iO.l9 kca1.mole—l
KA2 = (0.6:13) x 105 M"1
GMCZX = —06.8il.07 ppm
65 = 2.0 ppm
1__131

208

The results for CST are given in Table 39a. The average
standard deviation in the chemical shift is also 2.0 ppm
according to this analysis. In order to examine whether
this high standard deviation is due to the neglect of the MC+
concentration, we improved our model by assigning an average

weighted chemical shift, 8 to the chemical shift

MC+.x"
+ -
of MC .X at each temperature according to the equation,

' - = _. _ + -
5MC+.x XMC+.x 5Mc+.x XMc+5MC+ (0 l“)

in which X — and XMC+ sum to one and are relative mole

Mc+.x
fractions of MC+.X- and MC+ at R = l and the total cesium
concentration of 0.01793 M (the highest concentration at
which the 1:1 complexation was studied). The mole frac-
tions were computed from the 1:1 complex results (Table 33).
These average chemical shifts were then used as constants
in the calculations. The results are given in Table 39b.
The average standard deviation of the chemical shifts im-
proved slightly (66 = 2.1 ppm) upon correction for the MC+
concentration, but was still higher than the experimental
error.

In the case of cesium tetraphenylborate, we could not
. fit the data to Equations 0-11 and 0-12 simultaneously.
Apparently this is because the dissociation of the 2:1

ion-paired complex is large enough to result in very small

activity coefficients which invalidates the use of the

 

 

 

209

Debye-Hfickel equation. In addition we expect both MCE
+ _
and MC .X to have the same chemical shifts. Therefore,

2
we only fit the data with Equation 0-11. Two procedures

were used,similar to the cesium iodide case. First, com-
plete association of the 1:1 complex with tetraphenylborate
at R=l and (Cs+)t = 0.01 M was assumed. The results are
given in Table 00a. Second, an approximate correction for

the presence of (MC+) was made in 6 _ according to

Mc+.X
Equation 0-10. The results are given in Table 00b. In
the case of cesium tetraphenylborate a large improvement in
55 occurs when this correction is made. This is a result
of weaker association of the cesium tetraphenylborate 1:1
complex compared to the cesium iodide 1:1 complex.

The cesium iodide and cesium tetraphenylborate results
(Tables 39a and 00a) show that the chemical shift of

MC +.X- is essentially the same for both salts. This value

2
also agrees well with the chemical shift of the 2:1 complex
in other nonaqueous solvents (201). The value of KX2 for
CsBPhu is larger than that for CsI which reflects the dif-
ference in ion-association of their corresponding 1:1 and
2:1 complexes. Finally, all of the thermodynamic parameters
for the formation of the ion-paired 2:1 complexes are very
well determined. Therefore this simple model (Equilibrium
0-12) describes the main features of these systems very
well. The only problem is that the average standard devia-

tionscfi‘the chemical shifts are higher than the estimated

experimental error. However, these high values for 65

 

 

209

u +
Debye-Huckel equation. In addition we expect both M02
+ _
and MC2.X to have the same chemical shifts. Therefore,

we only fit the data with Equation 0-11. Two procedures
were used,similar to the cesium iodide case. First, com—
plete association of the 1:1 complex with tetraphenylborate
at R=l and (05+)t = 0.01 M was assumed. The results are
given in Table 00a. Second, an approximate correction for

the presence of (MC+) was made in 6 _ according to

Mc+.x
Equation 0—10. The results are given in Table 00b. In
the case of cesium tetraphenylborate a large improvement in
66 occurs when this correction is made. This is a result
of weaker association of the cesium tetraphenylborate 1:1
complex compared to the cesium iodide 1:1 complex.

The cesium iodide and cesium tetraphenylborate results
(Tables 39a and 00a) show that the chemical shift of

+ _
MC .X is essentially the same for both salts. This value

2
also agrees well with the chemical shift of the 2:1 complex
in other nonaqueous solvents (201). The value of KX2 for
CsBPhu is larger than that for CsI which reflects the dif—
ference in ion-association of their corresponding 1:1 and
2:1 complexes. Finally, all of the thermodynamic parameters
for the formation of the ion-paired 2:1 complexes are very
well determined. Therefore this simple model (Equilibrium
0—12) describes the main features of these systems very
well. The only problem is that the average standard devia—

tionscfi‘the chemical shifts are higher than the estimated

experimental error. However, these high values for 56

 

210

Table 39. Thermodynamic Parameters for the Formation of
the 2:1 Complex of CsI with l8-crown-6 in Methyl-
amine at 25.0°C; Assuming Complete Ion-Pair For-
mation of Both the MC+ and MC2+ Complexes at (Cs+)
= 0.02 M.

Assumptions

 

Only the equilibrium MC+.x' + C : MC:.x‘ was considered._

Adjustable Parameters

 

 

 

a) Complete Formation b) 5MC+ X‘ Corrected According to
+ _ .
of MC .X at R=l and the Equation (0-10)
+
(Cs )t = 0.02 M

 

KX2 = 0.66:0.11 0.29:0.09 M‘l
AH§2 = -5.09:0.09 -5.00:0.08 kca1.mo1e‘l
6MC2X = -06.02:l.35 -08.6tl.22 ppm
6% = 2.05 2.1 3 ppm
1

(AG298.15)x2=-O'86i0'01 kcal.mole

AS;2 = -15.22:0.27 e.u.

 

 

 

 

211

Table 00. Thermodynamic Parameters for the Formation of the
2:1 Complex of CsBPhu with 18-Crown-6 in Methyl-
amine at 25.0°C; Assuming Complete Ion-Pair
formation of both the MC+ and MC2+ Complexes
at (Cs+) = 0.01 M.

Assumptions

 

Only the equilibrium MC+.X‘ + c 2

Adjustable Parameters

 

MC+.X- was considered.

 

 

a) Complete Formation of
MC+.x' at R=1 and
(Cs+)t = 0.01 M

b) 6MC+ X‘ Corrected According
tx>theEquation (0-10)

 

KX2 = 18.3:0.95 27.00i0.5l M“l

AH§2 = -7.12i0.27 -6.99iO.ll Kcal.mo1e"l

6MC2X = -5l.2il.07 -09.07:0.00- ppm

55 = 2.7 1.1 ppm
(A0398.15)X2=-1.95:0.01 xcal.mole'l
A80 = -16.90:0.37 e.u.

x2

 

 

212

are not surprising since the complete scheme (Equilibria
0—3) was not used but rather only the major equilibrium (0—12)
was used to describe both the mole ratio and the tempera-
ture dependence of the chemical shifts. In addition to the
inexactness of the model, experimental errors can also pro-
duce high standard deviation in the calculated chemical
shifts. Although the calculations based on this simple
model are sufficient for the determination of the thermo-
dynamic parameters, attempts were made to refine the cal-
culations and to assess the factors which might cause the
high average standard deviations in the chemical shifts.

These factors are:

1, The neglect of the concentration of (MC+) at the
total concentration of the cesium cation is one of these
factors as described earlier. An approximate correction

to 6 due to the presence of MC+ was made according

MC+.X-
to Equation (0-10). The results were given in Tables 39b

and 00b. The value of 55 decreased substantially in the

case of cesium tetraphenylborate but only slightly in the
case of cesium iodide. It was mentioned that since the
cesium iodide 1:1 complex is more strongly associated than
the cesium tetraphenylborate 1:1 complex, the contribution

of MC+ in 5 - is less important for the former. In

Mc+.x
addition, it should be noted that the calculated values

for 3 _ are merely approximations. These values were

MC+.x
not calculated exactly at the total cesium concentrations

213

where the mole ratio studies were carried out, but at the
highest concentrations where 1:1 complex formation was

studied. Also, plots of 6 - versus temperature were

MC+.x
curved. Since the 1:1 complex formation and the mole ratio
studies were not carried out at the same temperatures, the

values of SMC+ - were evaluated approximately from these

X
curves. However, even with such approximations the de-
crease in 56 for cesium tetraphenylborate indicates the

importance of the contribution of MC+ to 6MC+.X';

.2. The formation of MC+.X_ from M+.X' and C is not
complete nor of the same extent at various temperatures.
Therefore the presence of M+.X- would contribute to the
average chemical shift of the 1:1 complex. The concentra-

tion of M+.X- depends on the concentration of the ligand

through,

(MC+.x‘)
KX(C)

 

(M+.X‘) (0_15)

and can be obtained at each concentration and tempera-
ture. Then an average chemical shift for MC+.X- can be

calculated according to,

1 _.
6 = X 6

MC+.x' MC+.x ' (“‘16)

+X

MC+.x’ M+.X’6M+.X

in which X's are the relative mole fractions of the species

 

 

210
_+ _: -+_' - .
(XMC+.X XM+.X l), and 6MC .X is defined by Equation
(0-10). Equation (0—16) approximately corrects for the
contributions of both MC+ and M+.x‘ to 6MC+ x“ The addi—

tiOnal correction for (M+.X_) did not change the values of

56 even though the errors in the chemical shifts of some
of the points at high temperatures became more random upon
this correction.

It should be noted that in the calculations of these
corrections, the thermodynamic parameters obtained by
fitting the concentration dependence of the chemical shift
of the 1:1 complexes were used. These parameters, in turn,
were obtained from ion association parameters of the salts.
Therefore, the accumulation of errors increases the un—
certainty of these corrections.

3. The preparation of samples for the mole ratio
studies was described in Chapter II. Since we did not use
stock solutions of the salts, the total salt concentrations
were not exactly the same at various mole ratios, and in the
treatment of the data, average values were assigned for the
total salt concentrations. To examine whether this ap—
proximation affects 56’ the total concentration of the salt
at each mole ratio was used as an additional variable to—
gether with its proper standard deviation in the treatment
of the data. This correction caused noticeable improvement
in 66 for both salts. The values obtained for 56 after

all corrections mentioned so far were 1.55 and 0.82 ppm for

cesium iodide and cesium tetraphenylborate respectively.

215

The thermodynamic parameters for complexation,after all
corrections were made,are given in Table 01.

The above mentioned factors which affect 56 could be
handled quantitatively. There might be other factors which
cause high values in 66 but we would not be able to account
for them quantitatively. These are:

0. It was mentioned previously that the ion-pair forma-
tion constants of the 2:1 complexes could not be obtained

from the NMR data since the chemical shifts of MC+ and

2
MC5.X- are expected to be the same. We expect 6MC+ to

2
be independent of temperature, but the chemical shift of
MC2.X- might be temperature dependent as is the case for

the chemical shifts of M+.X_ and MC+.x‘. If this were the
case, the neglect of the temperature dependence of

MC:.X- might affect 66' However, an independent measure-
ment of KA2 is required to account for this effect.

5. The mole ratio study of the complexation of CsBPhu
by 18-crown-6 in liquid ammonia indicates that the solvent
molecules and/or the anions interact with the cesium cations
in the 2:1 complexes (Section 3). Even though methylamine
molecules are larger than ammonia molecules, we cannot
reject the possibility of similar interactions in this
solvent. If such interaction occurs, then at least two

kinds of ion-pairs (ligand separated and solvent separated)

may be present in the solution according to the equilibrium

216

Table 01. Thermodynamic Parameters for the Formation of
the 2:1 Complexes of Cesium Salts with l8-crown-6
in Methylamine at 25.0°C.

Kx2
+

+

Only the equilibrium MC+.x’ + C MG;.X- was considered.

6MC+ X' was corrected approximately for MC+ and M+.X’

concentrations.

Total concentrations of the salts were used as variables
at each mole ratio.

 

 

 

CsI CsBPhu

KX2 0.03:0.05 22.82t0.35 M'1
AH§2 -6.05:0.08 -7.35:0.12 Kca1.mo1e'l
GMC; X‘ -06.1710.56 -09.0010.19 ppm
85 1.55 0.82 ppm deg”l

_ -l
(AG398.15)X2--0.83:0.01 - 1.85:0.01 kcal.mole
AS° = —l7.52:0.27 -l8.00i0.00 ’ e.u.

x2

 

 

217

"K"
MC x I [MC2X1' (0-17)

2

in which MCZX and [MCZXJ' are ligand.separated and solvent
separated ion—pairs. Although this equilibrium is not con-
centration dependent, it might be temperature dependent.
Since the degree of association of the 2:1 complexes
with iodide and tetraphenylborate anions are different,
the equilibrium is also expected to be anion dependent. The
neglect of the above equilibrium (if it exists at all) would
affect the average standard deviation in the chemical shifts.

6. E. Mei gt gt. (201) studied the complexation of the
cesium cation by dicyclohexano-l8-crown-6 in nonaqueous
solvents. The variations of the chemical shifts as a func-
tion of the mole ratio were indicative of the formation of
both 1:1 and 2:1 complexes in pyridine, propylene carbonate,
dimethylformamide, and acetonitrile solutions. However,
they were not able to obtain the formation constant of the
2:1 complex in these solvents. The reason for such failure
appears to be the unusual linear variation of the chemical
shift above R = 2. For example, in acetone, at R < l a

linear downfield shift occurs as a function of the mole

 

ratio (Kl > 10“). In the range of l < R < 2 a nonlinear

downfield shift occurs with increasing mole ratio. Above

 

R = 2 an upfield shift results when the mole ratio increases.

This unusual upfield shift seems to be linearly dependent

218

on the mole ratio. The unusual variation of the chemical
shift above R = 2 might be due to the dependence of the
chemical shift on the concentration of the complexant.
This would interfere with the ability of a simple equilib-
rium scheme to describe the system. In the case of the
complexation of cesium salts by 18-crown-6 in methylamine
this effect (if it exists at all) cannot be seen from the
mole ratio plots, since the variation of the chemical
shift with mole ratio is large and masks minor effects.

The discussion about the possible contributions to the
average standard deviation of the chemical shifts clearly
shows the high sensitivity of the model to minor approxi-
mations. However, in spite of these problems, the simple
model with appropriate corrections defines the system very
well and the calculated thermodynamic parameters of Table
01 can be trusted with a high level of confidence.

In addition to the mole ratio studies, the concentra-
tion dependence of the 133Cs chemical shift for CST in the
presence of a 6.0-fold excess of l8-crown-6 was studied in
methylamine at various temperatures. The results are
given in Table 02 and shown in Figure 37. The expected
chemical shifts at each concentration and temperature were
calculated from the parameters in Table 01 and the solid
curves shown represent the calculated values. Although
the calculated and experimental chemical shifts follow the

same trend, they are not identical, probably as a result

219

Table 02. Concentration Dependence of the 133Cs Chemical
Shift of CsI in the Presence of a 6.0-Fold Excess
of l8-Crown-6 in Methylamine at Various Tempera-

 

 

 

 

tures.
_Eobs (ppm)

Conc. Temperature, 0C

(M) 25.0 -2.5 -10.2 -l6.2 -32.0
0.00511 66.89 06.26 38.70 32.80 9.5
0.01001 59.13 32.92 23.90 16.09 -3.37
0.01302 50.02 25.90 15.78 7.35 —11.75
0.01768 ————— 17.26 9.05 0.70 _;—__
0.01932 ”7:58 15.86 5.93 -3.95 -19.89

 

 

 

 

'32.4° C

' l6.2°C
‘l0.2°C
“25°C

‘V CI
/I 25.0°C
I I I__
8C’00 0.8 LB 24
[CS’] x IO2 (M)

806s (ppm)
0

40-

 

 

 

Figure 37. Concentration dependence of the 133Cs chemical
shift of 031 in the presence of a 6.0-fold

excess of l8-crown-6 in methylamine at various
temperatures.

 

221

of the problems discussed earlier.

In summary, the ion-association equilibria of the 2:1
complexes could not be fully understood. However, even
with the average error in the calculated chemical shifts of
1.55 ppm for cesium iodide complexes and 0.82 ppm for cesium
tetraphenylborate complexes, the fit is sufficient to de-
and AH° Attempts to improve

X2 X2°
the model did not give more information about the system be-

termine the values of K

cause of the incapability of the NMR technique to separate
different kinds of ion—association. The best values for

K AH° and the limiting chemical shift of the 2:1 com-

X2’ X2
plexes on the basis of the model used are those listed in

Table 01.

 

3. Complexation of Cesium Tetrgphenylborate by l8-Crown-6

in Liquid Ammonia

 

A. Results

Cesium—133 chemical shifts of cesium tetraphenylborate
in the presence of 18-crown-6 were measured as a function
of (l8-crown-6)/(Cs+) mole ratio (R) at fixed Cs+ concentra—
tions. The results for (CS+) = 0.001 M are given in Table
03 and illustrated in Figure 38. Another set of experi-
ments was carried out with (Cs+) = 0.0075 M. Measurements
at R > 1 were not possible below 10°C due to the insolu-
bility of the ligand. The data are given in Table 00

and shown in Figure 39. To examine ion-association of

222

Table 03. Mole Ratio Study of 18C6.CsBPhu Complexes in
Liquid Ammonia at Various Temperatures; (Cs+)
= 0.001 M.

 

 

 

 

6obs (ppm)
Mole Ratio Temperature, °C
(1806)/(Cs+) 10.5 0.5 -0.0 —20.9 -33.0
0.000 118.05 120.70 122.09 125.03 127.68
0.25 106.90 108.10 110.00 111.09 ------
0.095 98.05 98.21 98.52 100.28 101.07
0.60 90.88 90.18 90.18 90.57 95.26
0.70 91.86 90.62 90.15 90.77 —————
0.90 86.12 80.09 83.08 82.55 83.71
1.00 81.50 79.99 78.36 77.98 77.90
1.20 77.07 75.88 70.09 73.32 73.01
1.39 73.90 71.77 70.30 69.21 69.76
1.59 70.61 68.90 67.66 66.27 67.00
1.80 68.00 66.11 60.72 60.60 65.57
1.99 66.50 60.78 63.07 63.32 63.90
2.22 65.26 63.01 62.08 62.50 63.07
2.38 63.86 62.08 60.76 61.85 62.62
2.575 63.01 61.06 60.80 61.69 62.85
3.00 60.30 58.36 58.05 59.75 60.99
3.32 58.82 57.81 57.58 58.70 60.80
3.97 56.30 55.72 55.60 57.35 60.06
0.97 53.63 50.01 50.01 56.26 58.98

 

 

223

 

 

 

 

 

 

 

 

 

~40
‘50
~€K>
Swjppm) ‘70
T - 80
40- +90
50' 500
601- 4110
1
‘ I I
70.. ,l ‘ / l '240 0.4 08 12 -I20
. // | [Cs'] x IO‘ (M)
. _ - 1. ________________ _
so / /\© :30
. . // /
sot . ’23,
. / //
(- y
IOO ///b \/
no / / to
- /
' ’03" $0
// // «of
- v
1!, 1
30 1 l 1 I
' I 2 3 4 5
Mole RafioflB-crown-GMCsBpm )
- —->

Figure 38. Cesium-133 chemical shift versus (18-crown—6)/
(CsBPhu) mole ratio and temperature in liquid
ammonia; (05*) = 0.001 M.

220

Table 00. Mole Ratio Study of 18C6.CsBPhu Complexes in
quuid Ammonia, at Various Temperatures; (Cs+)

 

 

 

 

= 0.0075M.
Sobs (ppm)

M016 Ratio Temperature, °C

(l8C6)/(Cs+) ‘ 10.5 6.0 —25.5
0.00 112.60 110.96 120.08
0.12 105.89 107.99 113.10
0.395 90.38 91.70 96.70
0.55 83.17 80.01 89.22
0.63 79.29 80 77 ' 85.02
0.725 73.71 70.09 78.98
0.83 68.13 68.67 72.62
0.895 66.02 66.81 ‘ 70.61
0.985 62 50 63.16 65.65
1.09 59.13 ————— 62.07*
1.02 53.01 ————— 57.12*
2.19 06.57 06.80* _____
2.30 05.95 06.26* -----
2.69 00.17 00.62* _____

 

 

 

 

 

 

* u .
Some precipitate in solution.

 

 

225

 

SODS ( ppm )

 

 

 

. A l 4__.
0 LC 20 3.0

Mole Ratio
[l8C6 ]/ [CsBph4]

Figure 39. Cesium-133 chemical shift versus (18C6)/(CsBPhu)
mole ratio in liquid ammonia at various tem-
peratures; o l0.5°C, A6.0°C, o -25.5°C; (Cs+)=
0.0075 M.

226
the salt, the chemical shift of cesium tetraphenylborate
was measured as a function of concentration at 6.0°C. The

results are given in Table 05 and shown in Figure 00.

B. Discussion

 

Figure 00 shows that a downfield shift results as the
cesium tetraphenylborate concentration decreases. This
indicates that the cesium cation interacts more strongly
with ammonia molecules than with the tetraphenylborate anion.
The degree of interaction of the cesium cation with ammonia
is much greater than that with methylamine, since in ammonia
the chemical shifts are much more downfield (compare Figures
00 and 15). The concentration dependence of the chemical
shift also shows that cesium tetraphenylborate is associated
in ammonia. The determination of the association parameters
in ammOnia would require an extensive study similar to that
in methylamine which was not possible due to time constraints.
However it is expected that ion-association in liquid am-
monia would be considerably less important than in methyl—
amine solutions due to the higher dielectric constant of the
former (D = 23 at -33°C). The mole ratio plots show the for-
mation of a relatively strong 1:1 complex followed by the
formation of a weaker 2:1 complex. The data above R = l
were analyzed according to the equilibrium,

II II
+ K

MC + C MC+

2

assuming that the 1:1 complex is completely formed at

227

Table 05. Concentration Dependence of the 133Cs Chemical
Shift of CsBPhu in Liquid Ammonia at 6.0°C.

 

 

 

Conc.
(M) GODS (ppm)
121.00
0.00000 121.56
0.00079 120.32
0.00363 117.05
0.00755 110.96

0.00899 113.96

 

 

228

 

 

 

 

((2-
% ”6-
3 _
“‘33 l20r
l l '
'240 0.4 0.8 - (.2
[05*] x (0° (M)

Cesium-133 chemical shift versus concentra—
tion of CsBPhu in liquid ammonia at 6.0°C.

 

 

229

R = l. The chemical shift of the 1:1 complex was fixed at
each temperature as the observed chemical shift at R = 1.
" and 6

Two parameters, "K C+ were adjusted for each data

2 M

set. The results are given In Table 06a. The enthalpy and
entropy of formation of the 2:1 complex were obtained from
the Van't Hoff equation with the aid of the KINFIT program.
In addition,data at various temperatures were analyzed
simultaneously, with a linear temperature dependence for

6 The results are given in Table 05b. Even. though

MC‘E'
separate fits at various temperatures are good, AH° and AS°
obtained in this way have high standard deviations. The
simultaneous fit has an average standard deviation of the
chemical shift of 0.02 ppm which is about two times the
experimental error.

A comparison of Tables 01 and 06b indicates that the
formation constant of the 2:1 complex in liquid ammonia is
much larger than in methylamine. If ion association of the
1:1 and 2:1 complexes could be ignored then one would
expect the reverse order, because ammonia is a better
electron-donating solvent than methylamine and consequently
can compete better with complex formation. The limit-
ing chemical shift at high values of R in methylamine is
almost temperature independent and practically equal to the
values in other nonaqueous solvents (201). Surprisingly,

the limiting chemical shift in ammonia is about 90 ppm

downfield compared to other solvents. This huge downfield

230

Table 06. Complexation Formation Constant, Limiting Chemi-
cal Shifts,and Thermodynamic Parameters for the
2:1 Complex of 18C6, CsBPhu in Liquid Ammonia at

 

 

 

 

Various Temperatures, assuming K1 3 104.

a. Separate Fit at Each Temperature
[Cs+] _

(M) t C:0.5 K2 (611m)2 1 06
0.0075 10.5 395:252 38.0 13.3 0.39
0.001 10.5 1025180 05.08:0.80 0.01
0.001 0.5 17001125 09.17:0.01 0.28
0.001 -0.0 19021182 09.89:0.08 0.35
0.001 -20.9 25661301 53.50:0.06 0.39
0.001 -33.0 3937i669 57.52:0.36 0.37
("K59298 = 85611000 M“l
(99298)2 1 =_0.0:0.7 xcal.mole'l
(AH°)2:l = -3.6:0.67 xcal.mole'l
(AS°)2:1 = 1.3:3.3 e.u.

 

b.~ Simultaneous Fit at All Temperatures. Reference Tempera-
ture = 25.0°C.

 

"K2" = 609200 M-l
0H°)2:l = -0.91:0.28 xca1.mo1e"l
GMC; = 00.07:0.65 ppm

bMCE = -0.3:0.l ppm.deg_l
E6 = 0.02 ppm
(AG298)2:1 =-3.88:0.00 kca1.mole

(AS°)2:1 =‘3-u5i0095 e.u.

