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MKCEEGAR STATE UMVE‘RSETY

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flare G. DeBacker

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This is to certifg that the

thesis entitled

METAL-AMIN'E AND SOLVATED ELECTRON SPECTRA AND
REACTIONS: EVIDENCE FOR THE EXISTENCE OF M-

presented by

Marc G. DeBacker

has been accepted towards fulfillment
of the requirements for

M degree in W y

 

mm fell/c,

Major profes/

[hm September 23, 1970

0-169

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(1) The
CT: the 660 m
t

ABSTRACT

METAL-AMINE AND SOLVATED ELECTRON SPECTRA AND
REACTIONS: EVIDENCE FOR THE EXISTENCE OF M’

BY

Marc G. DeBacker

The nature of the absorbing species in metal-ethylene-

   
   
    
  
    
 
  

diamine solutions was investigated. The reactions and
equilibria of these species were also studied. The following
results were obtained:

(1) The molar absorptivity and the oscillator strength
of the 660 nm band of sodium (V—band) were used to determine
jthe nature of the V-species. The molar absorptivity was

measured by using the reaction
Na+ + e-(IR-band) ———->— V—band

1;; molar absorptivity e = 8.2 i_0.5 x 104 M-l- cm'1 and
I an oscillator strength f = 1.9 1.0.2 was obtained. It was

i,¢oncluded that Na- was responsible for the sodium V-band.

2%;557 .The rate of formation of the V-band was studied by

rhyming pulse radiolysis techniques. It was noted that both

.te
.‘

depend upon
tration ran
of ion-pair
was obtains
By using th
ity of the '

reaction to

it was possi
91€Ctron in
the oscillaf

The eff
hater in 9th
.455 deteCtec‘
with respeCt

Ma
by water

 

~_-

Marc G. DeBacker

depend upon the concentration of sodium ions in the concen-
tration range 0.0055 to 0.5 M. This was interpreted in terms
of ion-pair formation. The value k = 1.6 x 109 til-J'osec"l

was obtained by using the expression §é%:l = -2k[e']2.

By using the pulse radiolysis results and the molar absorptiv-

ity of the V-band, and by assuming the stoichiometry of the

reaction to be

2e' + Na+ —-—9 Na-

it was possible to calculate the molar absorptivity of the
electron in ethylenediamine e = 2.0 i 0.5 x 104 M-Locm-l and
the oscillator strength f = 0.88 i 0.12.

The effect of hydroxide ion on the reaction of Na‘ with
water in ethylenediamine was studied. No hydroxide effect
was detected. It was found that the reaction was first order
with respect to sodium and close to third order with respect
to water. No simple mechanism could account for this.

A shift of the equilibrium Na- 2;:2' Na+ + 2e' to the right
by the addition of water was suggested.

(2) The addition of potassium ions to a cesium solution
in ethylenediamine resulted in the formation of a band at
850 nm (R—band) attributed to K-. The evaluations of equi-
librium constants were complicated by the presence of ion-

pairing equilibria and by ionic strength effect.

The adc
not produce
proposed til
the change
for this 0‘:

(5) T1
anemia an
using puls
consisted
intermedie
shape was
Of the mi
Electrori
to 0.9.
tures. t}

Solvent 1

ts)

Marc G. DeBacker

  
  
   
 
  
  
  
  
  
  
  
  
   
 
  
  
  
  
  

- The addition of potassium ions to a sodium solution did
not produce a R-band, but did produce an IR—band. It was
proposed that the change of activity coefficients caused by
the change of ionic strength of the medium was responsible
for this observation.

(5) The spectrum of the solvated electron in water-
ammonia and water-ethylenediamine mixtures was observed by
using pulse radiolysis. The spectrum in a given mixture
consisted of a single absorption band whose position was
intermediate between those of the pure solvents. The band
shape was studied, and found to be of the same form for all
of the mixtures. The oscillator strength of the solvated
electron in each of the pure solvents was found to be close
to 0.9. Assuming that this was also true for solvent mix-
tures, the molar absorptivities of the solvated electron in
solvent mixtures were calculated.

(4)‘It was observed that a solution of dicyclohexyl-
18-crown-6 in THF and in diethyl ether could dissolve
potassium or cesium giving deep blue solutions. These solu-
tions were found to contain paramagnetic species but their
L optical spectra showed only the R—band. The species M- was

considered to be the main absorbing species in these

uwfvtrrf.wrv "4 - ' ' ‘ ' 'va' “I""“.W'.1

METAL-AMINE AND SOLVATED ELECTRON SPECTRA AND

REACTIONS: EVIDENCE FOR THE EXISTENCE OF M“

BY

Marc G. DeBacker

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Chemistry

1970

   

  
  
  
  
  
  
  
 
 
  
  
  
  
 
  
 

.2. nn‘ M m-rmm

author ”1:... ,« . . _ hr . ,3 3;”, p.‘ 39C “taxation
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ACKNOWLEDGEMENTS

   
 
    
     
 
   

The author wishes to express his sincere appreciation
to Professor James L. Dye for his guidance, assistance,

, and encouragement during the course of this investigation
.and the preparation of this thesis.

The author is grateful to Professor Leon M. Dorfman
of the Ohio State University for permitting the use of the
linear accelerator for the pulse radiolysis studies and
for much helpful advice. He would also like to thank Drs.
Earl M. Hansen, E. Randall Minnich, and Vincent A. Nicely
for valuable suggestions and for their help with the
acquisition and analysis of the data.7

-' Financial assistance from the Atomic Energy Commission
.is gratefully acknowledged.

0-4
0

H.

INTRO:
HISTo}

2.1.]

2.2.

2.5.
2.4

2.5

BXPE

 

Lit-

I.

II.

III.

TABLE OF CONTENTS

INTRODUCTION . . . . . . . . .

HISTORICAL . . . . . . . . . .

2.1.

2.3.
2.4.
2.5-

Metal-Ammonia Chemistry .

2.1.1. Properties of Dilute Solutions
2.1.2. Models for Metal-Ammonia Solutions

Metal-Amine Chemistry . .

2.2.1. Properties of Metal—Amine Solutions

2. 2. 2. Models for Metal-Amine Solutions .

Metal—Ether Solutions . .

Rationale for Thesis Research . . . .

Theoretical Background:

EXPERIMENTAL . . . . . . . . .

5.1.

5.5.
5.4.

General Techniques. . . .
5.1.1. Glassware Cleaning
5.1.2. Vacuum Techniques.

Metal Purification. . .

Oscillator

5. 2.1. Storage of Small Quantities of

Metals . .

5. 2. 2. Breakable Metal Ampoules . . .
5. 2 5. Analysis of the Alkali Metals.

Solvent Purification. . .

Solution Preparation. . .
5.4.1. Metal Solutions. .
5.4.2. Salt Solutions . .

orption Spectra. . . .
1. Spectrophotometer.

s
5.5.
5.5.2. Variable Path Length
5.5.

5. Stopped—flow System.

iv

Strength.

Page

qfisp p P

TfifiECfi C

3.6.

3.7.

TABLE OF CONTENTS—-continued

' 5. 6.

Data Analysis. . . . . . . . . . . . . . .
5. 6.1. Calibrations. . . . . . . . . .
5. 6. 2. Data Analysis with a CAT. . . . .

5. 6. 5. Typical Measurements Made During a

Run a o I o o o o o o o o o o o o o 0

Computer Treatment of the Spectra. . . .
5. 7.1. Linearization of the Energy Scale
5. 7. 2. Calibration of Absorbance . . . .
5. 7. 5. Band- -shape Analysis . . . . . . .

Pulse Radiolysis Experiments . . . . . . . .
5.8.1. The Accelerator . . . . . . . . . . .
5.8.2. Optical System. . . . . . . . . . . .
5 8 5. Reaction Cells. . . . . . . . . . . .

IV 0 RESULTS 0 o o o o o o o I o o o o u I I o o o o o

4.1.

Sodium Solutions . . . . . . . . . .
4.1.1. Influence of the Sodium Ion Upon the
V-bando . o o o o o o o o a

4.1.2. Molar Absorptivity of Sodium—
Ethylenediamine Solutions . . . . . .

4.1.5. Reaction of the V—band Species with
Anthracene. . . . . . . . . . . . . .

4.1.4. Kinetics of the Reaction of Sodium
Ions with the Solvated Electrons. . .

Equilibria in Metal—Ethylenediamine Solu-

tions. . .

4. 2.1. Equilibrium, R—band fiIR—band in
Potassium Solutions . . . . .

4. 2. 2. Attempt to Study the Reaction e' .+ .K+
——9'R-band by Pulse Radiolysis. . .

4. 2. 5. Equilibrium, V—band + K+ 2:3- R-band.

Reaction of Sodium—Ethylenediamine Solutions
with Water: Hydroxide Effect. . . . . . . .