 

 

 

 

shift could be due to the interaction of the cesium cation
with both the anion and the solvent, since the chemical
shift of the free cation in liquid ammonia is larger than
122 ppm and the chemical shift of the ion—pair with tetra-
phenylborate seems to be larger than 100 ppm (Figure 39).
The large temperature coefficient of GMCE might also arise
from the interaction of the solvent and/or anion with the
cesium cation in the 2:1 complex.

In any event, a more quantitative description of the
formation of the 2:1 complex is not possible since the ion-
association parameters of the salt and the 1:1 complex are
not known and also the 2:1 complex may form various kinds

of ion—pairs which cannot be distinguished from each other

by the NMR technique.

0. Summary

The thermodynamic parameters for the formation of the
2:1 complex between l8-crown—6 and cesium salts in methyl—

amine and ammonia solutions are summarized in Table 07.
+ _ KX2 +
The 2:1 complex formation (MC .X + C 3 MC2
O
AHX2
thalpy stabilized but entropy destabilized in both solvents.

.X-) is en—

The entropy of formation of the 2:1 complex seems to be
almost anion independent, but strongly solvent dependent.
However, the enthalpy of formation of the 2:1 complex is
both anion and solvent dependent.

In methylamine solutions, differences in the stability

 

232

Icoo Houop pew

.Uopoospoo no: mm: Ix.+oz

a
. m mmme

Ix +02 mxx o + 1x +02

.Esfipofiafisqo ocu op mcflppooow powmamcm opoz sumo oseo

.oapmh oHoE comm pm moanwfihm> mm pom: who; mpamm one no mQOHpmspcoo

.mcoHpMLucoocoo Ix.+z paw +0: pom zaopmefixopddm popooppoo mm: Ix.+ozw
m mmma

. x. o: N o + x. o:

I + mxx I +

Esfippflfifisvo ocp op wcflppooom commamcm opoz wasp ones

 

 

 

 

 

.s.o ms.osms.m- os.esss.ma- sm.esmm.sa- mmma
HIoaoe.Hsos mm.esad.s- ma.ewmm.s- mo.e.me.o- mmma
Huoaos.asos so.owmm.mu Ho.owmm.en Ho.ohmm.ou mxflma.mmmosv

mficofie< oceemwmnuoz mafiEmamnpoz Lopoempmm
c m c m C no
.mcofipzaom aficoEE< paw oCHEmahnpoz :fi muamm Edfimoo
pew woma mo ondEoo Hum on» no soapmegom can now mpouoEMme oHEmcmpoELoze .w: magma

233

of the 2:1 complexes of cesium iodide and cesium tetra-
phenylborate with 18C6 are mainly determined by the en-
thalpy contribution to the free energy of formation. The
larger complexation constant for cesium tetraphenylborate
compared to that for cesium iodide reflects the difference
in the degree of ion—association of their corresponding
salts and complexes in methylamine solutions. The much
more positive entrOpy of formation in liquid ammonia might
be due to the stronger solvation of the cesium cations by
small ammonia molecules than by methylamine molecules.
However, more data in other nonaqueous solvents are needed
to rationalize the thermodynamic parameters of the complexa-

tion.

0. Conclusion

 

The mole ratio (R = (l8-Crown-6)/(Cs+)) and tempera-
133

ture dependence of Cs chemical shifts in methylamine
and in liquid ammonia show the formation of a relatively
strong (K1 3 10”) 1:1 complex followed by formation of a
weaker 2:1 complex. If we could neglect ion-association

of the salts and the complexes, the data could be analyzed

according to the simple equilibria,

230

However, the results obtained from these equilibria were
unsatisfactory since the formation constantsand the limiting
chemical shifts of the 2:1 complexes were anion and solvent
dependent. In addition, the chemical shifts of the 2:1 com—
plexes,especially for Csl, were strongly temperature dependent.
The chemical shifts at R = 1 were also very different for
different anions and solvents. Therefore it is clear that
both the 1:1 and the 2:1 complexes are associated in methyl—
amine and presumably in liquid ammonia as well.

The concentration and temperature dependence of the 1:1
complexes in methylamine showed that three processes are
involved in complex formation. These are ion—associa—
tion of the salt, ion—association of the 1:1 complex and
simple complex formation. A complete analysis of the CsI
data (with reasonable assumptions) was carried out and the
thermodynamic parameters of the complexation processes were
determined by using the ion—association parameters of CsI
from Chapter III. The complexation formation constant
(M+ + C is MC+) should be independent of the anion. There—
Vfore KC and AHg obtained from the Csl data were used in the
treatment of the CSBPh0 data and the thermodynamic parameters
for the complexation were obtained. The ion-pair formation
constants of the 1:1 complexes are of similar magnitude to
the ion—pair formation constants of the salts. This could
indicate that both the salts and the 1:1 complexes form

mainly "loose" ion—pairs and only small relative concentrations

 

235

of contact ion—pairs are present in methylamine. However,

the separation of the effects of these two types of ion—pairs

 

was not possible by NMR techniques. The equilibrium con—
stant for the reaction M+.X- + C 58 MC+.X_ shows a trend
with, SCN- < l' < BPhu— which indicates a competition be-
tween ion—pair formation of the salt and complex forma—

K
tion. The formation of the 1:1 complex (M+ + C E:

MC+) is
enthalpy stabilized and entropy destabilized.

The thermodynamic parameters for the formation of the
2:1 complex of CsI with l8—crown—6 were obtained from
the equilibria,

K
X2
MCX + C 2 MC X

2

M0: + x‘ K22 MC2X

However, since the complex and the ion-paired complex have
the same chemical shifts, KA2 is only "determined” from
changes in the activity coefficient, which results in a
high standard deviation for this parameter. The situa-
tion for CsBPhu is even worse since the degree of dis-
sociation of the 2:1 complex of this salt is expected to
be large and therefore activity coefficients become too
small to be estimated by the Debye-Huckel equation. Be—
cause of these complications we treated our data according

KX2
to the simple equilibrium MCX + C 2 MC2X. In this treatment,

236

weighted average chemical shifts were assigned to MC+.X- in
order to correct for the presence of MC+ and M+.X- species.
In addition the total concentration of the salt was used as
a variable at each mole ratio. The thermodynamic param7_
eters obtained in this way were well—determined. The only
deficiency was that the average standard deviation in the

calculated chemical shifts, E , was larger than the ex-

6
pected experimental error. Various effects might cause
this deficiency such as the interaction of the solvent
molecule with the cesium cation in the 2:1 complex, the
neglect of dissociation of the ion-paired 2:1 complex, and
the neglect of the concentration dependence of the chemical
shift. However, even with 36 m 0.8 to 1.5 ppm the system
is well defined, and improvement of the model in order to
decrease 36 would probably not have an appreciable effect
on the calculated thermodynamic parameters.

The mole ratio (18-Crown-6)/(CsBPhu) data in liquid
ammonia were analyzed according to the equilibrium MCX +
C K82 MC2X or MC+ + C K32 M02. The formation constant
of the 2:1 complex of CsBPhu with 18—Crown-6 was much larger
in liquid ammonia than in methylamine which reflects the
difference in the degree of association of the complexes
in these two solvents. However, since the formation
constant of the 2:1 complex in ammonia is both temperature

and concentration dependent, it is clear that the 1:1 and

the 2:1 complexes are also associated in this solvent.

CHAPTER V

1. RUBIDIUM-87 NMR INVESTIGATION OF RUBIDIUM SALTS
AND THEIR COMPLEXES IN AQUEOUS AND

NONAQUEOUS SOLVENTS
2. LITHIUM-7 NMR STUDY OF COMPLEXATION OF LITHIUM

SALTS BY C211 IN METHYLAMINE AND

LIQUID AMMONIA

237

 

1. Introduction

The concentration and counter—ion dependence of the
chemical shift of all alkali cations, except the rubidium
cation, have been studied extensively in our laboratories
(125,126,129—135) and elsewhere (120—122,120) by the alkali
metal NMR technique. Similarly, the thermodynamics of com-
plexation of all alkali cations but the rubidium cation,
has been investigated by this method (152,170,175,176,
200—209). The reason that 87Rb chemical shift studies are
sparse is that 87Rb NMR lines are very broad due to the
large quadrupole moment and large Sternheimer antishielding
factor (210) of this nucleus. For the sake of completeness,
we have used 87Rb NMR in an attempt to investigate ion—
association and complexation of rubidium salts with 18—
crown—6 and C222 in solution. Three solvents were used
in this study: water, methanol (protic) and propylene car—
bonate (aprotic).

Landers' (8) suggestion that the exchange rate of the
lithium cation between the solvated and C211—cryptated
species in methylamine is extremely slow, motivated us
to study this system by 7Li NMR technique. In addition
a mole ratio study of the complexation of the lithium
cation by C211 in liquid ammonia was carried out. The

results of these experiments are described in this chapter.

238

 

 

 

 

 

2. Investigation of Rubidium Salts and Their Complexes

in Aqueous and Nonaqueous Solvents
A. Salt Solutions

The concentration dependence of the 87Rb chemical
shifts and linewidth of rubidium salts in water, methanol,
and propylene carbonate (PC) was studied. The results are
given in Table 08 and Figures 01 and 02. Our results for
aqueous rubidium bromide solutions in the range of 0.2
to 1.0 molar agree well with those of Deverell and Rich-
ards (121). In addition, pulsed Fourier Transform tech—
nique allowed us to study solutions as dilute as 0.02 M.
Over the complete concentration range, the variation of the
chemical shift with concentration is nonlinear. However,

a plot of chemical shift versus the mean molar activity

of the solution is linear and in agreement with the results
obtained by Deverell and Richards. The same behavior has
been observed for aqueous cesium bromide and iodide solu—
tions in our laboratories (211). As has been pointed

out in Chapter III, the origin of this behavior is not
known quantitatively. In methanol (D = 32.7) and propylene
carbonate (D = 69.0) solutions, the curvature in the plot
of chemical shift versus concentration is more pronounced
at lower concentrations. The mean activity curves show
linearity at high concentrations, but become nonlinear as

the concentration decreases. In these two solvents,

 

200

00 000000 sec 00.0

c .pco>aom 65p mo zpflafioflpdoomzm 00062005006 6:0 mm 0062

000006 onoaomH 050 00% 660060000 600 mpmficm 0000Eosom

 

 

 

 

 

 

 

000 00.0 000.0
000 00.0 000.0
000 00.0 000.0
000 00.0 000.0
000 00.0 000.0
000 0.00- 000.0 000 0.001 000.0 000 00.0 000.0
000 0.00- 000.0 000 0.00. 000.0 000 00.0 000.0
000 0.00- 00.0 000 0.00. 000 0 000 00.0 000.0
000 0.00- 00.0 000 0.00- 000 0 000 00.0 000.0
000 0.001 00.0 000 0.001 000.0 000 00.0 AS000.0
000 0.001 00.0 000 0.00. 000000.0 000 00.0 :00000.0
000 0.00- 0000.0 000 0.00- 000.0 I--- 0.0 0.0
0000 Asddv 020 0000 05000 00: 0000 02000 020
m\0>< 0900 .0200 m\0>< mno .ocoo m\0>< .mnomV .ocoo
000 000 000 000
opmcooLMo 0c00>dopd Hocmnpoe 0mm
:0 000 :0 0000 :0 0000
.moLSmedeoB pcofinE< pm muco>aom
moses c0 h0000 20000000 0o hsse0sos00 0:0 000000000 00002000 00120000030 .00 o0ome

 

201

.pqm>Hom oEmm ogp CH mpCHOQ hogpo mo page mo moEHp 03p pmmoa pm 606

m
AppflonHH can mpgflgw 00005050 CH mcoflpmfl>mp pmeCMpm .mamcwflm 0m00: ogp 0o omzmoom

p
.00 Q0 mm 000 pew .HOQNonE
20 N: omfl .00p63 Q0 mm 000 CHQpfls ow ©006> osw Am\0><0 pgmflocImHQQ pm msppflsocfiqo

0cm . .00 Q0 sad 00.00
0ocw£poe Q0 Egg m.00 .ONE :0 Egg 00.00 :0g003 op 00605006 006 mpwflnn HMOHECQQQ

.poszflpcoo I monoCQoom

.0oss0eso0 .00 00000

 

 

242

 

    

 

 

   

 

 

 

E 2 052 0.64 O.L06 '
0:
3% 3L d
'8

6CD ‘1' .

\ \
55- \\ ‘

\
£5 _L. J_ 41, L \’
O 0.2 0.4 0.6 0.8 LO
‘ Conc. (M)

Figure “1. Rubidium-87 chemical shifts of rubidium bromide

versus concentration (-) or mean molar activity
(---) in aqueous solutions.

2M3

0.02 ' 0.04 0.06

 

-28- -
’g -26 -
CL
.9
g -24
060
-22 .-
-20 _

 

 

 

 

l l I l L
0.02 0.04 0.06 0.08 DJ 0
Conc.(M)

Figure 42. Rubidium—87 chemical shifts of rubidium bromide
in methanol_(—) or rubidium iodide in propylene—

carbonate (-——) versus concentration (0) or mean
molar activity (A ) of the solution.

 

244

especially in methanol, ion—pair formation is also res-
ponsible for chemical shift variations. Attempts were
made to fit the data to a simple ion—pair equilibrium in
these two solvents. The variation of chemical shift with
concentration does not follow the simple ion—pair model,
presumably because other interactions in solution are also

responsible for chemical shift variations.

B. Complexation

Attempts were made to study the complexation of the
rubidium cation by lB—crown—6 and cryptand—222 by using
87Rb NMR techniques. The results in H20, methanol, and
PC are given in Table A9.

The exchange rate of the rubidium cation between the
solvated and Rb+-18—crown—6 complexed species in aqueous
solution is fast on the NMR time scale (213). Therefore,

a single population averaged signal is expected for this
system at all mole ratios. At mole ratio (lB—crown-6)/
(Rb+) = 0.A7, where the concentration of RbI is 0.1A m,

the linewidth of the signal is about 1100 Hz; therefore

the chemical shift determination is not precise. If there
is any variation in the chemical shift as a function of the
mole ratio, this change is not detectable because of line
broadening, and a mole ratio study of this system is not
possible. Above mole ratio 1, the signal is undetectable

at this concentration. The complexation constant of

 

245

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0 00.0 00 00.0
0000 0 000.00- 00.0
000 0.000.00- 00 00.0 00 0000 00.0 000
0 00.0
000 0.000.00I 00000.0
000 0.000.00I 00.0 0
0mm 0.000.00I 00 00.0 00 00 0000 00.0 0000
0 m0.0 0
000 0.00m.m 00 000.0 0 0 0000 000.0 000
0. 00.0
000 0.00 0.0 00.0 0
000 00.0000.0 00 00.0 0 0 0000 00.0 000
0000 00 0 00.0
0000 00 m- 00.0
0000 00 0- 00.0
0000 00 0 00.0 0
000 0.000.: 00 00.0 0 0 0lczopel00 00.0 000
0 0.0 00 0.0
0000 0.00 0.0 00.0 0
000 00.0000.0 00 00.0 0 0 0103000100 00.0 000
IiIrIIIIrIrIrIIIIIII1IIIIIIaI1IlIItIIIIIIIltlrlltltrlllltllrlllllII
0000 00000 0000 00000 000>0om 000000 020 0000
m\0>< 0900 .9000. 0002 .2000
0000
I1IIlJ1IIIIIIIIII1IIIrIIIIIJIIIIIIIIIIIIIIIIIIIIIItIlllllllllllltllllllllll
rIIIIJ1IIIIIIIIIIIIIIIIIII|IIIrIIII
.00000 0002 0+000\00c00000 msmp0>000000 00000000 00-00000000 .00 00000

 

 

246

 

.x000 00050 >00>0

.0050: 00 00 00>00000 003 002000 020

 

 

 

 

 

.m . .
0m 0 op 00 0
000 0.000.001 00.0

000 0.000.001 00 00.0 00 0000 00.0 000
1111111111111111111111111111111 11
mwmv Asgav 000V 0000m pcm>0om 0Q0000 sz 0000

>< 0000 .QEOB 000: .0500

0000

HHHw11111111111111111111111111111

 

 

 

.Umscflpsoo .m: manmfi

 

247

Rb+-18-crown-6 in water is 36.3 (173), so that at a mole
ratio of n.5, more than 90% of the Rb+ should be complexed.
Therefore, above mole ratio 1, the signal disappears because
the line is very broad and weak, and cannot be discriminated
from the noise. However, a broad signal (Avl/2 >3000 Hz)
was detected above a mole ratio of one for a solution which
was 0.5 M in rubidium iodide. The rate constants for the
dissociation of Rb+C222 cryptate in H20, methanol, and PC
are 1M0 (21M), 0.8 (215), and 0.17 s‘1 (216), respectively.
Therefore, two NMR signals are expected at O < mole ratio <
l in all three solvents. Dye et al. (217) reported a peak
for aqueous Rb+C222 which is about 50 ppm downfield from
that of 0.1 M aqueous rubidium iodide solution with a line-
width of 1300 Hz. However, they were not able to observe
the complexed peak in alkali metal solutions containing
cryptand 222. The authors also reported a broad signal
(Avl/2 2 H000 Hz) for the complex in methanol solutions at
about 100 ppm downfield from a 0.4 molar rubidium iodide
solution in methanol. Our attempts to observe similar
signals failed even though different experimental condi-
tions, such as different delay times, different sweep
.widths, different concentrations, and different spectrom-
eters were used. The complexation formation constant

of Rb+-C222 in H
u

20, MeOH, and PC are of the order of

2 x 10 , 9.5 x lO8, and l x 109 (216) respectively.

In methanol we have been able to see a very small peak

248

at mole ratio of 0.98 even though the fraction of the free
cation is very small. A broad signal (Avl/2 = 1300 Hz)

was also observed in PC at mole ratio 0.U6. The above
facts show that if the linewidth of the complexed cation
signal in water is indeed only 1300 Hz we should have been
able to observe it easily. In the case of Rb+c222 in water
no peak was observed within i200 ppm of the free rubidium
cation signal. It appears that the complexed signals
broaden as a result of some kind of exchange. Perhaps the
exchange occurs between inclusive and exclusive complexes
as in the case of the cesium cation complexes with 0222
(152). Another possible explanation is that the true line-
width of Rb+-C222 in water is much larger than that re—

ported (217). However, we expect narrower lines for this

complex than for the complex with 18-crown-6.

3. Complexation of the Lithium Cation by C211 in Methyl-

 

amine

Solutions of lithium bromide and C211 in methylamine
were prepared as described in Chapter II. The solutions
were mixed and the 7Li NMR spectra of the resulting solu-
tion were taken more than 90 times over a 2.5 hour period
at -51°C. Only part of the data is given in Table 50,
since no distinct changes occur between the reported data
points. All data consisted of two signals, one for the

free cation and the other for the complexed cation. The

 

 

249

Table 50. Lithium—7 Chemical Shiftsrofthe Free, 6F, and

C211—Cryptated, 5 Lithium Cation in Methylamine

 

 

 

 

 

as a Function of Time. (211)/(Li+) = 0.5, (Li+)
= 0.069 M.
Time 5F Sc
Hr Min Sec (ppm) (ppm)
0 (mixing)

15 0.75 —O.82

40 0.66 -0.93

4 02 0.62 ~l.03

7 19 0.55 —l.05

ll 24 0.59 -l.06

13 43 0.70 —0.90

20 26 0.76 -0.82

23 25 0.84 —0.75

27 40 0.84 —0.79

35 00 1.00 —0.65

46 56 1.03 -0-52

57 14 1.05' -0.52

l 04 00 1.08 —0.52

1 ll 00 1.04 —0.58

l 38 59 0.97 -o.61

2 22 37 0.96 —O.56
96 1.16 -o.u2*
>10 days 0.67 —O.98*

 

 

*
Precipitate was formed in the solution.

 

 

 

250

chemical shift of the reference solution, which was measured
both before and after the experiment, had values of 15.11
ppm and 15.19 ppm respectively. It was noted that some
precipitation occurred in the solution after 2—1/2 hours
even though both C211 and lithium bromide were completely
soluble at the time of mixing. This precipitate could not
be dissolved even after 96 hours at room temperature. The
precipitate dissolved gradually in a few days but the
chemical shifts of the free and complexed species were
0.67 and —0.98 respectively; It should be noted that the
difference in the chemical shifts of the free and complexed
lithium cation was constant at all times (1.59 i 0.04 ppm).
The ratio of the intensities of the two signals remained
almost constant at a value of 0.8 — 0.9 during the 2-1/2
hour period. The signals had almost equal intensities
after 96 hours. The final chemical shift of the complex
was -0.42 ppm, in good agreement with the corresponding
chemical shift in other solvents (170). In addition, the
chemical shift of lithium bromide in methylamine was
concentration independent over the concentration range
studied (0.0058 to 0.094 M), and had a value of 1.11 ppm
at —52°C.
The data show that the exchange rate of the lithium
cation between the free and bound species is slow on the
NMR time scale, but it is not extremely slow, since most

of the complex is formed immediately after mixing (within

 

 

251

15 seconds). The data also demonstrate that the chemical
shifts of both species change with time. The fact that the
difference between the two chemical shifts is constant, and
the chemical shifts of the dissolved solution after a few
days is equal to the chemical shifts at the time of mixing,
suggests that precipitate formation is involved in the
chemical shift changes. It is possible that the C211

sample had absorbed small amounts of carbon dioxide during
weighing. Then if the formation of the complex occurs Via
the formation of an exclusive complex, it is probable that
both the lithium cation and lithium exclusive complex form
ion—pairs with the carbonate or bicarbonate ions which would
affect the chemical shift. The role of the precipitate
cannot be assessed without information about its composi—
tion. It is important to point out that the first attempt
to make the solution failed, because even before the solu—
tions were mixed, precipitation occurred in the lithium
bromide solution. In this attempt, some of the isopropanol—
dry ice solution, which had been used for cooling, col-
lected on the Kontes Teflon vacuum valve accidentally.

The isopropanol—dry ice solution may then have been trans—
ferred to the lithium bromide solution to form carbonate
in the solution.

In any event, our experiment showed that the complexa-

tion of the lithium cation by C211 is not as slow as has

been predicted (8)-

 

 

252

4. Complexation of the Lithium Cation by C211 in Liquid

 

Ammonia

A mole ratio study of the complexation of lithium
bromide solutions by cryptand 211 in liquid ammonia was
carried out. The results are given in Table 51. The ex-
change rate of the lithium cation between the solvated
and complexed species in liquid ammonia (as in other sol-
vents (170)) is slow on the NMR time scale, and therefore
two signals were observed below mole ratio 1. The chemical
shifts of the free and complexed species are nearly tem-
perature independent, and the complexed signal is 1.9 ppm
upfield from the solvated Li+ signal. The chemical shift
of the complexed lithium cation agrees well with the results
in other nonaqueous solvents (170) indicating that the
lithium cation is effectively isolated from the solvent

and the anion by the ligand.

5. Conclusion

 

Rubidium-87 chemical shifts of rubidium salts in water,
methanol, and propylene carbonate show a nonlinear de-
pendence on concentration over the complete range of con-
centration which was studied. However, the chemical shifts
in water are linearly dependent on the mean activity of the
solution. In methanol and propylene-carbonate, the non-

linearity in the plot of the chemical shift versus

253

 

 

 

 

 

 

 

 

 

 

 

 

 

 

me.o- m:.o- »--
om.o- -- s:.o- -- 33.0- -- OH.H
:m.o- Hm.H wm.o- om.H mww.o
52.0- mm.a mm.o- m:.H m:.o- w:.a mwm.o
wm.o- mm.H
mm.o- mm.a sm.o- :m.a mm:.o
mm.o- om.fl 53.0- s:.H sm.o- em.H mwm.o
-- H:.H -- m:.H -- om.e 00.0
poonQEoowl momma UmonQEoom momma poonQEoow oopmw oepmm mama
coo.em- ooo.w ooo.m
AEQQV on©

 

 

 

 

 

.2 No.0 n A+eqv .eflccee< cussed he Hem cemeeseo

eo cocchcee see an emeu eo eehem HmcHEceo flue cap eo sesem checm cue:

.Hm cease

 

fl

 

254

concentration cannot be accounted for only by considering
ion-pair formation in the solution. This suggests that
other effects are also responsible for the chemical shift
variation.

Rubidium-87 NMR signals are broad in the presence of
C222 and especially l8-crown-6 in aqueous and nonaqueous

87Rb NMR techniques are not suitable

solvents. Therefore
for studies of the complexation of rubidium salts by crown
ethers and cryptands in solution.

Lithium-7 NMR data show that the exchange rate of the
lithium cation between free and C211 cryptated complex
species is slow on the NMR time scale in methylamine and
liquid ammonia. The chemical shift of the complexed
cation is the same as in other solvents which indicates

that the lithium cation is effectively isolated from the

solvent and the anion in the complex.

 

CHEERVI

SUMMARY AND SUGGESTIONS FOR FURTHER STUDIES

 

 

CHAPTER VI

SUMMARY AND SUGGESTIONS FOR FURTHER STUDIES

255

 

1. Summary

The concentration and temperature dependence of 133CS

chemical shifts of cesium salts in methylamine was studied.
The variation of the chemical shifts of cesium iodide and
cesium tetraphenylborate as a function of concentration
indicated strong ion-association of these salts in methyl-
amine. However, the data did not follow the behavior ex-
pected for simple ion-pair formation. Instead of leveling
off at high concentrations, the chemical shift versus con—
centration showed a gradual downfield shift for CsI and a
gradual upfield shift for CsBPhu. The chemical shift of
CsSCN was concentration independent in the range of concen-
tration and temperature studied.

The cesium iodide and cesium tetraphenylborate data
at various temperatures were analyzed according to the
equilibria for the formation of ion-pairs and two kinds
of triple ions (cationic and anionic). In this analysis,
determination of all the thermodynamic parameters from
the NMR data was not possible. Therefore, we had to make
justifiable assumptions about some of the parameters.
For example, the triple ion formation constants were cal-
culated from the Fuoss equation and used as constants;
linear temperature dependence was considered for the

chemical shifts of the free and ion-paired cations; equal

256

257

probability for the formation of the two kinds of triple-
ions was considered; and the chemical shift of the cationic
triple—ion was assumed to be the same as the chemical shift
of the ion-pair. A long extrapolation was required to ob-
tain the chemical shift of the free cation, and since the
fraction of this species was small even at the lowest
concentrations, the determination of this parameter from
just the data with CsI and CsBPhu was not possible.

The fact that the chemical shift of CsSCN was inde-
pendent of concentration, together with other experimental
facts led us to propose that the chemical shifts of the
free cesium cation and the ion-paired CsSCN are the same.
This was the major assumption in the treatment of the
data. Other assumptions did not have significant effects
on the ion-association parameters.

The ion-pair formation constants, K at 25.0°C for

ip’
these salts (averaged from the models with different as-

sumptions) were found to be: (Kip)CsI = (2.65:0.19)

5 -1 O O = + -l
X lo M Wlth (AHip)CSI 3.7—O.3 kcal.mole , (Kip)CSBPhu

4 -1 ° 0 _
M Wlth (AHip)CsBPhu - u.0:1.o kcal.

mole-l. The equivalent conductance of Csl in methylamine

= (1.30:0.19) X 10

was measured as a function of concentration at -15.7°C.
The conductance data were analyzed according to various
conductance theories. The value of (Kip)CsI obtained

from conductance at -15.7°C depended on the theory ap-

plied and had values ranging from 8.7 x 103 to 1-4 x 106 M-l,

258

The Onsager limiting law fit the data the best but Kip
obtained from the limiting low was only about 35% that ob-
tained from NMR data (corrected to -15.7°C).

Cesium-133 chemical shifts were measured as a function
of the (l8-Crown—6)/(Cs+) mole ratio (R) and temperature.
The variation of the chemical shift with R indicated the
formation of a relatively strong 1:1 complex followed by
the formation of a weaker 2:1 complex. The formation
constant of the 1:1 complex is too large to be calculated
from mole ratio studies at a fixed total cesium salt con-
centration. The data for CsI and CsBPhu above R = l

were analyzed at various temperatures according to the

Kc2 + Kx2

equilibrium MC+ + c 1 M02 or MC+.X‘ + c z MC+ '

2.x

The fact that KC was anion dependent together with the

2
behavior of simple salts in methylamine and with the fact
that the limiting chemical shift of the 2:1 complex was
temperature dependent, indicated that the 1:1 and presum-
ably also the 2:1 complexes are associated in methylamine.
Therefore, to analyze the data above H = 1 it was necessary
to investigate the ion-association of the 1:1 complexes.
The concentration and temperature dependence of the
chemical shift of the 1:1 complex showed that ion-pair
formation of the salt competes with complex formation and
that the 1:1 complex also forms ion-pairs. The variation

of the chemical shift as a function of the concentration

of the 1:1 complex and temperature was analyzed according

259

to the equilibria,

+ _
M .x M+
+ +
Kt
M+
+
K K

_ i _ - t _ _
M+ + X 2p M+.X + x z x .M+.X

+ +
c 0
ii KC ,p, KX
K
+ _ A _
MC + x z MC+ X

The internally consistent thermodynamic parameters ob-
tained from NMR studies of ion-association of the salts
in the absence of complexant were introduced as known

constants in the above equilibria. The KA values for

CsI and CsBPhu ((1.51ro.06) x 105 and (1.16:0.3u) x 10

M.1 at 25.0°C respectively) proved to be comparable to

4

the K values for the uncomplexed salts, indicating that

1p
the formation of solvent-separated ion-pairs of both the

salts and the 1:1 complexes probably dominates over contact-

pair formation. The value of Kc’ which is anion independent,

260

was (1.07:0.08) X 10“ M-1 at 25.0°C with AH: = -l6.72i0.08

-l
Kcal.mole . Other parameters were found to be. (Kx)CsSCN

= (4.87:0.53) x 10"3 < (KX) (6.33:0.40) x 103 <

(KX)CSBPhu =

responding AH; values of -l3.50t0.73, —l6.40i0.53, and

CsI =
(8.u:1.u) x 103 m‘1 at 25.0°C with the cor—

-l8.8i0.95 Kcal.mole“l respectively. The order in KX for
various salts reflects the difference in the degree of ion-
association of the corresponding salts in methylamine.

The mole ratio data in methylamine for R > 1 were ana-
K
lyzed according to the equilibrium MC+.X_ + C $2 MC

0
AHx2

with proper corrections applied for the ion-association of

+
2.x

the salts and of the 1:1 complexes. The thermodynamic

parameters were found to be: (K = 4.03:0.05, and

l

x2)CsI
at 25.0°C with (AH

O ) _
x2 CsI
= -7.35:0.l2 Kcal.mole. The

(K = 22.82i0.35 M-

X2)CSBPhu

O
-6.05:0.08, and (AHx2)CsBPhu

dissociation of MC:.X- was not included because the ion—pair

formation constant of the 2:1 complex could not be obtained

from the NMR data, (presumably because the chemical shifts
+ _

of M02.X and MC+ are nearly the same). The corresponding

2
approximate values in ammonia are: (K = 649144 M-1
l

x2)CsBPhu

at 25.0°C with (AH = -4.9li0.28 Kcal.mole-

° )

x2 CsBPhu
Rubidium—87 chemical shifts of rubidium salts were

measured in water, methanol, and propylene carbonate.

The variation of the chemical shifts as a function of the

concentration was nonlinear in all of the solvents.

However, a plot of the chemical shift versus the mean

molar activity of the salt was linear in aqueous solutions.

261

The variation of the chemical shift with concentration in
methanol and in propylene carbonate did not follow a simple
ion-pair formation model. Attempts to study complexation
of rubidium salts by l8-crown-6 and cryptand-222 failed
either because the NMR lines were broad or the chemical
shift changes were small.

The exchange rate of the lithium cation between the
free and the 211-cryptated complex species in methylamine

and liquid ammonia is slow on NMR time scale, consequently

(0211)

(1.1+)

was formed in less than 15 seconds in methylamine. The

two signals were observed at 0 < < 1. The complex

chemical shift of the complexed species was the same in
both solvents and equal to the value obtained previously
in our laboratories indicating that the lithium cation is
effectively isolated from the solvent and the anion in the

complex.

2. Suggestions for Further Studies

 

The studies already made stimulate the following sug-

gestions for further studies:

(1) It has been shown that the 13305 chemical shift
in methylamine and liquid ammonia changes gradually at
high concentrations instead of leveling off. The oc-
currence of similar behavior in methanol and ethanol solu-

tions and with 87Rb chemical shift in methanol and PC

 

 

solutions suggests that the chemical shift is concentra—

tion dependent even when ion aggregates do not form. To
study ion—association by the NMR technique accurately, it

is necessary to separate the contributions of concentration
and ion—association to the chemical shift. Determination of
ion-association constants by various methods such as elec-
trical conductance measurements, calorimetry, and UV spec-
troscopy and the comparison of these results with the NMR
results would provide a useful probe for the study of this
problem.

(2) Since ion—pair formation constants and the limit—
ing equivalent conductances, A0, obtained from electrical
conductance measurements depend on the theory used, an
independent measurement of A0 would help to test the validity
of various conductance theories. The best method for ob—
taining A0 is to measure both conductances and transference
numbers.

(3) An extensive study of ion—association and complex
formation of cesium salts in liquid ammonia and the com—
parison of the results with those obtained with methylamine
would provide valuable information about the role of the
solvent in these processes.

(4) The study of complexation of the lithium cation by
cryptand—211 in methylamine has already shown that the
exchange rate of the cation between the free and complexed

species is slow on NMR time scale, but the reaction takes

 

 

 

263

place in less than 15 seconds. In this study complications
arose because of the formation of precipitate in the solu-
tion. A more careful experiment is required to explain

the complications we encountered. iMore study is also re-

quired to understand the mechanism of complex formation.

APPENDICES

264

 

 

 

APPENDIX 1

DETERMINATION OF ION-ASSOCIATION PARAMETERS BY NMR
TECHNIQUES; DESCRIPTION OF THE COMPUTER PROGRAM
KINFIT AND SUBROUTINE EQN

A. Simple Ion-Pair Formation

The equilibrium for ion-pair formation can be expressed

as
Kip
M+ + x’ + M+.x‘ (lA-l)
+ -
K := (M .XI) = l-d (lA-2)

 

 

. + _
1p (M )(x >yi oa2y§

in which M+, X', M+.X- are the solvated cation, solvated

anion, and ion-pair species, respectively, the terms in
parentheses are the molar concentrations of the correspond-
ing species, Kip is the thermodynamic ion-pair formation
constant, a is the degree of dissociation of the ion-pair,
and y: is the mean molar activity coefficient of the solu—

tion. The latter can be calculated from the Debye-Huckel

equation,

265

266

-4.l9764xlO6IZ+Z_I/I
Y = exp( /_ ) (IA-3)
(DT)3/2[l + 50'29 3 1]

 

H-

 

in which Z+,Z_ are the charges of the ions, D is the dielec-
tric constant of the solvent, T is the temperature in °K,

3 is the distance of closest approach of the ions in
Angstroms,and I is the molar ionic strength of the solu—

tion (I = 1/2 EC dZi).

i
i
The observed chemical shift is a population averaged

chemical shift and can be expressed as,

6obs = XM+6M+ + XM+.X-6M+.X- = 6M+ + (l'a)5M+.X- (lA’u)

where XM+ and XM+.X‘ are the relative mole fractions of the
free and ion-paired species, respectively, and 5M+ and
6M+.X- are the chemical shifts of the corresponding species.
Three parameters should be obtained for each salt from the
fitting of equations lA-2,3, and 4 to the NMR data. These

Q. .
parameters are Kip’ 5M+’ and 6M+.X-' since 6M+ in a glven
solvent is independent of the anion, the above equations
can be fit to n_data sets at a given temperature to obtain
3n—1 parameters. In our case, data for CsI and CsBPhu

at 25.0°C were used to obtain five parameters. These are,

267

U<l> - 505+.1‘ U<u> = (Kip)CsBPhu
U(2) = (Kip)CsI U<5> = 6Cs+.BPhu'
U(3) = 5CS+

The values of D, T and 8 were introduced as follows,

l/2

Const(JDAT,l) (DT)

O
const(JDAT,2) 3 = 5.3 A (Chapter III)

The value for D was taken from Reference 194. The sub-

routine EQN is given on the next page.

B. Ion-PairszmxiAnionic Triple-Ion Formation

 

The equilibria for the formation of ion-pairs and

anionic triple-ions can be expressed as

(lB-l)

- - _ + _
M .X + X 2: X .M .X

where

*
...

NMR TECHNIQUE

FROM

268
MULTIPLE DATA SET
*iitttiittttttt*****i*titiitiitii*tittttitttkiitttttitt

FORMATION

f“

H

DA

CH-PAI

Y

ittiiiittititii*ttiifi*tt‘tiiiifii*tititii‘kiii‘kifiiiiititi’
l

i
i

O

4

TI.

F
0N
II
LoK
E0:
A64
2LT

$9U99:Do
Crab-LT LNFAC
x...” CANAFr-nwfivlohkoruw
PJFHRHFMLLT

9F.
RdQNB
AKTI:
QFKDn
FUN. ’9 T

DEIEO
DCRNKYGTN
PRONODLRI
ALHAHN.‘ :AHK
BPLBPQ

NODD

'

\l

QC

)1

1‘
2Y9!
' .U)’
)0 0.00
0.2)r3p3
((nUl“
XTllD-VI
XC‘YY
QCYTY
’v 0x ’
o O’R)
0’0 1.0
31nu)5
0.23041
49(5T
I‘VUTI‘P
vrnCSMunU
T‘XIL
XHQF 9M“ C
x 0. 9’5)
X)\IPJIO
9002 95
T209()l\
.P‘SLHUTI
GU(AAC¢F.
d9UV‘O
H .)FP0TIM

ITYo

79809910911912.13)

“350 9N01 9
IKOC)!5(5
//41uh-u.\ll\x ’
TT(l\n¢6xxa.
DNXO(1RXQ

EUU 9 QSCI F0 91 93
NO ’PYTRON 9T0 Q) Q

IKXYQSFPO)95)62E01
T 9TJN//IO)(01(U6625 U U

UNKXJCNNQVOOSRVI\

C C
C \I C
C E C
C 9 SC
C U MC
C T CC
C A RC
C 1.». R TC
C H E SC
C T P P 5C
C IA 8 M NC
C S 84.: AC
C CN CHT C
C 0 pt NC
C TF1 FBT IC
C SOT OSN C
C C A CA EC
C TC T T CC
C TFN NFS NC
C NFOAS AON AC
C 01 TC T 0 TC
CM IHTS STC SC
CC TSFNE NF IC
CI A 10E OIC DC
CT TRLHCR CHI C
CA NTAS F SR NC
CI ENC N N T CC
CC IEILOFNOLC IC
CC CCMAIOOIAE C

CSFINECT ITCLQ...C
CSTFOHIATTAIE/ C
CIGFCCMMFUHMIINC
CONE ERILREDtOC
C EOTDHOHIOH‘tIC
CFRCLECFSDFC: :C
COT AV ) )C
C SYSRGRLERGI 2C
CE T FNIATINQ 0C
CECILSIACIAIT TC
CPIVABTPINPTA AC
C.U.NITOI M1... ...-.0 DC

CEOT0:MNEFNVJ JCECCLQ
C..UI»CTSIOHNOI( (CU
N: : : :NNNNNC: :A: : LICIILS
OCNRJCCONSCT‘TOIEERKRIPJRCAN:)) : : : : :T TCI: 0.1

)/(2o*U(2)*XX(1)*(€ANA**?))

)*(GAMA**2)

0910011JDAT

olUlM‘ ZR
SCNI‘N : C 2

)
no
7R
3L,
(
0T
TR
Pu
OS
6*
)
”Uh-V
O 0
AUG
.4

+ OlXN.L/O
.XELT

09

T61
RANSR4

RVU999MVL(3$ISTTPPAAUTUTUCfiEA12))) ))S SCTATTMAHE:A.

BMOXMYMMVHP‘NIN

127g Q C;

C

C C
C C

C C
CCCCCCCCCCCCCCCC

C
C C2

NAAVUTNTNTCPRN((125 45W NCNM NG(PRG(:
DUONXQYOCICLOXOOOTTOOEOEOECLTAXX((( ((0 OCOAOORFLTRFA
RSC9OLYCCUFZCDCGCIJNNRCRCFCASGXXUUU UUC CCCGGCAIASAIA
l Cc 1C 4

*
*

ifi*tt***kt~kfii*~kiiii

NMR TECHNIQUE
**r**ttt**t**tii***ii

SET-CONTINUED

2'69
MULTIPLE DATA

ION-PAIR FORMATION FROM

 

iii-*ii'tti'i'iii*‘k‘kiti’t‘ktttttiittttti'ii'
************i*‘kitt‘k‘ki‘ki-t‘k-kti'ii‘tik‘k

*
it

) )

) \I

1 \I l

’ \I 9

1 ... mi 2 t

( K ... ( K

S N t S N

T 0 A T 0

S C M S C

N t A N t

O o G U a

C 2 ( C 2

/ ( .w / (

\I / ) ) / T A

\I \I 1 \I \l A Ml.

G \l l\ G \I D A

R ) X R ) Iu G

A 1 VA A 5 9 9

I\ l\ \l * I.\ l\ A A

T U 2 \l T U M H

R _ ... 4- R _ A Dr

Cu ) i ( Aw. \l mu L

S ) 3 A U S T 3 9 A

i U 0 I\ M t .x .--d 1 l\ A Q.

\I E C U A o \I E C U H- J

2 N 0 I\ G 2 2 N no /\ D- l

9 A l) * 5 (71\ \I O. A l) t r? L) (\I ..L

1 M O \I 3 i~Ql F0 2 M D \1 .3 A5 X4. 2

( A 0 o 7.) ) ) TR ( A 0 o 7) 91 X o

S .6 T2 3:- O 10) 3A 5 6 T2 3F 0 0’1 10 O

T. / ... + T (TM (\ Tr / ... + T c1 9 T1; T-

QV ) 0* 0 o X G OT S \I 0* O o C(X AE

N )A GW T1 0 XORA TR N )A va T1 0 X5 03 0
30 OM \IE) I\ G *IUAH Pu—DO D” )E) l\ G OVA 0. IV V G
*C DA lNlOT ))(P OStC DA INIOT )T)4 )X
it ’5 0A(GR ) AUTL G*t* /G 0A(GR ) 2 4. 35 )
’01 A . OMX Q l ( oDnA \I )9 A - CMX Q T. (030 C 9 1
12 Ann 0AX)S . non-0* 0312 Ann DAYTIS . X611 15 _
9. (...-TI“ oCi0+xl¢ .x .S) 0.9. I‘LL)“ orUtO+slo VA) Orr. 9T. 0
lnu D-NTEO( o cit-L orL+l 0020 PNT-LO‘ o 95E .3E3 E1 E
(5 XAAN.*K11(NC 4L-( 04(5 XAAN.*K11(NC CoP9 5P9 N
Sl\ EMRA,T\IN. . U 0L + fixutuuLLrbS‘ EM...HAT)N. .U o-L |:LAX EAX o
TI\C:A(M5520 0(+HA r10 _XEL7T(C__A(MhGa-O 0(+HA EANTFOFL .L 0T5 E r... EH E F. 2..
S+CHGSA0(CE()TC U1M(:R-9S+CWGSA.(CE()TC UC.J(U UIJ( U U UT U U U
NGtE‘BGTU*L()E:NN:G: TGINOiE‘BGTU...L()rr_:.NA:D-(TNNN:(TNNNNNNENAHNNAK
0.5N(A:A:co:)M)RI RANSRQO.BN(A:A:oo:)M)RIDAEAIRIDEARIRIRIMRIRTRIR
CIEA::AFKAFCIIZUTMAHE:A.CIBA::ARKAFCIIQUTILTVTUTITMUTUTUTIUTUTUTU
__ : .....P-TT-MuI‘N: (L(((TNG(PRG( __ __ : __M-..TITM.I\.N__ (Ll‘((TNS/KIRHNTNSIRTNTNTN‘TNTNTNT

DDCDAAAHAF.O FAXFXEOSHFLTHHFABCDAAAAFO EuAXE.-XEOEFROHUFEOEROEOEOEOFPZOEOPLOCL
BCDG—nRFUIFVFICXIXRCAIAAbnkTAI-HD._DCRUGRRPOICFICXIXRC..KIHW.FCRPCDAHFRCRACRCIDAACQHCRCQ
TL 1

1 5 Q- ..U 7 ‘3 .3 Q. 5 ...-... O ... .
O I) CC «C n.» 2 1
. ... T. (C 11

\i

270

*izi’iiiflkitiiii*t******i*‘k*iiiiiiflkii******t***i**itt*i'*it
* ION-PAIR FORMATION FROM NMR TECHNIQUE *
MULTIELE DATA SET-CONTINUED *

itiiiiiti****ttititiit**tRk****tiiflittit*iu**tii***i***

11 CONTINUE
RETURN
12 CONTINUE
RETURN
13 CONTINUE
RETURN
END
7
P
: CARD

fittiiii*****iii*iiti**i*******i******i**i**t*iit******i

CCTTROL CARD

TITLE CARD

MUDT ARRAY CARD

VCST ARRAY CARD
CQHSTS ARRAY CARDS
IR‘ ARRAY CARD

ISMIN ARRAY CARD
INITIAL ESTIMATE CARD
DATA CARDS

t**i***i*t*ti*fi**tk************i*t************i**tt****

BLANK CARD
6

‘9 CARD

 

271

_ (M+.x')
- ‘ “_—:—_— —2
1p (M+)(X H: (1B )

and

Kt = —£§:*¥:*§:l (13-3)

(M .X )(X‘) .

in which Kt is the anionic triple—ion formation constant and

(X_.M+.X_) is the molar concentration of the triple—ion.

Other symbols have the same meanings as before. Equal

activity coefficients are considered for X' and X_.M+.X_.

The mean activity coefficient, vi, can be obtained

from the DebyefHUCkel equation (Equation 1A53).

The mass balance and charge balance equations are,
+ + _ — —
00*: (M ) + (M .x ) + (X .M+.X )

(X') + (M+.x‘) + 2(x‘.M+.x‘) (lB—4)

(M+) = (x‘) + (x‘.M+.x‘) (1B-5)

in which CO is the total concentration of the salt. Sub—
stituting for (M+) and (X‘) from Equations lB—4 and 5 into

the triple—ion formation constant expression gives,

272

_ (X.M.X)
Kt ' [CO-(M)—(X.M.X)l[(M)-(X.M.x)7 (13’6)

in which charges are omitted for simplicity. Equation

lB-6 can be solved for (X.M.X) as a function of CO, Kt’ and

(M),

 

. (Ktco+l):\/(Ktco+l)2-4K§(M)[C -(M>J
(x.M.X) = O (lB-7l

2Kt

 

The negative root has to be chosen to satisfy the boundary
conditions. Similarly, substituting for (M.X) and (X’)
from Equations lB-4 and 5 into the ion-pair formation constant

expression yields,

Kip = Co-(M)-(x.M.x) 2 (lB-8)
(M)[(M)-(X.M.X)lyi

This equation can be solved for (M) as a function of Kip’

CO, and (X.M.X),

 

2 ‘ 2 2 2
Ki (x,M,x)Yi—1+\/[Kip(X.M.X)yi-l] +4KipyiECO-(X.1VI.X)]

(M): J 2
2K Y
ip i

 

(lB-9)

273
The concentration of M+.X_ is given by,
(MX) = CO—(M)—(X.M.X) (lB—lO)

The concentrations of the species can be obtained by an
iteration technique. Starting with initial estimates of

zero and unity for (X.M.X) and Y the first value of (M)

+3

was obtained from Equation (lB—9) and used to calculate
(MX), and more accurate estimates of y: and (X.M.X) from
Equations (lA—3) and (lBO7) respectively. This procedure
was repeated until convergence occurred. Then the final
values of (M), (M.X) and (X.M.X) were used to calculate
the relative mole fractions, Xi“ The values of the ad-
justable parameters were then obtained by fitting the

calculated chemical shifts to the values obtained experi—

mentally according to the following equation,

= 2X16. ' (lB-ll)

The ion—pair formation constant at each temperature, (Kip)T
can be expressed as,

o
AHip

1 I 1
_ _ — _ lB—l2
(Kip)T ‘ (Kip)298.15 exp[ R (T 29 15)] < )
in which AHip is the enthalpy of the formation of the ion—
pair. Four parameters were adjusted for each salt. These

are,

 

274

CsI CsBPhu
(Kip)298.15 = U<l> ’ U(3)
Ang = U(2) , ' Um
6M.X = U(5) , U(7)
6X.M.X. = U<6> ’ U<8>

Triple—ion formation constants were calculated from the
Fuoss equation (l-8) and used as constants. The chemical
shift of the free cesium cation at various temperatures
was chosen from the CsSCN data. The FORTRAN expression

for this problem is listed on the next page.

C. Ion—Pairs and Two Kinds of Triple Ions

The equilibrium for the formation of ion—pairs and two

kinds of triple ions can be written as

K.
M+ + x‘ ip M+.X‘

Kt +_
M .X- + X_ #: X-.M .X (lC—l)

K
t _ +
M+.X‘ + M+ z M+.X .M
where

_ (M.X) (lC—2)

ip (mom:

t
*

FROM

275
0F TRIPLE-ION
*iikiiiifittttit*t*ii****tt**tit**i*itiittitiii*****tiii

KIND

QUEyMULTIPLE DATA SET

 

3.
l\

‘MR TECHNI

*t**i*fi*********tiiti********t**i*i**ii****t**t****itii
ION'LATR AND ONE

*
*

RD. 99 C C

AYTT q C ) 5 C

VTIDF \I C _ l C

011 90 9.0 C R u C

N 9TL )1 C U 8 C

98 9 9 1‘ C T. T Q; C

TPTT. 2V: 99 C A N 2 S C

PESP 990)) C R A 81 C

OoKU )C900 P C E T T E. C

NR 9M 41;)55 v: C D. S A 18 S C

’AL 9 ((0(( T C M N CQ) N C

RIAT XTlPY. T. C E C S N E2 50 C

C9VA XC(YY C T C T 0 P TPI C

NOGD 9..LYT.Y. C .1 N Tun ST .1. C

.11qu )V 9X 9 ) C T N AG .0 ATAF C

XSE9 09)R) 3 C N 0 TN EI F APL C

9E 9T 0‘10 90 l C A .15 ST. LT 0N .P C

PROA 310.15 9 C T Tl NR PA ONPI C

A 9TB 9230‘ 2 C S A» 0 01 IC SIOOR C

LV9N 49(5T 1 C N MSTCA R RNTIITW C

9AM.L 9 (..UTI‘D: 9 C O rug... 5 TLIOAHT OTC

T 97:... XESNC l C C DEAN. ALICQFFIFC

kI9S T(XIL 1 C FzTON FTPT COOTIC

19PM XHP9M9 9 CEC E810 OE.CE AHC

9T 90 X 9 9)S\l nu CRT. ..HRNTIT M AFC—LQVQCRSC

..LSUT. vn))UInu 1... CUP OUOA wa NRRCTTT C

PEF 9 9532 95 9 CTT ITCMFEOFOFFQFFNLC

ATQT T20()( 9 CAC .A ROIIOI FIIEAC

T 905 PlwaLCT 9 CRE EPWO CT rLF HHCCC

IuXth CUI‘AEF cu CELCLFCFSIANF.L2CISSK.IC

9T. 9N J 9UV(0 9 CD E/PPI EFROOO O OHC

0 END: 9 H 9)FGTM 7 CMIlIMTRIFTI MT LLPELC

4 FOOT TT09IS9)9 CED*FEAIWENTN:FTAA HC

T AXFC. EPU)EC\IIJ1 CTlxtTITM ALOEAOAIFCCTCC

F TA9E W0309N019 C:: : RPACCRIGiIIIC C

n N NIMIV IK9G)05(5 C)) )E0.H FTTESHMVADC

I I G9Tl9 //430)(X9 C12 3CFNTYONAM SEESEC

LoK ETIXY TT((26XX4 C99 9N ONTCEROL HP VC
[0: N 900 DNXO(1RX 9 CTT TERIEI:CT 9ALCCLRC05
A64 EUU99SEI F09193 CAA ARlszNNhACAzzAECol
ZLT NO 9PYTRON 9T0 9) 9 , COD DEA))ILUETTC))TSC1 a
DA 9:! - TLKXY 9SFPO) 95),.02Enul CL C “UnU ECICJ JFrH34TACCEVr178OFTC+8
RH4N3 T 9TJN//IO)(01(U6628 U U o a UC(( (E.(I\CC:N«D_LM..((TCCSQJ
AHKTI: o UNKXJONNSGCOSC‘Cl‘ N: __ __ :NNWN 10NNCSS CURNUHUATNO 9HEUU : :CTnd
C9FKR 4 OONRUCOON5OV.TI\TOIEF._D.KRIR.1..U: :RICTT TI:O99: 9MCACH99)\ICT:
RN 99 T RMU 999MVHE(ZQOQI¢.VTTD.PANUTUT:ALUTCCVS SF.1\I\)/ALE:H__C\I)ln/LC:F
DECIEG 0F BMOXMYMVWMDri‘NlN NAAVUTNTNQCMATNCNN Nr._:lncM..A 9XPR:56(I\CSE
DDRNKYGTN NUUONX QYOOIOLGCXOOOTTOOWLOEOTACEOCOO ORK(I\ACMVMLMM((XXCTR
RRON9OLRI RSC9QLYCCDFZCDCGCIJNNRCRCIGTRCCCC CTFUUGTEEADDUUXYCIT

AAWAthAK A 1234 12345 C C

CC BEnLEDr 9 C 1 7 «C 2C AC

8 9U 9 92D 0 C C

Cn SLTLTLD ......C c C C

NCEAZLATAOC cw. C C

PiPHRHFMLL? CCCCCCCCCCCCCCCCCCCCC

l
'k

flu...»— on," y. ..

*it‘kfii‘k‘k’kiii*t‘kfi'ii‘kii‘fit‘kiii‘ktt

ULTIPLE DATA SET-CONTINUED

276

UEQM
tank

r
Lx

 

MMR TECHNI

ION-PAIR AND ONE KIND OF TRIPLE-ION FROM
*ttfitttttifiifiiiitittit

ii*****t******t*‘kii‘ki‘ki*******i*~ki**ii**i**~ki***‘k‘k****i

‘k
‘fi

‘1 )
\I )
L L
AA A
C ) C
T ) T
. E _
) I.‘ )
l ) U l )
( \I * I‘ \I
\l \I X 2 \l A \I \l X \l n...
) ) X t 3 G ) ) X 1; *
7 L ( i t) E 7 L ( *)*
8 A ... A tT M 8 A ... *TA
9 C \I M. TD 0 9 C ) TDM
o T ) A Us I\ u T \1 03...,
1 _ 2 G S/ + 1 _ 2 S/G
) / \l nvt I\ (\l \l / ) .rlufi ()l\
F ) 1 )0t * /) l ) ) l )o* /)*
FL rK l\ \I ) TIA K \IN C r: R Ix \I ) TlAH \Ixh'n
in. Cr VA .5 \l D: _ M D: )MI .1 ( D: X Cu ) D: _ M: \lAw. r
T 01 M” X S 1 *)A 1 NE U5 M X S l *)A Mr:
/ 0C E ( * :\ 0N6 07M( 0 *3 E I. ... ( DING M1107
O 2: T *7C X 70L(705ET ) T A T *70 X 70L(7CT03 )
a .11. t )5 o X 32!n*32 (Du f. )TC .w )3 o X Tidahirorxnnnx. h.
) l ) S 2 . (CK (OTC M NO FET ) S 2 . (CK TQ(O M
1)( 00 2 SO( M O/TPO/TRS E LG 15 4 SO( M O/TPORS/T rr.
QJL- TT. (‘1 *T/ E T)... 1T.) 51.... / A) \I hi..l\rU (\l *T/ E T.)* *Tfiu...) /
T 9) U? U: ) 0(sl ‘1)0 )037 ) C1 1.. T+G U74 nun: \; U() ))\1. S7.)O )
ATP 00 _ 9) o .0) 0*3062 oODFGtZJ)M T0) ( *)\I . 9) o .0) oinUAUAJZ 00*3DAU)MH
Dank—Cree (TALIQAUS 1)tG(*4GPu\anauF—L _nUl)x 4M1 (Tn/...anbs 1)*GI\* AGOCJP..H)FCL
.dnUILfL)) (At—1.x)? +MU)T*I\\I(O 0 IF- NU‘1.X n2D_ (At .()Dn +~C)Til\) o o‘turr—
(«uTJH77 FCi)(n_( \lrL oORAI‘OT taro/N Mu oX(/ 2... a PD*)(U( )E ‘ORA(UC6T o/h.
S(/T o - XdAL+ 0T. )t 4. oQM+ cannon/DEM. ECXXN oAE XIuAL+ :1 )* u. oQM... ca. DRUEM
TSU . ET. C(MHAA)UR 1)(USA\I3Q .62EE _ o/XL .UHrWC EIxMA)nUR l)(FJSA)Cb2Am lLE
ST cPLG (SACE 1U (2+ 0 . U2 .SE7((( )TN/«AZ _ u- 0L (SACZ .9 (2+ - _ 52 u7r\.,\:L((

NSlN . oEtTGTtESEXt)EAH(*E+L9(D.( lGMXCT‘LHfl EtTGT*ESEXx\IEAI\tEQ/(+er(
ON‘ETTU)S(* tL+UXi2L<i *LC o1+XS ( orLMT o+AHTC U)S(t *L+UX*2L(* *L1+C aXS
CO__TA~AN1N*SR oRMntT... 0:KC 0CN40—LENXT:CLIHURleZNNsNtSR .RNtT... -:KC .40CNEBN
:PCR....UnUTx‘OKSnRSRITpi NPCD‘M- o:«AMXAA:ArDM,__M)H1(UKSRSRITP* NPCD. 0(M.:AM.,
P:PFJJTUCP((R(TP(AGL((D:E(1A:E:FHAG:UC12UTUCP((R(TP(AGL((D(1:EL:E

VHTMlI((MN: : Z __ :(_.LW((((A: :(N‘: :MT.:X(DrTrLDn:L.-\(TIN__ __ __ __ :(:N(I\((A __ Z (: :Nl‘MuT :
ESEDFFOKTSRSFMO : : :FCCDF.MFEFAAMMFLEMMMLAFXEOKTSRSFMO__ : :FCCDFEFMFAAM
TSTTIICPPSRDuIECABGITCCIEIEFGREEIABODUCIXRCPPSRRIECABGITCDICF:.IGRE

O 1 l 2

0 0 O flu

3 l . l

l ...

277

f
*

ONE KIND OF TRIPLE-ION FROM
NIQUEyMULTIPLE DATA SET-CONTINUED

NMR TECH

...! OEMT o ... ATC

XT :CL :0R(E 2 nNmN :PltTNSSSNN 2 (TNNNNNENNNNNNNVNNNNNN.

UC.J(Uooo

U1J(U U HUT

EPLE
UUUUUU

 

*u***********tii*********************************i*****
ION-PfiIR AND

iii***********t‘k‘k‘h*‘ki'kiflt'k'ki'k‘k‘ktitttfikfittii’i‘ktti'*tiiit

i
*

... ...
t *
... t
t t
.1 t
A .w ...
M t i
A A. .u .r
G M * t
\I 9 EH .1 .1
\l N PD * .I
8 L 9 t t
l. A A * ...
U C G ... ...
... Tl E ... ...
AH 9 M. ... t
G X 0 * ...
..L M 9 t .x
M F. A ... ...
O 9 T ... ...
( M., E .r i
+ E R. t *
\l 9 9 i *
n2 ) ) A r *
G 7 1 H ... t
1 I9 1‘) D1 flu * *
. U5 X4 L) 2 ... ...
C *5 X. o 000 A4 * ...
T A 0 99 o u o 9 o O .r .r
)....0 CT»... 561 .10 T. + ...
NC ELLT erAE : z : A1 * *
LG .15 05 SLAM DE 0 * ...
AH) ) 0(0 0d 9 TAM“ Iva. G * ...
C1... 1 73.76 \ITR)X ICAH \l 9 ... .1
T0) l\ ...)3 2 25 91.16 4.x ) t .x
.01)X 4M1 (O2 9 T)) 05 1... * *
N3(1X 2D. X625 P50 1 9 . ... *
MoX(/. 2... o X) 9.1 On. 95 o .... ...
EUXXN oAE .3E1 N00 551 E * t
. o/XL CHNC C 0P 9 o o 0 ED: 9 N ... . ...
)TN/A3.PoL LEAX QGQ 03X o * DOA RT *
lenXCTIKLHA CANTSEEEE oTSE C... CH ... HRCCAA ...
.x ...
*nU CCVIAH T... *
XAA:A6M :M.)RIDAEAITTTRIDEAIRIRIMRIRIRIRIRIRIR *R ACYT *
:RHAG:DClndUTILTMTIIYlUTITMTUTUTIUTUTUTUTUTUTU ... ACYYR ASStD
X‘PTER_.L(I\TNS(IRN(((TNSIRNTNTN(TNTNTNTNTNTNTD *CRAARYREDtR
MFLEM..MMAFXEOEFROUFFFEOEROOEOEOFEOEOEOEUEOEUEN D... ARRAAR Rid.
r51AflKXUDP¥§XRPETIHFEBLITEQEKNFkENCnRfilRPEQLRFEQLRFEQLRrL 9*.ECRHHMHAlfatC
A10 «HAS: AC...
.5 20 7 4.3 4. 5 G O). nu 1.. 2 3 Cthu TANI *K
3 2nd 3 0 2 1 l I 1 *TLTTS ITA*N
26 .1 .c. .r MVTPSN \pu... 1T .x ..H “C
n. .rCIGCCRSNfliL 7-
7. *CTMNCIIID :86

CAR

_ (X.M.X) _ (M.X.M)

Kt ‘ (M.X)(X) M.X) m)

— (lC-3)
in which (MXM) is the concentration of the cationic triple—
ion and the other symbols have their usual meanings. The
activity coefficients of M, X.M.X, and M.X.M are considered
to be equal. The charges are omitted for simplicity.

Equal probabilities for the formation of two kinds of
triple—ions are considered. The mass balance and charge'

balance equations are,

CO = (M) + (M.X) + 2(M.X.M) + (X M.X)
= (X) + (M.X) + (M.X.M) + 2(X.M.X) (lo—u)
and
(M) + (M.X.M) = (X) + (X.M.X) (lC-5)

From Equations lC-3, M, and 5 we have

(M.X.M) = (X.M.X) (lo-6)
and

(M) = (X) (10-7)

Substituting (M) for (X) in ion-pair formation constant

expression gives,

_ (MX) (lo—8)
K. _ ——————
1p (M)2Yi

 

OI1

MX
(M) =‘/ L—g (lC—9)

KipYi

Equations lC—M, 6, and 7 give

(XMX) = (MXM) = £91£M%:$M§l (lC—lO)

Substituting for (XMX) or (MXM) from the above equation

into the expression for Kt gives,

K = CQ—(M)—(M.X)
t 3(M.X)(M)
01”
c _
(M x) = gii%%¥%j (lC—ll)

The concentrations of the other species can be expressed

as

(M.X.M) = Kt(M.X)(M) (lC—l2)

(X.M.X) = Kt(M.X)(X) (lo—13)

The solution to Equations lC—lO, ll, 12, and 13, and the

Debye—Hfickel equation (lA-3) can be obtained by an

280

iterative method as was described in Section B. The cal—
culated concentrations then are used in the observed chemi—
cal shift expression (Equation lB-ll). The temperature
dependence of the ion-pair formation constant is obtained

from,

(K

 

rAH.
ip)T = (Kip>298,15 expE— Rip (l = l )J (lC-lll)
The subroutine EQN for use with the KINFIT program is given
on the next page.

It should be noted that all equations and iteration
methods described in these Appendices were checked by
testing the numerical values of all concentrations and
activity coefficients for consistency with the equilibrium

constants and conservation conditions.

 

 

 

i
i
W
7
“ **** RP99 C C
... .w AVITT 9 C ) 5 C
W, ... .. VTDP ) C E l 8 SC
i ... .. 01.90 9)... C R c E NC
3 * * V9TL )1 C U 8 I CC
1 * t 9599 l( C T T 9 C IC
g * a. TPTT 2Y19 C A N 2 E5 .C
m i t PESP 99D)) C R A P1 LC
*M ... OqXO )0 900 P C E T T S . PC
w *0 .. ....R 9M 42.25: Y C P S I.» 8 ....C
*AK ... 9A]. 9 ((0(( T C M N F01 RC
...Er ... RIAT XTIPY I C ..L 0 Tab 9.02 STC
i .x C 9VA XC(VIVu C T C T .N TD. C
...N ... NDGD QEYTY C * TN OST ICC
iOTt IIIJ )V9X9 ) C T N AAG INATAIC
*IEt XSE9 nUI).K\I 3 C H... 0 TN. R _0 APNC
i.S* 9E9T U)99U l C A IETSI I EIN .OC
tr: ... DROA 34in )5 9 C T TlNNR AN LTOvNaNIC
*LA* A9TD 9230‘ 2 C S AoAUI PO PCIOONC
*PTi LV9N 49(5T 1 C N M8TCA .I IfiTIIAC
1.1/Ht 9AL9 (fiuTQP 9 ”C C ROS C. NT HKRAT C
tRDi T 9ZT. XafiCuNmO 1 C C OOLWN. 0A TFCAFFC
*T i “I 98 T‘VAIL 1 C F__CON 1C COOC ‘1
... E... I 9PN XHwD: 9M. 9 9 CEC ECIO FEE C C!
*FLt 9T90 X99)S) 9 CR1 1R TITFLNOLEESSC E
#00:... COQUC X))~.UIC 1... CUDI. OJMAP CCAO OBKETTC R
l t 1* PEF9 900295 9 CTT ITOMFE TINMFRFFC T
8 *ST* AT9T T20()( 9 CAC .AIRCINENO: FIIC I
2 iDLt T905 P(3LGT 9 CRE ERTO COMAIAF HHC 0
thumb... .UVAFC CL‘AHCVC. Q. CEL LL—LLCEICI TCCF:¢..C 0
*IM... 9T. 9N .U 9UV(O 9 CPPL/PPM EFTFFAE O C \i 1
*K9* . EUP9 H9)FGTM 7 CMIlIMRRIFAOORMT LLC 1 (
... E* a. D. 90.] TT0 9.135 9) 9 CE U... REQIPEDu TCFTIIAAC 9. .
..CU... T. ..HXFC CPU)_LC\I51 CTlxiTTFAHLOTNKJh. oIFCPvC T. )
... ”HG..— F TA 9E M030 9V01 9 C: : : PAnvNOOEAHIIIC A 0..
*T1* o N NIMIV IK93)95(5 C)) )EP.H EIICTShMMC D NF
* N... T. I G 9T1 9 //4.2J.L\lr\x 9 C12 3CINTYCTTNE SEEC J FCC
*SHt LoK ETIXY TT((26XX4 C99 9NA0NTNAAOTL HHC ( TR
«NC* E0: N9DD DNXO(1RX9 CTT TEPIEIORRC9ALCCC $5/T
.1 ..ME* AG“. . EUU 9 9nQEI F0 91 93 CAA AR. __ :VCTT: ACA»: :C T18—
... T... Z LT NO 9PYTRO.N 9T0 9) 9 COO DEN)\II:NNXTIC))C13 o .0.
*R * DAsF. TKXY9SFPO)95)62E13 1 E E 0 ECJJ JF034TNEEMCM178C+N81N
*IR... HRH/4N3 T 9TJN//IG)(01(U6621 U U UC(I\ (EI(1\CXCCXBrLMJ(I\CSOQ/(r_
.x «hum... AKTI: o UNKXIUAUNNSUOSRu‘ N: : : :NNNN INNCSS SR :UUAMNNE 9HEUUACTCACZT
iDNi C9FKR I4. «UnUNnnIUCOOvV 3.JT(TOIEERKRIRI(U:RICTT TIHN 992500 9APCH99C7.::DH:
*— 1 Phi? T D.MU999MNE(3SISTTP?ANUTUT:AUTCSS SFO)}AQCCMH:C))C:PFPF
*N .x DEIEO or: BVHOVAVHV..M.M..V..P(N1N NAAVUTNTNSMTNCNN NELIlnéuxhX: :anR__quDCSVPLM-T.
to * DDRNKYGTN DUAUNX 9YOOIOLOXOOOTTOOEOEOTAFLOCOO OR.I(I\AMMXMLMM(I\CTESULD
... I t R.,.KON 9DLDnvl RSC 9 9LYCCDFZCDCGCJIH..NDxCRCICDnCCCnL CTD.UUGFL_LE_LADDUUCITTTT
.x * A«HH...AN.* :AK A 1:2/2&4. 19:34.3 C CV
i * CC BRLBPQ C l 7 .8 2C C
i * S9U99:U- C C
.t * C:_._(.._LT.LN._.rAO r. P» C
... i .\C». AEATAOG Q. C C
... * ... t PJPHRHFMLLT CCCACCCCC~CCCCCCCCCCCC

 

 

i
*

FROM

CF TRIPLE-ION
NMR TECHNIQUEoMULTIFLE DATA SET-CONTINUED

*iiii‘it*******tti'kti‘k*titfittiii'iiiifiitfi*iiit**titt***ii

*iiitiiitiitttttiittt*ttiitttiittiiii*ttittttttittitttt
ION-PAIR AND THO KINDS

‘I
i

)

7

8 \l

9 0

O c

1 1

I. +

\l )

R M

P P:

M... t

..L N
.1) T. 0
ll 1.. ... I
‘(00 \l TI
XXUO 2 P .1
XXnul ( ... .3
* *1A “L n.»
51 0 . o )0
0007.! ( 3 MT
0 CT ()I\ A
00 Pl“ 6»...
.. :00 X1/ *3
HMGG E‘) N)
CF?!) ...UM O...
.))7%I abir. 1;.)

1.1 o o )NN . 2 106
o 2LT. 10.U)* P QR
3......LG. (III... (EA
ENOOCUII‘FE/L‘
o oTTU..D.P.XM..UX 0T

)
M
X
v.
D
...
A
G
E
M
\l O
2 (
9 +
T- \a
A x \l
\l D M 7
O J x 8 \I
O l\ D 9 0
1 Q. ... o o
+ T. A» 1 1
\I S) T I 4
NH NB E \l \l
E on T R M
* C9 ( P E
N ,0 + M... t
0 \a a nu ‘1 F. N
I ))1 .0 Y. T O
T 7N..\.l\ \l 1 MAD * I
0. SEE... N at. ) T.
.1 RR, X 0 ... a. Dr 7.
a OTTvJ MM .1. LC 1.. i 7...
o T89... E \I ) TT. .U Q.
3 ((fi / 0 F F r... . o )0
(M OTT) ) G I I 80 l\ 3 Mil.
(E GRR2 x \I D D (G ()|\ A
It \Ihuauu 9 Mr 0 \l TI TI .7 Dull! 60
)N 088T.) pr. 1 )1 t t )\I X1, *G
"X 0* *AC - .\l\l1..l\ Q. \I M1 E‘) N)
EM“ MIOCSDA N E11¢X 2 6 D. *Uum CC
..L Xooclu/ X 0((Xx 2 ( ... 0 Rip... 1.)
)* MECS‘AAQ." IXXX/ 0 U Ar. )NMm . 2 71.06
1N EL“ iSAiE oXX/M C 1| HIHC 300).! P QR

(0M+069T(*( T/lxxs.)+ )POL (111* (EA
XIXMN?2SPA(NGMXNM.7(:.RX7LHA EUII‘AE/L‘
XTMEEQI. oNXumSX oEMXE «+(quCATC U_.D.D.XMUX 9T

.(0M 9 orDG/TI.‘ t (

)
N))/CONSTS(JDAT92)
100+§9)

2C0

DIG. .

3
RE
RE
)*

01:15....
Tc..c.....
(C...
OTT)
GRRZ
)Qru 9
OSST)
9.. ... AC
MUGBCL
X o . oJ/
).. M.Env5(nuncur
.lN rfL4*Q7A*E

MX)/£FXN)

’

-9-

E.)/((3.0*PTION*EM)+1o0)
7
f
N
(

- u
E-XN*EM

XN
ToluE’lG’GO T0

XIXM. N7ULSPAHI\NnC
XTMHEtzw/ ONXVISX o

ADSAAAKR: ..XANMGR ‘PE:R100EABMT:ErL._rURUM.nUU(E:nN-NRZ..XANMGR (PE..R100EAEV-T
TTUUIMNNMH‘G~1£RGMH .. Z ..nNTaR..C:GAHEAA 2 ...HIDM:nU: .. ..N)RIHHNN(GIER..UM: : :NTQQ.C:GAFCA
IIIUIUTOOO: ..T. I ACQEMmNXF.S . ((AH _. ._ ..RHAAPO_.DR: M.XC12UTAUOO: :T. ..ASENMXES . ((A: .. : F

(((‘NIIIXMNG( : : XXMR(: : : MMHTX(PTT...LR:XXXML((TNIIIXMNG( : : XXMR( : : .. MM~TX(
FFFFOIITM.ACRFMXMMXTFABCAAAMFLEEMMu.MVNXAFXEOIITM.AORFMXMMXTFABCAAAVF
IIIICPPPEGCAIEEEEESIAAAGGREIABTODDDODDCIXRCPPPEGCAIEEEEESIAAAGGR...I

.U .C
0 n..
...... an.

1

1 0
0 0
.. 2
l

liflfi

283

i
*

it*fi*i*t**i*tifittii***t*****i******i

+ BETA*DMX)+(TETA*DXMX)+(OVEGA*DMXN)
0 TO 35

THO KINDS OF TRIPLE-ION FROM
MR TECHNIQUEvMULTIFLE DATA SET-CONTINUED

ititifiiii**fiii***i******i****ii****ii**itiititittfiiittfi

\I \I
F F
I I
D C ‘G
\l ..I T.
)1; t t ))
\l)1( 4. ‘1 M1
*11l\x 2 O, D-
C *(‘XX 2 ( to
N tXXX/ 0 ..U AC
A *XX/M nu ( \IHNC
*I/XXS.)+ UPoL
R *MWXM-M7(8RX1LHA
I ...—LVMXE 0+(XM(ATC
A *
Dust...
_ i
N t
O t
I ...
..
i
*
...
*
...tt

MQEX9EMX9EXMX9EMXM96AMAQJCAT

1.

F.
0 95
HH~)I
61.. 9
(x
0X5
TX 9
) )a-
Zone o
(600
X 31
VA) 9E
.2:L7
C 0P 9
‘Erflx

O).
MID

0.
0G

EAINTSEptrL

U

5
3

C e.u(U

0C .

039
36

M9EX9EMX9EXMX9EMXM9GAMA9UDAT

X 90
)4d
nu 0(
COT
41.0.
9CD

5E7”
€0.90
nUAHVrrU

EoTSE
U1J‘ o

7
3

o
U
4

23

ONEO-l) GO TO

345

..L

U U U U U U
..EE..nURUMhfiUUI‘E:NN:P(TNSSNN=(TSNNNNNNENNNNNNNNNNNKN
A 2 2 Arbum :D 2 ._ ZW...)DuIDAEAITITRIDPLATRIRIDH.IMRIRIRIihIRIRIP

«U 9 AU 1 0L 5

2

CL C r.

1 1;

FL E

HAAG 2 DP. ._ MXC12UTILTIHTIIUTITIMIUTUTUTIUTUTUTUTUTUTU

PTTER .. xXXML((TNSI‘IRNI\I\TNSIR(TNTNTN‘TNTNTNTNTNTNTD
LE.LMMwM MMMXAF,XEOPLFROOFFEOEROFF.O—LO.LOFEOEOPLOEOEOCOEMN.
AET:0.DDnUDDDCIXnK.PwRIUFCIIRCRdFIRCRPuRCIRCDucpcafirbRCRALRE

1; 1

7

5‘.

iiiitiiitt**********ii****it****i******************i

bNK CARD

S
D
R DE
DOA RT
...FRCDAAH
AAanCM“
CCYA I
ACVIT
DYVIR ASS
RAARVIRED
ARRAAR R
CRR RALA
AHASR AC

E

TAN].
LTTS ITA
- ...-.. $5.)» .17. a

“TROL CARD

0 CARD
tittitt*tiittttttifittit*t*****it****t***t*t*tiiittitttt

CC

IOCCFSKiaL 7
THNCIIID * Be

9

9 CARD

APPENDIX 2

DETERMINATION OF ION—PAIR FORMATION CONSTANTS BY
CONDUCTANCE MEASUREMENTS; DESCRIPTION OF THE

COMPUTER PROGRAM KINFIT AND SUBROUTINE EQN

A.' The Onsager Limiting Law

The Onsager limiting law for lzl weak electrolytes is

expressed as
A = d(Ao — s/Ea) (2A-1)
The ion—pair formation constant can be written as

— 1'“ 2A—l
KA ‘ __§_§ ( )
Cd Vi

which gives

I 2
— l+AK C
a = _E:_____A_:£ <2A-3>

2
2KACY:

in which a is the degree of dissociation of the ion—pair and,

Y+ = exp _ H.2Ol79XlOO/EE \ (2A_u)

50293 /E

3/2
(DT) [1+
(DT)1/2

281.l

 

 

 

 

285

In these equations A and A0 are the measured and infinite
dilution equivalent conductances respectively, 3 is the

distance of closest approach in Angstroms, and

S = 0””‘o + 5* (2A-5)
where
2
a* = _.___§_£_____
6DkT<l+q)Cl/2
3WnCC
and
2
8we NC l/2

K = (lOOODkT)
in which

e = charge on an electron = H.8032A x 10'10 stat coulomb

k = Boltzmann constant = 1.38066 x 10‘16 erg,m01e‘l,°K'l
N = Avogadro's number = 6.022OA X 1023 mole—1

F = Faraday's number = 9.6A8A6 x 10“ coulomb.mole—l
c = speed of light = 2.99792458 x 1010 cm.sec'l

q = l//2

molar concentration of the salt

0
ll

286

D = dielectric constant of the solvent
n = viscosity of the solvent in pose

T = temperature in OK

The values of physical constants were taken from Ref—
erence (218) and the dielectric constant and the viscosity
of methylamine at —lS.7°C were obtained from References
(194) and (219) respectively. A value of 5.3 A was chosen
for the distance parameter (Chapter III). The solution to Equa—
tions (2A—3 and A) was obtained by an iteration technique.
An initial estimate of unity was first assigned to y:
and the degree of association was calculated from Equation
(2A—3). This value of a then was used in Equation (2A-A)
to obtain a more accurate value of yi. The procedure was
repeated until convergence occurred. The ion—pair formation
constant and A0 were then obtained by fitting the calculated
equivalent conductances from Equation (2A—l) to the experi—
mental equivalent conductances. The subroutine EQN for

use with the KINFIT program is given on the next page.

B. Extended Conductance Equation

Various extended conductance equations have the general

form,

A=AO—S(Cd)l/2+ECdlog(Cd)+Jl(Cd)—KAA(Cd)Yi—J2(Cd)3/2
(2B-l)

a!

tit‘kttt‘ki’itttiti‘k

CCNDUCTANCE
iitii‘kiiiiftiittttiiiitii-‘ki

287
FOR

 

LAU

ONSAGER LIMITING

*ikiii‘k‘kii‘k‘k‘kiiii‘kii’itit‘ki’i‘kiiifi‘k‘ktii‘l’
*ii’t‘kii*iii‘hi‘kfi‘kiiiii’i‘kii'i‘i

PdPHRHFMLL?

1'

Dpvo C C
AYTT a CH. C
VTDD. \1 CO 2 C
0I90 90 CI / C
N 9TL \al CT. 1 C
98 9 9 1..." CU S... C
TPTT! 2V! 9 9 CL M* C
PESP ‘90)) CI 0) C
C 9X0 )PJ 9n;w D. CD Rf. r»
NR 9M 49’55 Y C TR C
9A1. 9 ((0(( T. CE SU C
FIAT XTlPY .1 CT CT C
C9VA yC(YY CI NA EC
NDGD 9EYTY CM AF CC
IIItU )V 9x 9 \I CI E NYC
VASE 9 0 9)R) 3 CF NP AC
959T O)O9U 1 CN T TM TC
PRO,» 310.): 9 CIT.“ E I“ CC
A 9.10 9GL30‘ 2 C NE RT A UC
LV 9N 4 9(5T 1 CTAI E... L CC
9AL 9 (nuT‘rr. 9 CATC TIT. KHC
TI 9.7T X7LCQNPU 1 C h...T1,-N.E.Mw rv 0C
NT. 95 T(XIL 1.. CENFOMAEXI. CC
I 9P~w XWWP 9M 9 9 CCOFIATCHI C
9T90 X99)S) U CWCFTRSIT TC
ESUC VI))nJT1u 1.. CA OAAANOTAAxaC
DIEF 9 9FJH§C 95 9 CTHCIPOP uIOrLC
AT 9?! TrdnU‘)‘ Q/ CCO C C IILC
TI 90?. PlvaLnUT 9 CUIYOF. NLTAC
lUVAErP. CLI\IPC C 8 CPUTITQ.C»LI AVC
9T9N J9UV(0 9 CNAISNI FRIC
[HP 9 H 9)FGTM 7 COM VIAPYOTUC
P. 907! T.T.nu 9.19 9) 9

TA 9E 9N01 9 anFC: IEnOTC C
NIMIV IK 90.) 9511.3 CN ACDLOHNHZL
Q. 9T1 9 //43C)(X 9 CER : ECF_0_.;C
ETIVHY TT((2{PXX4 CLIhENISICRC

N 909. DNXO(1RX 9 CAAEEUDIC UC

CVPNRleVITSC

. CI.AG:::FLLC
IKXY 9SFPO) 9co)6n/_E1~U r... r,

A 191—xv“ .lnlLIQAv—hu C
c l 7 8. "dc
C. hL

AL C
CCh..CCCCCnLCCC

)

.
)/(2.*U(2);XX(1)*(GAWA**2))
(

u

1)*(GAMA**

CwO
C Ch“

PV1L

\IAHA1(M.
ndI‘HnJTuA

+1_(E?.MRAT).U,O
E3 _.LCU\MF._)))FA.ECC_0 . X: oA(M.G.i50n

l

lO)GC TO 193

h.TTM(G((
QXXCORLTAIAHAAFix __ .—

RSC 9 9LVICCAUFZCDCGCJIM.NRPVRPXUDACCUUGACF.CAXXCAVCAHRACQGI\nhH.rUILCD;
C

 

288

tfitififi'kiiiifittiti’iiii**t*******i*itiii’tttiti'fiififii‘t‘liifi

*

0NS£GER LINITIU

G LAE FOR CONDUCTANCE-CONTINUED

*

tiiiifitttitiiit*itit.ti'tiii‘ti‘ktitti’t‘kiiti‘tiiiiittiiit'kt

7

,0

LY‘FD $054040 1‘
r" t x: ,A’I'JH’?

*4

rr M ’
O‘M
J? LA 0‘!”

(34>

Vim-429m >33”
r". 'U

021

Mb

0 5

In

HC

VA

0

xkflfir
c 1‘).

{'71. vx
Hmf'nx
")NOA
o N N

HCHT<-47H~4CNHC3 +
(Amml

—
so.

(

m m

U!

ONE-’1)

ac~4c4
:n I”:

R

‘0
'4’:

C
"1m

H

(T)

p.)

CCCCC-{CCCCALOOC

H rd
(N n) H
m P1 m

mHTUHXJHmHmH70H‘DXt-4D—4,V,‘HIU—-4DMDUHIJVTF. U;
C

("NC—IXNWDH 'annflninmnwnmnflnmfu U") xix—«nu?

zmomomomomomom‘nomomomoop11momx11>n

oqzqzazazqzazaazazazqzmHAmZAAAPD
cchcqca
2222224222322m22232224avHz?nmu

Q CARD

.OL CIHU

E CARD

TfiJT CARD

IQL ESTIVATE CPRD
A CARDS

«amt-*4

H

T
P

I
"T
i
L

NK CARD

M

9CAHD

l)-S*(SGRT(APG)))
GO TO 33

)

T0 45
)CANDoSTPEng ALPHA
a)

60 TO 2’

*ittfiit‘kittti’ifiti****itt*t*****i**fi******ii***i*it*i*t

*******************ttiititifiifiitttfiti‘hiiitttittit‘tit

289

in WhiCh E, J1, and J2 are the coefficients whic have dif—
ferent values according to different theories. Other sym—
bols have the same meanings as before. This equation can

be rearranged for use with the KINFIT program as,

AO—S(Cd)l/2+ECleg(Cd)+Jl(Cd)—J2(Cd)3/2

 

 

l+KA(Ca)Yi
where
-l+ Vl+uKACyE
a = ————2——‘ (213-3)
2KACYi
and
u 20179x106/EE
u = exp ' o/__ (213—4)
.2
(DT)3/2[l+50 Tii/ga]

The ion—pair formation constant and A0 can be obtained by
an interation technique similar to that which was described

in Section A. The values of the coefficients according to

different theories are,

 

290

(i) Pitt's Equation Linearized bx_Fernandez-Pirini

 

 

 

E = Ele + E2
E _ K2a2b2
l - 25C
E _ KabB*
2 1601/2
and
J1 = Ole + 02
2
_ (bKa) 2
ol - 12C [in n(——7§) + — + 1.7718]
* *
o — 3—53 + B bKa [0.01387 — 2n

2 ' 1/2 ‘17? “16%”
C 8C C

_ (bKaL3 [1.2929 + 1.5732]
03 — 6C3;2 b2 b

~w‘

 

2 2
_ 8*(Ka) B*b(Ka)

291

where

 

In all expressions a has units of gm. Other symbols have

their usual meanings.

(i3 Fuoss-Hsia Equation Linearized by Fernéndez-Pirini

E = The same as Pitt's equation.
J

_ (Kab)2 2 2
01 - —:flfiT—[l. 81U7 + 2Rn(* +—§(2b +2b-l)]

)
C1/2 b

 

02=d*8*+8*(

Kab
01/2)- 8*1601/2[l° 5337+; —+ 2n(——7—)J

 

 

 

2 3
b (Ka) u.u7u8 3.828u
o = ———————[O.609U+ + J
3 21:03/2 b b2
* b
on = 8 2i: )2 [— %(2b2+2b 1) - 1. 938”] +
2 2
8*(Ka) B*b(Ka)
“*B*(ET72) + 0 ‘ 160
2
(1.5405 + ELEZQl) 8* Kab [1* -2.2lgu]

 

b - 1611001/2 §5

 

292

i*******t*i*i***fi*******
i

CUCTANCE

ATIMEFORCON
*iiit*iiiitiiitti*tiii**********ii****i

plTTqS ECU

fitti‘k‘k‘kiflk‘ki*‘k‘k‘k‘k‘kiiti‘k‘k‘kii‘k‘k‘kii
*‘****i*********

*

DEIEO arr
DDRNKYGTN
RDAON 901:.th
rArMHWAN‘t :AK
CC BRLBP9

S 9U 9 920C -

NCAfiEATAOG
PdPHRHFMLL?

Us .

D
R
A
C

rt.

N

RD. 9 9 C O C

AYTT 9 C N I C

VTDD ) C 2 O T C

0190 90 C / I A C

N QTL )1 C 1 TI U C

93 9 9 1.( C ... U 0 C

TPTT 2V: 9 9 C t L F. C

FESP 9.0)) C ) I C

0 9X0 )0 '03 D: C E D E C

NR 9M 49.)»??? V- C P. C C

9AL Q. ((nUl\l\ T C U E WN nC

DnleTI XTIPY I C T T. AA C

CQVA XC(YY C A M. I LT EC

NDGD 9EYTY C R C N C CC

IIIIU )MV 9.x 9 \l C E I GU NC

VASE! 09)R) 5. C P N. F ND AC

9E 9T. 0’0 9C 1 CTN.” I N IN TC

pROb 3410):; Q. CNF. TI TIO «LC

A 9TB 9230‘ 2 CE?! RN 1C UC

LV 9N 4. 9(P3Tn 1 CI... EAT: V DC

9AL9 (3T1? 9 CCT TTA IN NC

T 97:]. XGLQVNO l CIPM ES L1 or

INT. 9C9 T(XIL l CFAHCLVVNE—t CC

I 9PMH XHD. 9M 9 9 CFTSAOCCFS C

97.. 90 VA 9 9’8) 0 CPLSIRCMNNCT TC

ESUC X))DIC 1 CONOA AIM ...uNNC

PEFQ 903295 9 CCOPPNTTSEOEC T

AT. 9T TOLfiLl‘)( 9 C C OCSTIILC C

T 905 D.(7JLUT 9 CV. NEIUIH‘HCTAC S 2 )

JXFC 0W(A5P P CTCICTCCEILVC / T 3%

9T QN J9UV(O 9 C11 KAN IFRIC \I D TY

END. 9 H9)FGTM 7 CVPYAMOECFTUC x / Dr.

Dr 907! TTnu 91$ 9) 9 CITTTRCSIENDJC E \I / t

AXFC EPC)EC)51 CTCISO RFOEEC t 3 )T

TA. 9E “0730 QNOI 9 “VCESIFTEE CC .u \I . 53
.NIMIV 1K onu) 95(5 CALOD NVEINDC ) 8 E 7.5
~.\ 9711.. 9 l/41v0)l.x 9 CZCLC RFNnUn/ZUEC ‘1 EA7. r31\
ETIXY T1((2€XX4 CHISNILICJCRC) )1 GIAO A/

N QDD CNY/Ol\lp\x 9. CCLCIOAAH :E UCl 2(\12*2 nUb
EUUQOSEI F09I93 CN(VIPVFA0TSC(23(X3¢AC 28
NO 9PYTROAV 9Tb... 9) 9 CA: I : ~IYT1LACT* *TXl‘fiunrl on».

IKXY0SFDO)95)62E1Q E E3 ECM)))NUBEJAECS**S(T5K7L8g
T 9TJN//Inu)l\nul(U/br022 .. UCA12SORQFZUEOJMnuNTTu....TIS(_L,DA(2
UNKXIVONNSOOSS‘ N..:::NNNN1NNCG(((IED 9 9: ..COUDORN(: 0/28
OONRJCOON3CT¢TOIEERKPIRI:RICoTTTzz:A2))CCSSCGC:AIEA:
EMUocvMME(3$ISTTPPANUTUTAUTCASSS))AHE12C::::SCAA(AHA
BMOXMYMMMP(N1N NAAVUTNTNMTNCMNNNIZPPo((CT23A::PP::PT
UONX 9YOOIOLOXOOOTTGOFLOECAPLOCAOOO((KL1XXCDTTTXAKKBD_L.L
9Cc9LYCCDFZCDCGCJINN?CRCGRCCGCCCUUEAEXXCSDDEEAEEABAE
123a 12345 C C

1 7 8 2C C

C C
C C

C AC
CCCCCCPCCCCCCC

 

1'

*‘k'k'ki

*‘k‘l‘k‘ktt‘k‘k‘kfii

-CONTTNUED
t******fitt***
**3)))*((1-

NCE
***
1))+((0-23484*BETA*

‘TA*AB*EKPA)/(8.0*EX))*

********tfi*‘kit*

NDUCTA

i*****
/(12¢U*XX(I)))*(ALOG(EKPAA/

/(6.0*(EX

293
*‘k'ki'i‘k‘ki-kirt

UATTON FOR CO
*************

 

PITT98 E8

***********i*****
**i**‘k***‘k**‘k‘kt

‘h

)M
NA.
R...
) TN
M Sr...
A (Dr.
G T
t 3 S
\l T 6*
1 D O)
I\ ,1) L1
X )(U) A‘
VA )Gw *U
i T/V.“ N+
‘1 nU)N 1 F.2d»
)1 SRAH 0 R O
M( ./TM .1 T1
AU )SA 31‘
6* Rtfi. C */5
*0 TIEQ/ T 7.7.13
) o S o) F.)
12 *lnh 0 ()0
(1‘ porn C #371
X/ A7A )t
X) *16 \1 Rio
i) 80. 0 THE
)F Enid. 1... ST
1F ’94.}. — *S)
((DN2.” E 8(1
UTHUE 0(AM 0 8* .

*RtRH7IMW o (2.
ZUQ)T5PAE12_JE
*oSlS(XGNo*)ENC

1'!

GO TO 2

‘2Equl,Ed2yDDQSTRENsGAMA9GAM

Eo‘l)

CARD

 

294

**fi**********i****************************t***********t

* PITTeS EQUATION FOR CONDUCTANCE-CONTINUFD *

**i***********iiii********************i****************

*********t***it***i***t**i**i*itittiit****i******t*****
CONTROL CARD

TI LE CARD

CONSTANT CARS .

INITIAL EST IMATE CARD

DATA CARDc

it***************t******iit**********ti***itfi**********

BLANK CARD
6

 

 

 

295

 

*

FOR CONDUCTANCE

EQUéTIOV

FUGSS-fiSIA
*iitittttiitttttiitttittiittiittittittit*ittitttiitiiii

*iiitii‘tiikiiiiitiiittiff*iiiitii***t*i**t*iiff‘kiiiiiit

*

nun... 9F 0
O‘HQNS
QKTI: o
CoFKQ 4
QM. 9 9 T
PJPLIEAJ 0F.
CDRNK.YGT.N
RRCNqoLRI
AAHaAN...” :AHK
CC BURT—BO: 9
cu 9U 9 9...”... o
r. r. (CLTLVJ. ..." r».

.., CLARK. LTAHCC u.

Plu.P.HD.\H.,FMH.LL7

RD. 9 9

.AVITT 9
VTHUP 9!

CI 90 90

N 9TL )1

9Q; 9 9 ll.
TPTT 2Y99
Burtr‘up 990))

fig. 9x0 )0 9n.n.\ Dr
NR 9M “2):”:4 Y.
9AL 9 ((O(( T
RIAHT XTIPY. I
C 9V.“ VAC‘YY
NnUGnC 9f._Y.TVu
1.1.1.0 )V 9X 9 \I
VASE 9 0 9)R) 3
9E 9T 0)nu 9P... 1..
PRO...» 31991.3 9
A 9T0 9230‘ 2
Lv 9N a 9‘5T 1
9AL 9 (UT-(P 9
T 97..T XZOQMAO 1
”I 9S T‘XIL 1
I 9PM“ xuwP 9M 9 9
9T. 90 X 9 9.13) 0
ESUC X)’3I.U 1
P??? 9 9002 9.5 9
AT. 9T T9..fi...l\)( c)
T 908 pl‘SLALT 9

.1»ch fi..uu(.ur.p 8
9T 9N ..u 9UV(0 9
CHIP. 9 H 9)FGTM 7.
P 9OT TTnu 9.13 9) 9
AXFC ED C)CC):,.1
TA 9F. MOQCO 9Nnul 9
NIMIV IK 90) 9c...(5
897.19 //a.&C)(X9
ETIXY TTI\(26XX4
N 90C DNXO‘IRX 9
EUU 9 955.... F3 9T. 93
.NO 9PYTCHON. 9T3“ 9) O

IKXV. 9$FD Pv) 95) bertlg

EMOXMYMMM Pl‘MNIuH

I...“
C O C
C N I C
C 9. 0 T C
C / I A C
C I T U C
C ... U G C
C t L E. C
C ) I C
C r... .b .rL C
C R C C
C U E UN C
C T T AA C
C .n as. I LT. CC
C R C N C CC
C E I GU NC
C P N F NU AC
CTN I N IN TC
CHE TI T0 CC
CET RN IC UC
CI... EAT .M. DC
CCT TTA IN «.....C
CTN ES LI 0C
CFAEMNEE CC
CFTSAOCCFS C

CESIRCNNOT TC
CCNOA AA NNNC
CCOPPNTTSEOEC
C C OCSTIILC
CY NEIUINCTAC
CTCICTFACFIAVC
CII NAN. IFRIC
CVRYAMHOECFTUC
CITTTPCSIENGC
CTCISO RFOEEC
CCESIFT....=.CC C
CALOD NVE:NDC ) rL
C:_.LC RENCECEC ) 27
COISHILICIUCRC \l )1. XiPJ
CCDIOAA :E UC21232()Q..A—L*2
CN‘VIPVEA QTCuC* (* * (quzA/CO
CA: : : .IYTILAC...T* *TX( airmail

Ac
Tu
ml.
03
I
)
I.»
.

E8)*EX)/FDT

{LCM ))\INUBEIUAHECAHSTTS(T.AUPC V 7

T 9TJNI/Ird)(01(U662n/. UCAIOL300.LBESMCMNJDDNTSSKKF.6
UNKXJONNSCGSE‘ N::::NNNNINNCG(((IED99::CAOSSCRN(EE:o
00M?JCOCV50T(TOIEERKRIRI:PIC9TTT:::A2))CGC::CGO(::2I
RVU99.MV§(3SISTTPPANUTUTAUTCQSSS))AHEIZC::23:SC:ACC(

NAAVUTMTNMHTNCMN4NM412PD: 9((CMTTTA: 29.9 0.9 :

DUONX 9YOOIAULOVAOGOTTOOF.OEODHFOCAOOFJ(I\KLIXXCA—UDWLTXAKKKKB

. .SC 9 9LYCCH.FZCDCGCJTNNRCRCSPC

«A. «In/:34. In....2.4.3
Pb

L ,

CGCCCUUEAEXXCGSSSF.EAEE:.:..A
C C

2pc

C
C C
C C
C C
CC CC PVCCC CCCCC

 

*

COKDUCTANCE-CORTINUED

296

EQUATIOK F3“
*i******i***i*t****tiiifiiifittitititi**ii**titt*tittt*ti

i*‘ktiifiiitttfiititiitt*tttitttitttititttttiittti‘ittttttt
FUOSS-HSIA

*

I \l
i / 1 ) ...
\I l 8 6 a. 1
\I D 4 7. c. ...U
3 O 7 n4 1 PL)
* 4 4 ) o 2 ()
.- ( o 4 2 o ...nu
E + 4 8 l‘ 0.. ‘1.“
EU 7 4‘ 7C + o )6 o
I\ 5 + 9. _.5 \I Nu...
I ~J a. O nJ \I \I EN
0 Cu O, 1 4 5 ML RE
0 O 0 n 5 P... A TR
2 1 (D ‘1) o * Pu Tu ST
1| l\ O Bad-I. 0 * TI (8
l‘ * 0 BC‘ 0 \I D 6*
+ 2 ( 89* 3 1 S 0)
\I E i i“) l\ 1| .9. L1
‘1 l\ \l )Ez I x )6) A‘
0 C - nU )iC 0 x )6“! i U
o P \I 0 73A; 0 * Tl/E N‘
1 K C) a *TV. .44 \l 0)“ 1E...
. E D.) 2 *EE (4 )1 SPA «URU
) ( K) / EP( (C M‘ [TM 1T.
8 G E) ) B(* *1 AU ’85 91
C... rU *C \l I\ +\l )7... Gt Rte 0*(—:
i «U II. AP 2v [‘.an ’.9 *0 T5,, TIE/3
n... .0 A ...IK i nUC 0 21v ) o S a) F.)
.2...) 4 o .- EE 1 ) .Prc (a. 12 *1A 0(30
2712x4446 aw. ...Ll‘nLS )_,/..K.1. “SQ (ls Ag»..- Pa... )T
(QTT/l o (GGP)(E/ ’16 XI A7A )3
+<VEE)/ 2 +01K2‘i’ ’21 VA) #16 ’R*n«
)ltad)’ l\ )LZFLt‘AHE 2.72 i) 83. NUT-*6
\I)T+r/“A .9 AHA+I\**TB E24 ‘15.. E2...“ 18R \l
253)...T2 7 T*)*3)Et *4) IF. )945 ......) 2 )
tES)*EE a. En;))P1D...A AG) ((DNZ . N £881 1! 1..
_ *5(2C..C..+ .1 ..h 0221\EtT 7.12 UTDE 0(A Ce..(. X .
94/(Bt) 8 tnnt‘t/iAEL [77‘ *RtRU(MH 3|... o X o
L..C6U(B) o A(U*4AH9 E+U CG)T5PAE21.2E . E
(zgttfiz 1 H+fiE9TP( (It oSlS‘XGNto)JNC C N
t-4A21( ( D)l?2§L( (43 4+(((E(AtT2EoL L o
Humia OHCCU * L)f0(80uahl\ (GFJPLI\rUXT+ ..(haAHG‘leAH SLAM 9L FL. PLH ...C. E E P?” rr.. 7L
£0‘2Pp0t 1 ACI(0((. .IIU+0XROUSAM.U.TC UC U U UT U U U U U U
/nL:8.LKV\1 C (92‘s....2 :wLZNOl:r& .. oEbGAT()E:Pu\:k\hN\NKE \N huh...\.\kxh..n.r\NK

El...» : AEEE
A : HA((((
.7509. : : : :
D...C..LES1..2E
EEABSFPEL

:) : ... (21.123sz : (I o . NSIM ”A :65 : ..uv )PV;DRIRIP\IM RIG 1.9 IKIRIRIQ
1):? ..3+a44)44:TlfruzffizA:chEIn. UTIUTUTUTIUTUTUTLTUTUTU
695olG)GGG)GGZN::RR:NTMM(LR((TNSTNTNTN‘TNTNTNTNTHTNTD
IQLISJIBIIIBIIJOFDJTTGAAAAFATFXEOrrhanEOPLOFrho—LOEOFCOEnurgOrT ....
252(EZEZZZBZZECFUSSGGRGGICCLIX KCQRCRCRCIRCRCRCQCRCQ C71...
1 1 1

1 5 3 a. 5 3 q 0 1 2 3

nau 3 hi— 9... 1 1 1

1..

CAR;

—¢.—.:y;fi.":_ ‘; _'_ F- ' _ , _. _7 <_ h, _,

297

*ik*************ti’i‘ktii‘k‘k'k'ki‘k‘k‘k*iiti********i*i****fiwt*

* FUOSS-HSIA EQUATION FOR CONDUCTANCE-CONTINUED *

iiifitti***********’k***i'k‘kt‘k'k‘kiii'iitttkttfi***i***iifiii**

I»

iiii******t****it‘ktiiiii*i‘titiifitti‘kti‘kitttt‘k

H—«Immt

we 01>» O 1*

fiébrznr*
X”

TD-IO'SU 41>
Hill C"
:0

'4!)

ATE CAR]

*i'k*i’*‘kiii’iiiii‘ki‘ki’it‘kiiii*****************i*

r" 1} T’T‘IQH’D *
‘.":v #- "QHETH? “

Zibflmrd*
-UtCJF'T 110*
5.3 :U‘ '10??? II-

$$tUHOdO$
XI-

...
s

298

(iii) FUOSS-Hgia_ Equation Corrected by Chen

 

J1 and J2 = the same as the Fuoss—Haisa equation. The

term EC lnC is replaced by

2

ECan = 12 O £n(Ka) - B u £n(Ka)

 

 

 

to satisfy the Onsager reciprocal law.

 

(iv) Justice Equation

 

The equation is exactly the same as the Fuoss-Haisa
equation except that the distance parameter is taken as the

Bjerrum distance,

 

The subroutines (EQN) of the conductance equations for

use with the KINFIT are given on the following pages.

t
i

FOP COMDUCTANCE CORRECTED

299
(OR JUSTICE METHOD )

ECUATICE

hY CHEN

*iiiiititi****iitiiit*ttttttttitttittiiit*tiitt*t*itttt
FOUSS-HSIA

tiiitit*********i***************i***i*tii‘kiiiitit‘kttiii

'k
*

AKTI: o

C QFKR a.
RN00 T
DEIEOoF
DDQNKYGTH
RRON ODLPI
AAHWQK.‘ :«kru.
FCC ERLBP 9

SOU’QtDo
pt, at?” LT. LN 01..» fl...
...... C .p A E e.u.—l A» 6...»...
PJPHRHFWLL7

.hr

RPQ! C C C

AYTT Q C N I C

VTDP ) C 2 0 T C

OT. 00 90 C I I A C

N ...-VI. )1 C 1 T U C

OS I Q. 1‘ C .1 U G C

TPTT 2Y9! C t L E C

PESP 090)) C ) I C

vao )0900 P C E D E C

NRQM 42)55 Y C 9 C C

CAL, ((0“ T C U E ”N C

RIAT XTIPY I C T T AA C

CQVA XC(YY C A M I LT EC

NDGC 'EYTY C R C N C CC

IIIJ )VQX’ ) C E I GU NC

XSE’ 0 O’R) 3 C D- N F N0 AC

QEIT 0’090 1 CT” I N IN TC

PPOA 310’s 0 CHE T1 T0 CC

AQTD 9233‘ 2 CET RN IC UC

LVQN 49(5T 1 CI* EAT M DC

OALO (OT‘P 9 CCT TTA IN NC

quT X2SNC 1 CIN ES LI 0C

“IDS T‘XIL 1 CFAEMNEE CC

IOPN XNPQH’ 9 CFTSAOCCFS C

QTOO X99)S) 0 CESIRCNNOT TC

ESUC VA)\Inv.InU 1 CHVNOA AHA NNMHC

PEFQ 000295 9 CCOPPNTTSEOEC

ATQT T20()( 9 C C OCSTIILC T 2
T908 P‘SLUT 9 CY NEIUINCTAC D T
dYFC CUCASP F. CTCICTSCEIAVC S D
QTON d9UV‘0 9 C11 NAN IFRIC I 5
CUP! HQ)FGTM 7 CVRYAMOECFTUC ) /
PQOT TTOQISQ}Q CITTTRCSIENQC X )
AXFC EP3)EC)51 CTCISO RFCEEC E 3
TAQE M0309N01! CCESIFTEFCC C t .
NIMIV IK90)95(5 CALOD NVE2NDC ) E
GoTlo //43O)(X9 CzEC RERCZOEC 8 7
ETIXY TT“26XX4 CUISNILICJCRC ’ )1 E Xig
NVCD DNXO(1RXQ CEDIOAA :E UC21232()9LE*2
EUUOQSEI F09193 CN‘VIPVEA9T5Ct(**(X320/C0
NOQPYTRON9T39)9 CA:::.IYT1LAC*T**TX(othpl
IKXY!SFPO)95)62£10 E EC ECM)))NUBEJAECASTTS(T8PPK7
T oTJN//10)(01(U6622 U U. UCA123OQEBESMCMNDONTSEKK56
UNKXJONNSCCSS( N::::NNNN1NNCG(((IED99::CA0850RN‘EE:o
CCNQJCOON3CT(TOIEERKRIRI:RICoTTT:::A2))CGC::CQ0(::21
RMU99OMMF(3SISTTPPANUTUTAUTCASSS))AHEIZC::23:SC:ACC(
fifloanMNNPCNlN NAAVUTNTNMTNCMNNNIZPP9((CMTTTA::PDPP:

DUONX9Y0OIOLOXOOOTTOOEOECAECCAOOO((KLIXXCAUDDTXAKKKKB
PSC9QLYCCDFZCDCGCJINNRCRCGQCCGCCCUUEAEXXCSSSSEEAEEEEA
C

1234 12345 C
1 7 8 2C C
C C
C C
C C

CCCCCCCCCCCCC

300

*
i

80 )-CCNTINUED

EQUATION FOR CONDUCTANCE CCRFECTED
(09 JUSTICE METH'

FY CHEN

FOUss-HSIA
**u*********tii*tfi*********i********i*i******ttttt*****

*i‘iti't‘kii'iiit‘ktiti‘kiiittiiiii****i******tiii’i’itittttiti

i
'k

)
I \l \I
i l 1 \I \l
) I 8 6 4 3
_ ) C 4 7 9 t
\l 3 O 7 n6 1 i
0 t 4 4 ) o 2 R
O t l! o .4. 2 0 TI
2 B + 4 8 ( 2 S
1 ...C 7 l\ 3 .7 . l\
l ( 3 + 9 5 ) t
) I 3 4 o 0 ) ) 2
\l 0 5 9 1 4. B M. [U
2 o o 0 . 5 B A E
( 2 1 6 ))o i Q 3 (
U ls l\ O 921 0 t T .-
t)( * 0.8C( o ) D )
)0+ 2 ( BP.‘ 3 1 Q» N
A.) E t *K) ( ( i, E
Pa.) l\ ) )EZ I x )6) R
0 K/C . 0 )*C 0 x )6” T
o E); \r o Infinp o t TIE S
1 ()K C) 4 tTK “a ) D)N 1*
. GAE DI) 2 OEE ‘4 )1 SRA 01
) 0P( K) I 88( (G "( ITM 1d
may LKPJ E) \l Bl\* *1 AU )SA E)
R. AEnC *C \I (+) )2 Gi R*G O()Eu a.-.
i .U *I:L AD..J /\8u )+ .0 715/ 7l+Mlu 2
«U DB’s-uh TK * 0c 0 23 \I o S 0) CA
03) 4020* EC *’0P6 (4 12 *1A OEGO O
2TAA?E*LC E(r,¢h)2vr1 U54 (( A0,”. 5+ ...T. T.
(DTT/liAo (GGP)(E/ IIG X/ A7A )N
+SEE)/Bi2 +01K2‘t) ’21 X) *16 ’REO 0
)/*8))BB( )LZE*(AB 2+2 *) 83. OTRG G
))T+2A(B+ AAO‘ttTE E2+ )F E2“ IST )
253)*Ttt7 T*)*B)Et *4) IF )945 .t5) 2 )
*FS)*E)A4 E0))BIBA AG) ((DNZ—N E811 ( 1
*:,.I\n/_Q...EALD.1 D. 022(E*Tn T12 UTDFH I‘A OS). x .
9.4/(Dirt *K8 ind‘t/iAE EZ‘ *RiRnU‘MuHH 0‘1 0 VA 0
BOEU‘BtE. A‘thAHB B+U 0G)T5PAE21.(E . E
(28*t8At1 H+*58TP( (1t oSlS‘XGN*0)UNC C N
*04A2tPX( P)152EL( (43 4+(((E(A*T2(0L L o

AGQOHCCKgi L)G(BPA(

ABII‘ Ol‘l‘.

(GGECCXT+:(MAG(+HA EA E E EH E E E E E E
A.(2PPPE*1 .IIU+.XR0USAM¢U0TC UC U U UT U U U U U U
/2:8LKK(AE (82(3::: :22N01:QoEBGAT(0E:NNzNNNNNNENNNNNNNNNNNNN
B(A:AEE(T:):*(:(123)4:(Io.NSINA:GA:1M)RIDRIRIRIMRIRIRIRIRIRIR
A:HA((((E1)2U:3+&44)44:Tl‘F:(A:AzPCCI2UTIUTUTUTIUTUTUTUTUTUTU
:BPT::::BGBGolG)GGG)GG2N::RR:"TMM(L/((TNSTNTNTN(TNTNTNTNTNTNTD
BBLESI2C(IEI$JIBIIIBIIJOFDTTGAAAAFA FXLOEEOEOEOFEOEOEOECEOEOEN
Run/A95EEE(7...5Z(F_ZBZZZBZZECF DSSGGRGGIC IXRCRRCRCRCIRCRCRCRCRCRCRE
l 1 1 1 1 1

1 5 3 4 5 5
0 3 2
1

9 0 1 2 3
1 1 1 1

CADD

--.=.-. .‘._.-~. -.‘.--«v'.

 

301

*ii*****t*******t*t***********i***********************i

* FOUS§-HSIA EQUATION FOP CONDUCTANCE CORRECTED *
* :Y CHEN (OR JUSTICE METHOD )-CONTINUED *

********i**t******tit*********************i**********it

**i*************t*****iti*****i*i*****iitit*****i*t****

COETROL CARD

TITLE CARD

CONSTANT CARD

IfiITIAL ESTIMATE CARD
OflTA CARDS

******it*****it****ii***t********i**************i******
ELfiNK CARD '
6 .

E
9 CARD

 

 

 

APPENDIX 3

DETERMINATION OF COMPLEX FORMATION CONSTANTS BY
THE NMR TECHNIQUE; DESCRIPTION OF THE COMPUTER

PROGRAM KINFIT AND SUBROUTINE EQN

A. lzl Complex Formation in Media of Low Dielectric Constant

The equilibria involved in a solution which contains
equimolar concentrations of a salt, MX, and a ligand, C,

in a mdeium of low dielectric constant can be written as,

M+.X‘.M+
++ Kt
M+
K +
M+ + x‘ 4p M+.X' + X K+ X'.M+.X1
+ +
(3A-l)
c 0
KC M '++ KX
MC+ + x' E? MC+ X—

in which MC+ and MC+.X_ are the 1:1 complex and the ion-

paired complex respectively. The other symbols have the

302

 

303

same meanings as in Appendix 1.

The equilibrium constants for these reactions are

(M.x)

 

 

 

 

 

 

ip = <M><x>vi (3A-2)
Kt = (iiefi i; = égigiflg> (3A‘3)
Kx = z§¥§S§c> (3A'u)
‘KA = (M(CM)C(.XX))Yi (3 A_ 5)
Kc = (%%%%7 = Kiifx (3A-6)

in which the activity coefficients of M, X.M.x; M.X.M are
considered equal and the formation constants of the two
kinds of triple—ions are taken to be the same. The mean

activity coefficient is expressed as

 

 

 

 

6
Y+ = eXp (-u.193:AxlO 5g<:;o+/:xwx: )) (3A_7)
’ 3 . a X + XMX
(UT) [1 + 1/2

(DT)

30A

The mass balance and charge balance equations are,

3
II
C)
II

(M) + (M.X) + (X.M.X) + 2(M.X.M) + (MC) + (MC.X)

t o
(3A-8)
Xt = C0 = (X) + (M.X) + 2(X.M.X)-+(M.X.M) + (MC.X)
(BA-9)
Ct = C0 = (C) + (MC) + (MC.X) (3A-lO)
(M) + (MC) + (M.X.M) = (X) + (X.M.X) (3A-ll)

in which M X and Ct are the total concentrations of the

t’ t’
cation, anion and the ligand, respectively. The solution
to the above equations can be obtained by an iteration
method based on the major species and successive corrections
for minor species in solution. If we assume that (M),
(X.M.X), and (M.X.M) are small, the major equilibria are,
Kx

M.X + C 2 MC.X (3A—12)

and

KA
MC + X it MC.X (3A-13)

The mass balance equations can be written as,

(MX) + (MC) + (MC.X) = cs z CO (3A-1A)
(C) + (MC) + (MC.X) = C0 (3A-15)
(X) + (M.x) + (MC.X) = cg 2 CO (3A-l6)

305

This set of equations yields

 

(MK) 2 (c)
and
(X) 3 (MC)
Then
Kx (MC)(X)yi ~ (MC)2yi
KA (M.X)(C) (0)2
01”
KX
(Mo) 3 (C) ——2‘ (3A-17)
K Y _
A i
and
(MC.X) = KX(M.X)(C) = KX(C)2 (3A-18)

Substituting for (MC) and (MC.X) from equations (3A-l7)

and (3A-18) into Equation (3A-15) gives,

K
x
2
KAY:

 

(C) + (C)

 

 

306

which can be solved for (C),

 

 

K Y K Y
(o) . A i A l“ ,_ (BA—l9)

 

The concentrations of the other major species are approxi—

mately,

are known.

 

 

(M.X) 3 (C) (SA—20)
K

(X) 2 (MC) = (C)‘/ X2 (3A—2l)
KAY+

(Mc.x) : xx(c)2 (3A—22)

Now the approximate concentrations of the major species

To correct the scheme for the minor species, we

utilize the exact mass balance equations.

Let us define

(M) + (XMX) + 2(MXM) = A

(3A-23)

(M) — (XMX) + (MXM) = A'

 

307
Subtracting Equation 3A-9 from Equation 3A-E gives,
(M) - (XMX) + (MXM) + (MC) - (X) = O (3A-2A)
and subtracting Equations 3A-lQ from Equation 3A-o yields,
(M) + (XMX) + 2(MXM) + (MX) -(c) = 0 (BA-25)

Substituting A and A' from Equations 3A-23 into

Equation 3A-2A and 3A-25 gives

(X) = (MC) + A' (3A-26)

and

(MX) = (C) (3A-27)

I
D

if we define

(C)' = (C) A/2 (3A-28)

and

(MC)' = (MC) + A/2 (3A-29)

Equations 3A-26 and 3A—27 give,

(X) = (MC)' + A'/2 (BA-30)

 

308

 

and

(MX) = (C)' - A/2 (BA—31)
Then,

K 1 I

MA = <MX)(C) = [(C) -A/2][(C) +A/2] (3A_32)

[(MC)'-A'/2][(MC)'+A'/2] 2

x (MC)(X)~{:

This equation can be solved for (MC)' as a function of (C)',

 

K K .
(MC') = ‘LA/2)2 + ——§§(c)'2 — ——§§(A/2)2 (BA—33)
KAY: KAY:

Substituting for (MC') in Equation 3A-26 gives

 

____ ' 2
K K v+

(MC) = X2 (c)' 1J1 — l 2[(A/2)2 - —%—L
A + (C') X

‘ (3A-3A)

(A'/2) -(A'/2)

 

 

(MCX) substituting for (MK) and (C) from Equa—

Since KX = (TDCYU77’

tions 3A-30 and 3A—31 gives

(MCX) = KX [(C)'2 - (A/2)2] (BA—35)

 

309
Rearranging Equation 3A—28 gives
(0) = (C') + A/2 ' (3A—36)
Now (C), (MC), and (MCX) are expressed in terms of

(C'), A, and A' in Equations 3A—3A, 3A—35 and 3A—36. Sub—

stituting these values into Equation 3A—lO gives

 

 

c0 = (c') + (A/2) + R(C') — (A'/2) + KX(C')2 - KX(A/2)2
' (3A—37)
where
2
K Ky+
R = _—§§ l — 1 2 [(A/2)2 - —%—:(Av/2) <3A-38)
KAYi (C') X

Equation 3A-37 can be solved for a new (C)' as a function

of R (or old (0')),

 

= -<1+R) + VIIiR)2+AX[Co-A/2 + A'/2 + KX(A/2)2]

 

(C')new 2Kx
(BA—39
Then from Equation 3A—28 we have
= ' A (3A-40)
(C)new (C )new + /2

 

310

and substituting (C')new into Equations 3A—3A and 3A—35

yields

 

 

K K
_ , l
(MC)new —‘/ X2 (C )new \/1 — (—c—'2— [(M2)2 — fim'mfi

KAY: )new
— (Av/2)
(3A—u1)
and
(MCX>new = Kxnc')new — (a/2)2] (3A—42)

The new concentrations of (C) can be used in Equation 3A—27

to give
(MX) = (c)new — A (3A—u3)
Then the concentrations of the other species,

new’ (XMX)new’ and (MXM)new ’

can be obtained from equilibrium constants (Equations 3A—2

to 3A—6) as follows,

 

311

 

 

( ) (MCX)new ( A“)
X = 3A-
new 2
KA<Mc)newY:
(MX)
(M)new = new 2 (3A_u5)
Kip(X)newY+
(XMX)I’18W = Kt(MX)new(X)new (3A-L‘6)
(MXM)new = Kt(MX)new(X)new ' (BA-A7)

The new value for the mean activity coefficient is,

6
—A.l976AxlO
) Qinew

 

 

 

(Y new = exp (3A-A8)
: 50.29X5.3 ‘F
(DT)3/2[l + 1/2 new .
(DT)
where
Inew = (X)new + (XMX)new

= (M)new + (MXM)new <3A-u9)
The procedure for the calculation of the concentrations is
as follows. Approximate values for (C), (MX), (MC), and

(MCX) are calculated from Equations 3A-l9 to 3A-22. These

312

values are used to calculate (M), (MXM), and (XMX) from
the equilibrium expressions for Kip and Kt' Now approxi-
mate values for A and A' are obtained from Equations 3A-23
and 3A-2U which are then used to calculate (C)' according
to Equations 3A-28. The value of (C') is then used to cal-
culate (C')new according to Equation 3A-39. Then improved
values for (C), (MC), (MCX), (MX), (M), (XMX), (MXM), and
Y: are obtained from Equations 3A-UO to 3A-48. These new
values are used again to calculate improved values for

A, A', (C') and so on. The procedure is repeated until
convergence on the concentrations occurs. The converged
concentration are then used in the chemical shift equation
to adjust thermodynamic parameters. The converged values
were tested to insure consistency with the original equa—

tions. The temperature dependence of the equilibrium

constants can be expressed in general as

_ o
e AH /R l _ 1

( ) (BA-50)
T TRef

KT = KRef

in which K and KRef are the equilibrium constants at TOK

T

and at the reference temperature (TRef = 298.150K) respec—

tively, and AH° is the standard enthalpy of the reaction.
The temperature dependences of the chemical shifts are

expressed as,

a = 5' ) (3A-51)

T Ref + b(T — T

Ref

313

in which 5 and 6 are chemical shifts at a given

T Ref
temperature T, and at 298.15°C respectively and b is the
linear temperature coefficient of the chemical shift.
Depending on the problem, equilibrium constants, enthalpy
changes, chemical shifts, and b coefficients are used as ad-
justable parameters (U(l), U(2),...) or as constants (CONSTS
(JDAT,l), CONSTS(JDAT,2),...). The FORTRAN expression for

the above solution is given on the next page.

B. 2:l Complex Formation in Media of Low Dielectric

 

Constant

 

If it is assumed that the lzl complex is completely
ion-paired in a medium of low dielectric constant, then
the equilibrium involved for the formation of the 2:l
complex, M02,and 2:l ion—paired complex, M02.X, can be

written as

K
MC.X + c $2 MC2.X (3B-l)
KA2
M02 + x 2 MC2.X (3B-2)

'The mass balance equations are

3
ll

(MC.X) + (M02) + (MC2X) (3B-3)

><
ll

(X) + (MCX) + (MC2X) (3B-U)

i
i

3114
FROM NWR TECHNIQUE
*i******i***kittititttttiittitttt*tti*tiiitttiittttittt

MULTIPLE DATA SET

itattittttiiiaittttttitiitttt*tttii*****i*t**i*iitttttt
101 COMPLEX FORMQTION

*
i

o
I
LoK
E0:
A64

INFT“.

2LT
DA 9F c
RH4N3
AKTI: o
COS-KR 4.
DANNQQ, T
DEIEOQF
DDRNKYGTH
RRCNQDLRI
AAHNpAWWt:AK

CC BRLBPQ
SQU$9:Do
C”..CaLTLM.nD.firb
Amounn “firth. Tr... ..Urt ,
PJPHRHFMLL?

RP 9 9
AYTT
VTDP
OIQU
NOTL
9599
TPTT
PESP
09XU
NPQN
GAL!
RIAT
CQVA
N060
IIIIU
VASE Q
QEOT
990A
AOTD
LVON
CAL!
T QZT
U195
IQPN
QTOO
ESUC
PEFO
ATvT
T905
dXFC
OTQN
[UPI
P90T
AXFC
TAQE
NIMIV
QOTlO
.LTTSAY
NQUD

9

)

9n»

)1

1‘
2Y9!
Q. 90))
)0 900
42x15r3
((0“
XTlva
VAC‘VIVI
OEYTY.
)V 'x '
0 ,)R\I
8,090
I..1..U)5
.230‘
49(5T
(\UT‘P
XZSNnU
T‘XIL
XNPQM’
x 9 9’s,
X))GUIC
9002 95
T2rhl\\lt\
P‘SLOT
CU‘ArJD.
.U ’UV‘O

H9)FGTM
TITO .IS "I 9
EP0)EC)51
MOSLQVOI'
IK90)95(5
[/435)(X9
TT((ZEXX4
DNXO(1RX!
EUUOQSEI FOOIQS
NOOPYTRONQT89)Q
IKXYOSFPO)!5)62ECI
T QTJN//10)(01(U6626 U U

ITYP

7,819,10911912913)

NTtTEMPERATURE)

CCCCCCCCCCCCCCCCCCCCCCCC

X

E
Lx
pE
ML

T OF
N CH
AT 0
TNIC
S‘-
NTll
OS 0
CNFl
00
NC F
0 N0
IND
TOIT
ATTN
MTAA
RANT
CMRS
FRGN
CFO
NF C
0 R
IRIN
.IAO
EAPI

CIEELQLP.T
CFPPE/P.NA
CFMMIIINOM
CESEDiROIR
Cn¥ll(tT;1 0

CC : :
C )E)
CY1C2

CTQNO

CITET
CVARA
CIDED

E E 0 ECTJFJ
UCC(E(

UNKXJCNNSUOSSC N::::NNNN INNCASRS
OONRJCOON50T(TOIEERKRIRTU:RIC:T:T
RMU99QMVE‘3SISTTPPLNUTUT:AUTCASFS
BMOKMYMMVP‘NIN NAAVUTNTNSMTNCMNEN

12,04

DUONXQYOOIOLOXOOOTTOOEOEOTAEOCAORO
RSC9OLYCCDFZCDCGCIJNNRCRCIGRCCGCTC
12345 C

2C

C
C
PL

:2FF

F
T 0
T S
5 N
C
X :4 I
E 1 T
L o C
P 8 N A
M 9 C PS
0 2 1 FE
CT T I
T A EC
lTA R SLE
0A T "OP
1 x N OMS
Fxc E I:
CC” C TA
M: N AG
T:C 0 RE
NC+ NC TN
A+X 0 NO
TXM IX E!
SN N TC CA
N FX 0 AL NT
Orr-CC I Rh..- 0......
CC MNT TMNCZ

T20ANNOO O
NTNCIROECISA
OVHAH+ TIT-.....C TNT

TTSMREAOoRIT
ASH TCRCIT.’
"NCFNNT NEA
ROCOEONXDELT

))0 50C CCEEECPL
34 RIF NYN CLRNIE

QOYIO

NIPOP“PIORD

TTPABROTLCIOMACTO
AALFglIAA ACOP :A
DEA-eATyHCP C.NXT

JJHN

PARTNcN NONE

((TOT.HONANOICTXB
SSNIANRFEGCIoITEQ

TTE:
SSZ)
NNAI
OOH(
CCDU

00::IIN13A9A
IF))L:A:XCMH
: :34 2 x..cc: XP
AX((CMXMMMML
PPUUEE~LEFE7.A

CCCCCCCCCCCCCCCCCCCCCCCC

315

' . ___.'- ...-~- - _

 

 

 

 

 

 

 

 

*
'k

NMR TECHNIQUE

MULTIPLE DATA SET-CONTINUED
iii*******************tt*i*t**t*i**t*****i**********tt*

*******t**********£*************k********i*ti******t*t*
1.1 COMPLEX FORMATION FROM

”k
i

C
I F C
. C C
E C
L T C
F XF C
NR I CI C
00 R LH C
I T PS C
TR M C
AI C 0L X C
CA I CA E C
P N C L C
E. 0 II P C
EN I 0M M C
R0 N 1E 0 C
FINA H C C
0 XDC C
FFIFEE I C
00.0LRF o C
E PIO I C
TTLTMA TC

FFPFOPT FFC
IIIIC.NXOIC
HHRH NEE HC

LLCLI IMILC
AAIA FFOTAC
CCNCFOFCACC
11.2.0710 E FTC
MMIM TCITMC
EETETFCoNEC
HfiAHFI IEHC
CCCCIHE CCC
:: :HSRDN C
I) )S UEOUC
56 7 LTRCEC
Q9 9LAAI VC
TT TACRALRC
AA ACIEPAEC

DD DIMP.TSC1*S

00o0/U(1))))

1.0/TREF)

(JDATQI)

T
7. u

0
TI

0

FMATTO(()G
EEOAA1((M)
RTJDD‘PPAO
285T/(JJ+XXGO)
*Tl-OS((OEE*CA

.TSS C((A OHAX

*XXTl)

)(
0T
0R
CG
05

dd dMEMNOEC+AN8MlSTTGt*PE(AP2CE+
(( (EHEOTOCSMO9E(NSSE))(LT+ttALB
SS SHCTI::CTAC2T:ONN813/0R00*+oAC*XPPXPN(:E/0¢XR*0(U*+0(CE/UotRPC
TT TC:: )ICIG:::RCOO3((XAQooBDH.ECE::M:I:TDQ
33 S:)) 12C::PFFP:CC:UUPHSIQAAH(:E:XXEMTTP(CIO:SAIX4DUD::(CIGA:XE
NN NC25 ((CSMMEIMT::A:::(:::::(:X2CCM:XNLL:::(8:::::::(PN:::(:CC:
00 OM(( XXCTAERDEDTIHAXAFABCCHFCMXMMXMMOEEABDFBARABDCEFCCAEEFRMHMX
CC CDUU XXCIGTTTTSPPDDC:HIAAAAHIEEEEEEEECDDCCGIHARDDDDCIEECCGIREEE

C
C
C
C
C
C

CPXLCFFXLCPKC

(EC**2)

EMX*EX
I*EX*G$M)
MX*EM

ELPT**2))

)/2
.0
(D

*X)

GMM

OEA

2(6)
(**2
+)A*
)XP *
VflMl‘)
MX‘TI
XE(L
E(-E
+)2.
)Mic

ME*EBOPHQR.X
ik(tEE(T(CE((SR)P2DED+T(CES**I
XT/TU((L(-L/T(+l**DL_PL‘.L‘RXX

l
0
1L

7
...g

0
TI

0)
GM
)A

\I
\l
D
6

CPU)‘
.*BT.
CABR

oDFGA

DELT+DELPT+(PX*(DELT**2))

*DB

PA*GAM)/PX)*(DELPT**2))
)**2)

)

)

X

P

t

C

O

2
71‘
Z/

)
0)
TE

5 (T
0‘ (L
GT (E
)R .C
SGT).
.SL2N
0+EtC

.AD*EB

oXoACE‘EDA

(DELT**2))

T.
P)
L2
E*
Di
-\l\l
)TM
)LA
TEG
)LCt

O)E—C
GECNM
)G.CE
0(NE*

oTC‘A
0RE(P

00(((

0EA(:W

 

316

t
*

FROM NMR TECHNIQUE
SET-CONTINUED

MULTIPLE DATA

tinniifiuirhntti“mit“”1ih”d**fluiihuitfiutt“Mitt
1.1 COMPLEX FORMATION

*iitiiiifitifiii******ti******iii*iiifitiiittiiitfittiiiiti

i
i

.T)
TM.
I...“
EsU

DiXM

nor... in? 0R

37

)GO TO

T
D
Cu)
[A
)F
R+R
TnUT

0’s OS)
0N * I t B
... XEEXnuEivl‘OF

o... o/

N-EC)/EC”)

o t XXXPLTSIOCZC
2.1M. HEELS *Ichfirr * E
(Pr—LE... 0(9t bolt ls

.(ttXNT2i7PA(
0T9XMS
CXPP:RQODIEABNT:EEE::NOCC2U(TE:(XTNN:P(XTNSNN:(XTSNNNNNNENNNNNNNR
EN::NTS554zGACAA:::A&0C::5::LM)EMARIDAEMAITRIDENATRIRIRIMRIRIRIRI
:EXMES:((.A::ERHAAATGC:MX:XCEIZTXMUTILTXVTIUTITXMIUTUTUTIUTUTUTUT
X:MXR(R:z:MMT:(PTTTLE:XXMCCLD((IERTNS(IERN(TNSIER(TNTNTNCTNTNTNTN
MHXMTFTABCAAACFLEEEEMMMVXMMA(FXR OEUEFR OCFECER OFEOEOEOFEOEOEOEO

N/TTEFLR

r. FprESISFFFsgbnhEI-A.HDTZDODODaUDDC .9 IX.”
1

_§)+(TETA*DXMX)+(ZETA*DMXM)

:5)JDAToXX‘l)9EC9£MC¢EMCX9EH1EXQEMX9

EnIC
MvGA
1591

)
1 F.
c I
1 D
T ”CS
0 t 0M3
T a. *0
8‘1Hi0 )
.r.» 9FTAT 4.
G ))9IEG o
) )bTZDBEO 0
1 )6 9 91T‘MG 1
0 . \J .3 9TT 0* +0) E
0 )\I1\I 9TAA0)\I( 0 M0

0))11(ITADO . 5M...1
011((X(AD.U.UI\(D\I-
o((XXXXDd((+U*Xo
fiLXXXX/XJ‘SSS‘ACE
oXX/lX/(STTJCOHMNCPX 9
T/IXHCCSTSSI)PD oLAan
GMXHXMMTSNNSELaHATES
OEMXMHEESNOO 0(AATCJ 9‘

6?
AM
15
=C

(

0

0

A

1
G.NOPT)ITS

UC olu 9(U o

1XX(1)QECQEMCQEMCXQENQEXQEMXQ

,
Tu. 4r,
AA o:
0608
IU 91.]
\IAEI
4M1)
OAT¢T
1.6 9p
9 9:40
[MIN

prpx 9 o

EAMXG

E ITERLC
UIIU 9‘ o

UUUT

ErtpLE
UUUHU

FRCRIH FCIRACRW FIRALRCRCIRabfiuCRCRC

1 1 1
5 5 60 7. a. 3 a. 5 no 9 3 I
O 3 CC 3 no 2 I 1..
1. 16 an;

 

 

 

 

. .. - .T—w-r. . - . .
*‘-L"-“,..a.a$'-_..a_;":n_ LLJ .. _._ -..‘uhi .A_ _ , __ __. k, _ __ __

317

*******t*****i****t*******************tt*it**t********t
* 1.1 COMPLEX FORMATION FROM NMR TECHNIQUE *
* MULTIPLE DATA SET-CONTINUED *

*ti*************ki‘kki*i‘k'ki'ki'kii'kt‘kit‘k'k‘ki'k‘k'ktik‘k'ki’iitiit

RETURN
12 CONTINUE
RETURN
13 CONTINUE
RETURN
END
7
9 CARD
****************t**t*i**i****ttii**t*t***********t*****
CONTxOL CARD
TITLE CARD
MCRT ARRAY CARD
NCST ARRAY CARD
CDNSTS ARRAY CARDS
IRX ARRAY CARD
ISNIN ARRAY CARD
IRITIAL ESTIMATE CARD
DATA CARDS
******************iii******************************tttt

BLANK CARD
6
7
E
9 CARD

 

 

318

ct = (C) + (MCX) + 2(MC2) + 2(MC2X) (3B—5)
Equations 3B-3 and BB—A provide,

(X) = (MC2) (BB-6)

Subtracting Equation 38-3 from Equation 3B-5 gives,

2U
II

(c) + (MC2) + (MCZX)

(C) + (X) + <MC2X> (33-7)

in Wthh R = Ct - Mt'

Equilibrium 3B-l gives,

(MC2X)

Kx2:=(Mc,X)(cj (38-8)

 

Substituting for (MCX) from Equation 3B-7 and rearranging

it gives

(MC2X)
(C) =KXEEMt-(X)-(MC2X)]

 

(3B-9)

If we substitute for (C) from Equation 38-9 into Equation

 

3B—7 we obtain,

(MC2X)
gdgwt—<X)—(MC2X)J

 

+ (X) + (MC2X) (3B—lO)

This equation can be solved for (X) in terms of (MC2X) and

gives

 

2 1
[Ct-2(MC2X)]-‘JECt-2(MC2X)] -A{RMt—(MC2X)[Ct+K;;(MC2X)]}

 

(X) = 2
(3B-ll)
then
(M02): (X) (33—12)
(MC2X) = KA2(X)2y§ . (BB—13)
(MCX) = Mt — (x) — (MC2X) (3B—1u)
(MC2X) (SB—15)

(C) = K (MCX)
X2

The activity coefficient can be obtained from the Debye—

Hfickel Equation (BA—7) with I = (X).

 

320

The numerical solution to the above equation was based
on an iterative method. Starting with (MC2X) = O and
Y: = 1, an approximate value for (X) was obtained which
was then used to calculate the concentrations of the other
species according to the Equations 38-12 to 38-15. Then
an improved value was obtained for y+. The improved value
for (MC2X) was used again to obtain a better value for
(X) and so on. The procedure was repeated until conver-
gence. Then the converged concentrations were used in
the chemical shift equation to obtain thermodynamic param-
eters for the complexation. The temperature dependences
of the equilibrium constants and the chemical shifts were

obtained as before (Equations 3A-50, 3A—5l). The FORTRAN

expression for the above problem is given on the next page.

 

 

 

 

 

i
t

*****t**********
*

NMR TECHNIQUE

321
1T

....

MUTTIPLE DATA S

I-

.1 COMPLEX FORMATIDN FROM

’1

fl-

***iiitittiitttfi**************************t***********

*****************************t*********

i

*

 

8
T9
2
T
AT
RP 9 9 C An
AYTT 9 C ) X
VTDP ) C E EX 5
07190 90 C “H LF. 1
NQTL )1 C U PL o X
scuao 1it C T wxr .5 E
TPTT 2V. 99 C A ON TC, SL
PESP 9D)) C R CO 2 N EP
0 9X0 0 900 P C E T: C T. O In!
NR9M ZISS Y C P L 1 AT IN C0
9AL9 (0(( T C M A .1 A TO EC
RIAT TIPY. I C .L S 2. X AT. D.
COVA C(YY C T T 2 2X RT 31
NDAUD EYTY C ... F LC Cad TA 0
IIIJ V9X9 ) C T D AOF MC NR F1
XSE9 91R) 3 C N S 0 :M ET 0 X
9F51T )nu90 11 C .A G:T T3 r:- ALN DR.
pROA 1915 9 C T 1N FNT +C N NE SEL
AQTD 23D( 2 C S 0A OAN X+ 0 0C NRP
LV9N 9(5T 1 C N 8T TA CX I NCN DIN
9AL9 nUT‘P 9 C 0 9c.» CCUT NRC T O 0 IADT-
TQZT 2SND I C C 2N NNS H A IXC TPCF
H6193 (XIL 1.. C :0 IONXF NR TE C.- T.
I9PN XP9N9 9 C EC EC RCOZDFDT ALX ANIH
9T90 X913) 0 CTRI R I CC DIN RPE R003
ESUC XTCIU 1 CNUR UN AN MT TE TML FIZ
PEF9 90295 9 CETT T0 PON:NTAC NOPN L
AT 9.... T0()( oI CIAC AI .ICCANRNNECMOEFFA
T905 DaluLnUT 9 CCRE RT NTI+TATGCOC AUILOCC
JXFC Dr‘AEF no CIELQF.A OATXSTNCIWDCTC I
9T9N UUV(U 9 CFFE/PN IMACNSE TOE ANTTM
o ENP9 H9FGTM 7 CFMIINR RMMONCDACRDRZFFE
4 PVDT TTQIS9)! CEEDiED FOR CONNR IETAIIH
T AXFC [PIECISI CDT(*TF DFDF COATXARNCHHC
F TAQE M009N019 CC:: FON CGNEPIEESS
o N NIMIV IKDI95(5 C )) ERDYR 0N TEL-ACN D
I I Q9Tl9 //33)(X9 CYIQ CTIPIRYIDTLCFNPNCLLE
LoK ETIXY TT(26XX4 CT99 NAoLAIFTIL NMO.U AAV
ED: NQDD DNG(1RX9 CITT EPBAPALATALODINCOCCR
A64 EUU99SEIF09193 CVAA R.9H.PAMASACC O AIIE
ZLT NOQPYTR09T89)9 CIDD EN2TN.HRM T IIDTMRS
DA9F. IKXY9SFP)95)6ZEDI E.ED ECTJJ FO NONTORLCNI. NEEED
RHQNE T 9TJN//U)(01(U6633 U U. UCCT‘ EITEIONFOATDoQIACHHD
AKTI: o UNKXUCNNODSS( N::::NNNNI NNCASS R:A::IE:FT:I2:069CC:
C cFKR or OONRdr..0058T(TDIEERKRIRI: CRIC:TT :R RL : : X :O)N : XIIA : : )
RN99 T RMU991NM(3$ISTTPDANUTUTA:UTCASS FF P2))2)T1A22:LHX)2
DEIEOoF BMDXMYMMPTNIN NAAVUTNTNMSTNCNNN EI IC32C1:(:CCX:FC4(
DDRNKYGTN DUDNX9YCDDLCXODDTTOOEDEOATEOCADD RK HK((K(SXXVMNCLN(X
RRDNQDLRI RSC99LYCCFZCDCGCIJNNRCRCCTRCCGCC TP DPUUPUEXEEEEERDUX
AANAN*:AK A 1234 12345 C
“LC QERLR5.0 P. 1 7..E maC
SQU99zDo C
‘EVUEQHLTLVHPACM 0. Ann
w:CA..L FIRTADC u..- r...

PIUPHRHFM LL? C‘LCnCCCCCPCCCCCCACCCCCCCAL ALCPC

...—l .‘-_-‘-~7-—-—~—-_wn-r ‘ ., »-

yw" ‘ "‘—

MW

 

 

322

*fi******i'i*******************************‘*****i*i'ki*i’i’i

*
*

NMR TECHNIQUE
xii*ttittitttittiiiti*i**t*ti***********t********tittii

T-CONTINUED

g
—

COMPLEX FORMATION FROF
DATA 8?

flUTTIPLE

2.1

*
t

\l
1)

99”
T9
AT.
0.5m
.UC
(J

*ST-

CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC

1 out
+AN88M1
SMO\H9F.(n.¢3DUUU»dlE+ AA

)-(l.C/TPEF)

PHD
FME
EEQJ

.1X
(E

PT88+(

28(5T/8
* Tab-l . CSCP)))
osbevOndl
OR.HI\I\I\

oRt

*(EXP((~DHC2X*TEMPR)/1o987))

9*PKC2AtGAM)

1* ...LALF.

RtES)-(ET*EX))
/PKC2X)-(2.0*EX)-(1.0/(PKC2AiGAM))

E0

Ix oOLC
\ISltAnanI—AH C(FLI\1*.AE - LTT7 On..!AHl\
cram/.TUi (* .LB 0RR9.UXMS

*PKC2£*GAP)

GD)

*Kgls

)(rU))nU 0/

AUT. oZN

M-EXJ/Exw)

.cQE((62( t (

CTACOZTzzzzz::O(.TAABCZPNO+BZoBZQQlSEAB
CIGZC Z : HRRAAXX OVATIC :Afi,..:xnuI oTDu.DD(X¢DS4(: GAXA : VA :MA: «A 2 VA: :Mu)n.hTLnUTunnEA—IRID
C: :D....rFPD¢D.fi/.20._2nu_XE:9..zAnd—LS?! “It :BD..E: :19 : nu : :..tcnmcn/CVACHAGXéa..¢CIOmUTIILTM.TUTT
CSMMTEIMIICCCC : : :AAB(2( :N ._ : 2: (2(NR : AMVLT. : (CCC : PTECCCL((TNS((IRNTNS
CTAEDRDEKHHKHKSTRAAGFXFXOCP._BDFXFXT.GKAAAXFMMMCLEMMMMAFXEOEFFROOEOE
CIGTSTTTPDDD,UPEEEAAAIEICCABSDIEIESGEGGREIEEEEABODDDCIXRCRIIHFCRCR

CCCCCC

\I
2
C x
M. 2
D C
t M:
A E
G 9
E x
M C
O M
l\ ...L
.7 9
\l C
X FL
1 2 9
0 C \l
1 Nu flu 1
D Z l\
C \1 ...-r3 S VA)
T M F A3 T X4
A I T I O. O
O G \I D PLO )roTnnU
n0 * VA TI, rCTI \Iéhaqv...
) C .7 ( TaDDE
) 2 M 6 +0 AH sub.
5 t E a. )Dv Dnu 9
C ... Xt «U Yr) )IVTI)VA
- VAZVA o C o 2‘. .35
E EC2 G M1 (T03 9.
n4 (MAFVSSS— D. XPTPUIVCJ
o *EKF‘CEI‘ * 0 X0) 9T;
1 AH . but/Ill + AME .M5E1 r3
0 n4X‘XXnéO/11XHNC C 0 CD: 9. ...L
T: CE/FCZC/DQé/RF 0L LQEAHVA ..u

G K.XNCM.(CLHA EAENTSE Co
oXPS2EME2UMATC UCooJ(U U1
NTEZEC2E:8:5(E:NN:SP(TNNN:

p? 36 7.
7" Bic 1V
... v.1?

 

 

 

 

 

323

titittittititit*iiitt*tiitiittittttit*itfiittitititititt
* 2.1 COMPLEX FOR”ATIUN FROM NMR TECHNIQUE *
* MUTTIFLE DATA SET'CUNTINUED *

tiiititttttii*iififi**i*i*i*t*iitiiiiiiiiii’iitiittiiiiiit

ARITE(JTAPE9222)JDAT9XX(1)9EC9EMCX9EMC2X
?22 FORMAT(5X911595X94E1504)
RETURN
3 CONTINUE
RETURN
4 CONTINUE
RETUPN
5 CONTINUE
IF(IWETH.NEo '1) GO TO 23
PETURN
25 CONTINUE
RETURN
9 CONTINUE
RETURN
1? CONTINUE
RE URN
11 CONTINUE
PETURN
12 CONTINUE
RETURN
13 CONTINUE
RETURN
END

7

L.‘

O CARD

*itiffittitiitiiiti*‘ktit*iitiff.*tittiiiitiitittitiititi

CONTROL CAQU

TITLE CARD
RCFT ARRAY CARD
NEST ARRAY CARD
CCASTS ARRAY CARDS
I?! ARRAY CARD
ISWIN ARRAY CARD
I‘ITIAL ESTIMATE CARD
DATA CARDS
tirtt'kttttt *tttttttii*iink-ktttitittiiiiiitttiittitttiifit
FLLNK CARD
5

9 CARP

 

«—~— A_—-— .. ..__..-- . ‘

 

 

REFERENCES

 

DUO

11.

12.

13.

l“.

15.

16.

17-

REFERENCES

C. J. Pederson, Am. Chem. Soc., 89, 7017 (1967).

Am. Chem. Soc., 92, 391 (1971).

C. J. Pederson,

B. Dietrich, J.
hedron Lett., 28

Lehn, and J. P. Sauvage, Tetra—

6 (1969).

E. Graf, and J. M. Lehn, J. Am. Chem. Soc., _1,
5022 (1975)-

J. M. Lehn, Acc. Chem. Res., 11, N9 (1978).

J
J
C. J. Pederson, J. Org. Chem., 36, 254 (1971).
M
8

J. M. Lehn, E. Souveaux, and A. K. Willard, J. Am.
Chem. Soc., 100, “916 (1978).

J. S. Landers, Ph.D. Thesis, Michigan State University,
East Lansing, MI (1981).

M. Faraday, Phil. Trans., 123, 379 (1833).
S. Arrhenius, Z. Physik. Chem., 1, 631 (1887).
P. Debye, and E. Hfickel, Z. Physik., 13, 305 (1923).

T. H. Grunwall, V. K. LaMer, and K. Sandved, Z.
Physik., 19, 358 (1928).

H. S. Harned, and B. B. Owen, "The Physical Chemistry
of Electrolytic Solutions", 2nd. ed., Reinhold, New
York (1958).

H. Falkenhagen, w. Ebeling, and H. G. Hertz, "Theorie
der Elektrolyte", Hirzel, Leipzig (1970).

J. E. Mayer, J. Chem. Phys., 18, 1&26 (1950).

N. N. Bogoliubov, in "Studies in Statistical Me-
chanics", J. deBcer and G. H. Uhlenbeck, eds. Vol.

1. North—Holland Publ. Amsterdam (1962).

H. L. Friedman, "Ionic Solution Theory", Wiley (Inter-
science), New York (1962).

32“

325

 

18. H. L. Friedman and W. D. T. Dale, in "Modern Theo-
retical Chemistry", B. J. Berne ed. Plenum, New York,

2, 85 (1977).

19. N. Bjerrum, K. Dansi Vidensk. Selsk. Mat.-Fys. Medd.,
_1(9).1 (1926).

20. R. M. Fuoss, and C. A. Kraus, J. Am. Chem. Soc., 55,
1019 (1933).

21. C. W. Davies, and J. C. James, Proc. Roy. Soc. (London),
195A, 116 (1948).

22. R. M. Fuoss, J. Am. Chem. Soc., 80, 5059 (1958).
23. H. Falkenhagen, and W. Ebeling, in "Ionic Interactions
From Dilute Solutions to Fused Salts", S. Petrucci

ed., Chapter 1, Academic Press, New York (1971).

2A. R. M. Fuoss, and C. A. Kraus, J. Am. Chem. Soc., _5,
2387 (1933).

25. R. M. Fuoss, and C. A. Kraus, J. Am. Chem. Soc., _1,
l (1935).

26. J. T. Denison, and J. B. Ramsey, J. Am. Chem. Soc.
11, 2615 (1955).

 

27. W. R. Gilkerson, J. Chem. Phys., 15, 1199 (1956).
28. W. R. Gilkerson, J. Phys. Chem., 11, 7A6 (1970).

29. L. D. Pettit, and S. Bruckenstein, J. Am. Chem. Soc.,
88, 4783 (1966).

30. M. Eigen, and K. Tamm, Z. E1ektrochem., 55, 93, 107
(1962).

31. S. Levine, and H. E. Wrigly, Discussions Faraday Soc.,
2“, “3 (1957).

'32. J. Stecki, Advan. Chem. Phys., 5, 913 (1962).
33. R. A. Marcus, J. Chem. Phys., 35, 58 (1965).

34. C. Rasaiah, and H. L. Friedman, J. Chem. Phys.,

J.
1g, 27u2 (1968).

35. H. L. Friedman, B. Larsen, Pure & Appl. Chem., 51,
21A? (1979).

m“-c - o-rw—r ' "

 

326

 

36. S. Winstein, E. Clippinger, A. H. Fainberg, and G. C.
Robinson, J. Am. Chem. Soc., 16, 2597 (1959).

37. H. Sadek, and R. M. Fuoss, J. Am. Chem. Soc., 16,
5897, 5905 (1954).

38. V. Gutmann, "The Donor-Acceptor Approach to Molecular
Interactions", Chapter 10, Plenum Press, New York

(1978).

39. R. M. Fuoss, J. Phys. Chem., 79, 525 (1975)-

*

40. R. M. Fuoss, Proc. Natl. Acad. Sci. USA, Z5, 16 (1978)-

Al. N. M. Atherton, and S. I. Weisman, J. Am. Chem. Soc
83, 1330 (1961).

° 3

42. P. J. Zandstra, and S. I. Weisman, J. Am. Chem. Soc.,
83, A408 (1962).

 

43. W. G. Williams, R. J. Pritchett, and G. K. Fraenkel,
J. Chem. Phys., §§, 5584 (1970).
AA. K. Hofelmann, J. Jagur-Grodzinski, and M. Szwarc,
J. Am. Chem. Soc., 91, A695 (1969).
45. N. Hirota and R. Krielick, J. Am. Chem. Soc., gg,
6“ (1966).
H6. N. Hirota, J. Phys. Chem., 11, 127 (1967).
47. H. Van Willigen, J. A. M. Van Broekhoven, and E. deBoer,
Mol. Phys., 12, 533 (1967).
98. W. Rutter and E. Warhurst, Trans. Faraday Soc.,

A.
6_, 1866 (1970).

“9. M. C. R. Symons, Pure & Appl. Chem., 39, 13 (1977).

50. M. Smith and M. C. R. Symons. Tran. Faraday Soc., 53,
338 (1957).

51. E. M. Kosower, J. Am. Chem. Soc., 89, 3253 (1958).

52. E. M. Kosower, "An Introduction to Physical Organic
Chemistry", Wiley, New York (1968).

53. K. Dimroth, C. Reichardt, T. Siepmann, and F. Bohlmann,
Ann., 661, 1 (1963).

54. T. E. Hogen Esch, and J. Smid, J. Am. Chem. Soc., 51,
669 (1965); ibid §§, 307 (1960).

 

 

55.
56.
57.
58.
59.
60.
61.

62.

63.

69.

65.

66.

67.

68.

69.

70.
71.

72.

327

H. E. Zaugg, and A. D. Schaefer, J. Am. Chem. Soc.,
91. 1857 (1965).

S. Claessan, B. Lundgren, and M. Szwarc, Trans. Fara—
day Soc., 55, 3053 (1970)-

M. F. Fox, and E. Hayon, J. Chem. Soc., Faraday Trans.
72, 1990 (1976).

M. C. R. Symons, Annu. Rep. Prog. Chem. Sect. A:
Phys. Inorg. Chem., 15, 91 (1976).

J. C. Evans and G. Y—S. Lo, J. Phys. Chem., 55,
3223 (1965).

W. F. Edgell, A. T. Watts, J. Lyford, and W. M.
Risen, J. Am. Chem. Soc., 55, 1855 (1966).

W. F. Edgell, J. Lyford, R. Wright, W. M. Risen, and
A. Watts, J. Am. Chem. Soc., 22, 2290 (1970).

B. W. Maxey, and A. I. Popov, J. Am. Chem. Soc., 55,
2230 (1967).

B. W. Maxey and A. I. Popov, J. Am. Chem. Soc., 21,
20 (1969).

M. K. Wong, W. J. McKinney, and A. I. Popov, J.
Phys. Chem., 15, 56 (1971).

B. G. Baum, and A. I. Popov, J. Solution Chem., 5,
991 (1975).

W. F. Edgell, J. Lyford, A. Barbetta and C. 1. Lose,
J. Am. Chem. Soc., 25, 6903 (1971).

W. F. Edgell and J. Lyford, J. Am. Chem. Soc., 55,
6907 (1971).

W. F. Edgell, and A. Barbetta, J. Am. Chem. Soc.,
96, 915 (1979).

W. F. Edgell, and S. Chanjamsri, J. Am. Chem. Soc.,
02, 197 (1980).

A. I. Popov, Pure & Appl. Chem., 51, 275 (1975).

D. E. Irish, and M. H. Brooker, Adv. Infrared Raman
Spectrosc., 2, 212 (1976).

W. Ostwald, Z. Physik. Chem., 5, 270 (1888).

 

 

 

 

73-

79.

75-
76.

77.
78.

79.

80.

81.

82.

83.

89.

85.

86.

87.

88.

89.

90.

 

328

C. A. Kraus, and W. C. Bray, J. Am. Chem. Soc., 55,
1315 (1913).

F. Kohlrausch, and L. Holborn, "Das Leitvermégen der
Elektrolyte", Teuber, Leipzig (1916).

L. Onsagerg Phys. 2., 55, 277 (1927).

L. Onsager, and R. M. Fuoss, J. Phys. Chem., 55,
2689 (1932).

E. Pitts, Proc. Roy. Soc. (London), A217, 93 (1953).

R. Fernandez-Prini, and J. E. Prue, Z. Phys. Chem.
(Leipzig), 228, 373 (1965)-

H. Falkenhagen, M. Leist, and G. Kelbg, Ann. Physik.
[61 ll, 51 (1953).

R. M. Fuoss, and L. Onsager, Proc. Natl. Acad. Sci.
USA, 31, 279, 1010 (1955).

L. Onsager, and R. M. Fuoss, J. Phys. Chem., 51,
668 (1957).

L. Onsager, and R. M. Fuoss, J. Phys. Chem., 55,
1339 (1958).

R. M. Fuoss, and K. L. Hsia, Proc. Natl. Acad. Sci.
USA, 51, 1550 (1967).

R. Fernandez-Prini, Trans. Faraday Soc., 65, 3311
(1969). _7

R. M. Fuoss and K. L. Hsia,_ Proc. Natl. Acad. Sci.
USA, 55, 1818 (1968).

D. A. MacInnes, and T. Shedlovsky, J. Am. Chem. Soc.,
21. 1929 (1932).

R. M. Fuoss, and C. A. Kraus, J. Am. Chem. Soc., _5,
976 (1933)-

D. S. Berns, and R. M. Fuoss, J. Am. Chem. Soc., 55,
5585 (1960).

R. M. Fuoss, and F. Accascinia, "Electrolyte Conduc—
tance", Wiley Interscience, New York (1959).

G. Atkinson, and S. Petrucci, J. Phys. Chem., 51,
337, 1880 (1963).

 

 

 

 

329

91. D. J. Karl, and J. L. Dye, J. Phys. Chem., 55,
977 (1962).

92. R. L. Kay, and J. L. Dye, Proc. Natl. Acad. Sci. USA,
32, 5 (1963).

93. R. J. Otter and J. E. Prue, Dissc. Faraday Soc., 55,
123 (1957)-

99. E. M. Hanna, A. D. Pethybridge, and J. E. Prue,
Electrochimica Acta, 15, 677 (1971).

95. J.—C. Justice,.I.Chim.Phys.Phys.-Chim.Biol.,55,353 (1968).
96. J.-C. Justice, Electrochim. Acta, 15, 701 (1971).

97. R. M. Fuoss, and L. Onsager, Proc. Natl. Acad. Sci.
USA, 51, 818 (1961).

98. R. M. Fuoss, Proc. Natl. Acad. Sci. USA, 11, 39
(1980).

99. H. G. Hertz, R. Tutsch, and H. Versmold, Ber. Bun-
senges. Phys. Chem., 15, 1177 (1971).

100. M. Eisenstadt and H. L. Friedman, J. Chem. Phys., 55,
1907 (1966).

101. F. W. Wehrli, J. Magn. Reson., 55, 575 (1977).

102. H. G. Hertz, M. Holz, G. Keler, H. Versmold, and C.
Yoon, Ber. Bunsenges. Phys. Chem., 15, 993 (1979).

103. H. C. Hertz, G. Stalidis, and H. Versmold, J. Chim.
Phys., 99, 177 (1969).

109. M. Eisenstadt, and H. L. Friedman, J. Chem. Phys.,
35, 2182 (1967).

105. L. Endon, H. G. Hertz, B. Thfil and M. D. Zeidler, Ber.
Bunsenges. Phys. Chem., 11, 1008 (1967).

106. A. Geiger and H. G. Hertz, Adv. Mol Relaxation Proc.,
2, 293 (1976)-

107. J. E. Wertz, and 0. Jardetzky, J. Am. Chem. Soc., 55,
318 (1960).

108. R. A. Craig, and R. E. Richards, Trans. Faraday Soc.,
59, 1972 (1963).

109. A. I. Mishustin, and Y. M. Kessler, J. Solution Chem.,
A, 779 (1975).

 

110.

111.

112.

113.

119.

115.

116.

117.

118.

119.

120.

121.

122.

123.

129.

125.

126.

330

C. A. Melendres, and H. G. Hertz, J. Chem. Phys., 51,
9156 (1979)-

G. W. Canters, J. Am. Chem. Soc., 55, 5230 (1972).

W. Sahm, and A. Schwenk, Z. Naturforsch. 29a, 1759
(1979). ~

H. G. Hertz, and H. Weingartner, J. Solution Chem.
3, 790 (1975).

E. Shchori, J. Jagur -Grodzinski, Z. Luz, and M.
Shporer, J. Am. Chem. Soc., 55, 7133 (1971).

B. Lindman, and S. Forsén, in'NMR and the Periodic
Table", Chapter 6, R. K. Harris, and B. E. Mann eds.,
Academic Press, New York (1978).

N. F. Ramsey, Phys. Rev., 11, 567 (1950); 15, 699
(1950); 5;, 590 (1951); _5, 293 (1952).

A. Saika, and C. P. Slichter, J. Chem. Phys., 55,
26 (1959).

J. Kondo, and J. Yamishita, J. Phys. Chem. Solid,
19, 295 (1959).

K. Yosida, and T. Moriya, J. Phys. Soc., Japan,
11, 33 (1956).

J. D. Halliday, R. E. Richards, and R. R. Sharp,
Proc. Roy. Soc. London, A313, 95 (1969).

C. Deverell, and R. E. Richards, Mol. Phys., 15,
551 (1966).

E.G. Bloor, and R. G. Kidd, Can. J. Chem., 55, 3926
(1972)-

C. Hall, R. E. Richards, and R. R. Sharp, Proc. Roy.
Soc. London, A337, 297 (1979).

G. E. Maciel, J. K. Huncock, L. F. Lafferty, P. A.
Mueller, and W. K. Musker, Inorg. Chem., 5, 559
(1966).

R. H. Erlich, E. Roach, and A. I. Popov, J. Am. Chem.
Soc., 55, 9989 (1970).

Y. M. Cahen, P. R. Handy, E. T. Roach, and A. I. Popov,
J. Phys. Chem., 79, 80 (1975).

 

 

 

127.

128.
129.
130.
131.
132.
133.
139.
135.

136.

137.

138.
139.

190.
191.

192.

331

J. W. Akitt, and A. J. Downs, in "The Alkali Metals",
special publication No. 22, the Chemical Society,
London, p. 199 (1967).

V. Gutmann, "Coordination Chemistry in Nonaqueous
Solvents", Springer: Vienna (1968).

R. H. Erlich, and A. I. Popov, J. Am. Chem. Soc.,
93, 5620 (1971).

-—_

M. S. Greenberg, R. L. Bonder, and A. I. Popov, J.
Phys. Chem., 11, 2999 (1973).

M. S. Greenberg, D. M. Wied, and A. I. Popov, Spectro-
chim. Acta, 29A, 1927 (1973).

M. Herlem, and A. I. Popov, J. Am. Chem. Soc., 55,
1931 (1972).

J. S. Shih, and A. I. Popov, Inorg. Nucl. Chem.,
Lett. 1;, 105 (1977).

W. J. DeWitte, R. C. Schoening, and A. I. Popov,
Inorg. Nucl. Chem. Lett., 15, 251 (1976).

w. J. DeWitte, L. Liu, E. Mei, J. L. Dye, and A. I.
Popov, J. Solution Chem., Q, 337 (1977).

A. K. Covington, T. H. Lilley, K. E. Newman, and G.
A. Porthouse, J. Chem. Soc. Faraday, I69, 963
(1973). '

A. K. Covington, I. R. Lantzke, and J. M. Thain,
J. Chem. Soc. Faraday, 170, 1869 (1979).

A. L. VanGeet, J. Am. Chem. Soc., 55, 5583 (1972).

C. Detellier, and P. Lazlo, in "Spectroscopic and
Electrochemical Characterization of Solute Species
in Nonaqueous Solvents", G. Momantov ed., Plenum
Press, New York (1978).

E. G. Bloor and R. G. Kidd, Can. J. Chem., 96, 3925
(1968). _—

C. Detellier and P. Lazlo, Helv. Chim. Acta, 55,
1333 (1976).

E. M. Arnett, H. C. Ko and R. J. Minasz, J. Phys.
Chem., 15, 2979 (1972).

 

 

 

 

193.

199.

195.

196.

197.

198.

199.

150.

151.

152.

153.

159.

155.

156.

157.

332

S. Greenberg and A. I.
1, 697 (1975).

Popov, Spectrochim Acta,

3’3

L. Fraenkel, C. H. Langford, and T. R. Stengle, J.
Phys. Chem., 15, 1376 (1979)-

R. H. Erlich, M. S. Greenberg, and A.
Spectrochim. Acta., A29, 593 (1973).

I. Popov,

A. Delville, C. Detellier, A. Gerstmans, and P.
Laszlo, J. Am. Chem. Soc., 102, 6558 (1980).

C. Moore, and B. C. Pressman, Biochem. Biophys. Res.
Commun., 15, 562 (1969).

Yu. A. Ovchinnikov, V. T. Ivanov, and A. M. Shkrob,
"Membrane—Active Complexones" (BBA Library 12),
Elsevier, Amsterdam (1979).

1. J. Tehan, B. L. Barnett, and J. L. Dye, J. Am.
Chem. Soc., 95, 7203 (1979).

R. A. Schwind, T. J. Gilligan, and E. L. Cussler, in
"Synthetic Macrocyclic Compounds", R. M. Izatt, J. J.
Christensen eds., Chapter 6, Academic Press, New
York (1978).

M. R. Truter, Struct. Bonding, 15, 71 (1973).

E. Mei, A. I. Popov, and J. L. Dye, J. Am. Chem.
800°: 22, 5532 (1977), and references therein.

N. K. Dalley, in "Synthetic Multidentate Macrocyclic
Compounds", R. M. Izatt, and J. J. Christensen eds.,
Chapter 9, Academic Press, New York, New York (1978).

G. W. Liesegang, and E. M. Eyring, in "Synthetic
Multidentate Macrocyclic Compounds", R. M. Izatt,

and J. J. Christensen eds., Chapter 5, Academic Press,
New York, New York (1978)-

J. D. Lamb, R. M. Izatt, J. J. Christensen, and

D. J. Eatough, in "Coordination Chemistry of Macro—
cyclic Compounds", G. A. Melson ed., Chapter 3,
Plenum Press, New York, New York (1979).

A. I. POpov, and J. M. Lehn, in "Coordination Chem-
istry of Macrocyclic Compounds", G. M. Melson ed.,
Chapter 9, Plenum Press, New York, New York (1979).

"Progress in Macrocyclic Chemistry", R. M. Izatt,
and J. J. Christensen eds., Vol. 1, Wiley Interscience,
New York, New York (1979).

158.

159.
160.

161.

162.

163.

169.
165.

166.

167.

168.

169.

170.

171.

172.

173.

179.

333

A. I. Popov, Pure Appl. Chem., 51, 101 (1979).

I. M. Kolthoff, Anal. Chem., 51, 1R (1979).

J. J. Christensen, D. J. Eatough, and R. M. Izatt,
Chem. Rev., 15, 351 (1979).

R. D. Shannon and C. T. Prewitt, Acta Cryst., B25,
925 (1969).

J. M. Lehn, and J. P. Sauvage, J. Am. Chem. Soc., 97,

6700 (1975)-

R. M.

Izatt, D. J. Eatough, and J. J. Christensen,

Struct. Bonding, 15, 161 (1973).

H. F.

D. J.

Frensdorff, J. Am. Chem. Soc., 93, 600 (1971).

Cram, R. C. Helgeson, L. R. Sousa, J. M. Timko,

M. Newcomb, P. Moreau, F. DeJong, G. W. Gokel, D. H.
Hoffman, L. A. Domeier, S. C. Peacock, K. M. Madan,
and L. Kaplan, Pure & Appl. Chem., 55, 327 (1975).

B. Dietrich, J. M. Lehn, and J. P. Sauvage, J. C. S.

Chem.

Commun., 15 (1973).

E. Shchori and J. Jagur-Grodzinski, Isr. J. Chem.,
11, 293 (1973).

E. Kauffman, J. M. Lehn, and J. P. Sauvage, Helv.

Chim.

Y. M.
Nucl.

Y. M.

Acta, 59, 1099 (1976).

Cahen, J. L. Dye, and A. I. Popov, Inorg.
Chem. Lett., 15, 899 (1979).

Cahen, J. L. Dye, and A. I. Popov, J. Phys.

Chem., 12, 1289, 1292 (1975).

K. H. Wong, G. Conizer, and J. Smid, J. Am. Chem.,
Soc., 55, 666 (1970).

S. Boileau, P. Hemery, and J. C. Justice, J. Solution

Chem.

M.
K.

. 9. 873 (1975).

Izatt, R. E. Terry, B. L. Haymore, L. D. Hansen
Dalley, A. G. Avondet, and J. J. Christensen,

: Am. Chem. Soc., 55, 6720 (1976).

J.

. J.

R
N
J
R. M.
D
J

Izatt, R. E. Terry, D. P. Nelson, Y. Chan,
Eatough, J. S. Bradshaw, L. D. Hansen, and
Christensen, J. Am. Chem. Soc., 55, 7626 (1976).

 

175.

176.

177.

178.

179.

180.

181.

182.

183.
189.

185.

186.

187.

188.

189.

190.

191.

192.

339

M. Shamsipur and A. I. Popov, J. Am. Chem. Soc., 101,
9051 (1979).

M. Shamsipur, G. Rounaghi and A. I. Popov, J. Solu-
tion Chem., 5, 701 (1980).

D. K. Cabbiness, and D. W. Margerum, J. Am. Chem.
Soc., 51, 6590 (1969).

J. M. Ceraso, and J. L. Dye, J. Am. Chem. Soc., 55,
9932 (1973).

J. M. Ceraso, P. B. Smith, J. S. Landers, and J. L.
Dye, J. Phys. Chem., 51, 760 (1977).

G. Binsch, and H. Kessler, Angew. Chem., Int. ed.
Eng1., 15, 911 (1980).

G. W. Gokel, D. J. Cram, C. L. Liotta, H. P. Harris,
and F. L. Cook, J. Org. Chem., 55, 2995 (1979).

B. Dietrich, J. M. Lehn, J. P. Sauvage and J. Blan-
zatt, Tetrahedron, 55 (1973).

J. L. Dye, J. Phys. Chem., 55, 1089 (1980).

D. D. Traficante, J. A. Simms, and M. Mulcay, J. Magn.
Reson., 15, 989 (1979).

D. Wright, Ph.D. Thesis, Michigan State University,
East Lansing, Michigan (1979).

E. Mei, Ph.D. Thesis, Michigan State University, East
Lansing, Michigan (1977).

(a) D. H. Live and S. 1. Chan, Anal. Chem. 92, 791
(1970), (b) M. L. Martin, J. -J. Delpuech, and _G. J.
Martin, "Practical NMR Spectroscopy", Heyden & Son,
Ltd. , London, 1980.

 

V. A. Nicely, and J. L. Dye, J. Chem. Educ., 55,
993 (1971).

"Handbook of Chemistry and Physics", The Chemical and
Rubber Company, 97th ed. (1966-1967); 0. Fox, "Con-
stantes Sélectionnées Diamagnetisme Et Paramagnétisme",
Masson, Paris (1957).

H. B. Thompson, and M. T. Rogers, Rev. Sci. Instrum.,
21, 1079 (1956)-

G. E. Smith, Ph.D. Thesis, Michigan State University,
East Lansing, Michigan (1963).

M. P. Faber, Ph.D. Thesis Michigan State University,
East Lansing, Michigan (1961).

335

193. J. Barthel, F. Feuerlein, R. Neueder, and R. Wachter,
J. Solution Chem., 5, 209 (1980).

199. W. T. Cronenwett, and L. W. Hoogendoorn, .1. Chem.
Eng. Data, 11, 298 (1972).

195. R. L. Kay, B. J. Hales, and G. P. Cuningham, J. Phys.
Chem., 71, 3925 (1967).

196. W. R. Gilkerson, Private communication.
197. M. Chen, J. Phys. Chem., 51, 2022 (1977).

198. W. R. Gilkerson, and A. M. Roberts, J. Am. Chem. Soc.,
102, 5181 (1980).

199. R. M. Fuoss, J. Phys. Chem., 51, 1529 (1977).

200. E. Mei, J. L. Dye, and A. I. Popov, J. Am. Chem. Soc.,
22, 5308 (1977)-

201. E. Mei, A. I. POpov, and J. L. Dye, J. Phys. Chem.,
g1, 1677 (1977).

202. E. Mei, J. L. Dye, and A. I. Popov, J. Am. Chem. Soc.,
55, 1619 (1976).

203. A. Hordakis, and A. I. Popov, J. Solution Chem.,
9, 299 (1977).

209. E. Mei, L. Liu, J. L. Dye, and A. I. Popov, J.
Solution Chem., 5, 771 (1977).

205. J. 3. Shih, and A. I. Popov, Inorg. Chem., 15, 1689
(19 0)-

206. A. J. Smetana, and A. I. Popov, J. Solution Chem.,
5, 183 (1980).

207. M. Shamsipur, and A. I. Popov, Inorg. Chim. Acta,
3;, 293 (1980).

208. J. D. Lin, and A. I. Popov, J. Am. Chem. Soc., 103,
3773 (1981).

209. E. Schmidt, Ph.D. Thesis, Michigan State University,
East Lansing, Michigan (1981).

 

210. E. A. C. Lucken, "Nuclear Quadrupole Coupling Constant",
Academic Press, London (1969).

211. Unpublished data.

 

 

212.

213.

219.

215.

216.

217.

218.

219.

336

A. Lowenstein, M. Shporer, P. C. Lauterbaur, and J.
E. Ramirez, Chem. Comm., 219 (1968).

G. W. Liesegang, M. M. Farrow, F. A. Vazquez, N.
Purdie, and E. M. Eyring, J. Am. Chem. Soc., 55,
3290 (1977)-

J. M. Lehn, J. P. Sauvage, and B. Dietrich, J. Am.
Chem. Soc., 55, 2916 (1970).

B. G. Cox, H. Schneider, and J. Stroka, J. Am. Chem.
Soc., 100, 9796 (1978).

B. G. Cox, J. Garcia-Rosas, and H. Schneider, J.
Phys. Chem., 55, 3178 (1980).

J. L. Dye, C. W. Andrews, and J. M. Ceraso, J. Phys.
Chem., 79, 3076 (1975).

E. R. Cohen, and B. N. Taylor, J. Phys. Chem. Ref.
Data, g, 663 (1973).

L. R. Dalton, Ph.D. Thesis, Michigan State University,
East Lansing, MI (1966).

 

STQTE UNIV. LIBRQRIES
l mum AA A
'ilgfl9flfiL2

9300

“77)