Optical Spectrum of the Solvated Electron in
Water—Ammonia Mixtures and Water-Ethylene—
diamine Mixtures . . . . . . . . . . . . . .

Preliminary Investigation of Cyclohexyl—18-

lcrown- -6. . . . . . . . . . .

4. 5.1. Ethylenediamine Solutions . . . . . .
4. 5.2. Other Solvents. . . . . . . . . . . .

Page

85
85
91
91

95

96

110
110
112

'3th 0? <

5.1.

(fl

   

{”750 or CONTENTS--continued'

v” . DIchsfloN . O Q C O C O C O O O O O O O I C O O

5.1. Oscillator Strengths and Molar Absorptivi—
ties C O O O O I I O I I O C l O O D O O 0
5.1.1. Solutions in Ethylenediamine. . . .
5.1.2. Solvated Electron in Water-Ammonia
Mixtures. . . . . . . . . . . . . .
5.1.5. mnclusions I O O O O C O O I O O O

5.2. Equilibria in Metal-Ethylenediamine Solu-
tions. . . .

5.2.2. Effect of Potassium Salt pon the
Spectrum of Sodium Solutions. . . .

5.5. Kinetics of the Reaction M+ + e- ——9~M-. .
5.5.1. Sodium Ion Reaction . . . . . . . .
5.5.2. Potassium Ion Reaction. . . . . . .

5.4. Reactions of Sodium Solutions with Water in
Ethylenediamine. . . . . . . . . . . . . .

5.5. Studies of the “Crown" Compound. . . . . .

’: Vi

5.2.1. Equilibrium IRlband ;‘R+.—;9:R:band .

Page
115
115
115
119
125

125
125

129
152

152
155

156
157
140

 

NELE

II.

III.

IV.

VI.

VII.
VIII.

Summi
Band

Abso
tion

REac
the

End

TABLE

II.

III.

IV.

VI.

VII.

VIII.

IX.

XIII.

LIST OF TABLES

Page
Summary of the Positions of the Absorption
Bands of Metal—Amine Solutions. . . . . . . . . 15
Absorbance of the V—band Produced by the Addi—
tion of Sodium Ions to a Cesium Solution. . . . 65
Reaction e- + Na+ —-*-V—band. Relation Between
the Absorbance of the IR-band at the Beginning
of the Reaction to That of the V—band at the
End 0 0 O O l O O O I O O I O O O O O O O I O O 7 5
Reaction e- + Na+ ——+ V—band. Comparison of
the Absorbances at Infinite Time. . . . . . . . 77
Kinetic Analysis of the Reaction Na+ + 2e—-—€>
Na- I O I O O O I O C O C O O C O I C O O O I C 81
Reaction Na+ + 2e_ -—+'Na-. Average Values of
the Rate Constants. . . . . . . . . . . . . . . 84
Equilibrium Studies: IR—band + K+ ?-*-R-band . 88
Equilibrium Studies: K+ + V-band . . . . . . . 95
Reaction Na_ + H20: Hydroxide Effect . . . . . 98

Solvated Electron Absorption Band Position and
Half—width for Ammonia-Water Mixtures . . . . . 106

Solvated Electron Absorption Band Position and
Half-width for Ethylenediamine—Water Mixture. . 107

Molar Absorptivities for the Solvated Electron
in Water-Ammonia Mixtures . . . . . . . . . . . 121

Summary of Molar Absorptivities and Oscillator
strengths 0 O O O D 9 I O O I I O I O I I O O O 124

FIGURE

FIGURE

1.

9.
10.

11.

12.

15.

714.

15.

16.

LIST OF FIGURES

Apparatus for the preparation of storage tubes
for sodium or potassium. . . . . . . . . . . . .

(a) Apparatus used to prepare cesium samples;
(b) Preparation of breakable ampoules. . . . . .

Freeze—purification apparatus. . . . . . . . . .
Solution make-up vessel. . . . . . . . . . . . .
Block diagram of the spectrophotometer . . . . .
Variable path length cell for optical spectra. .
Schematic of the stopped-flow system . . . . . .

Detailed view of a syringe used in the flow
system O O O C I O O O O C O O O O O D 0 O I C C

Block diagram of the data analysis system. . . .

Fit of the spectrum of cesium in ethylenediamine
to a Gaussian—Lorentzian band shape. . . . . . .

Fit of the spectrum of sodium in ethylenediamine
to a Gaussian-Lorentzian band—shape. . . . . . .

Block diagram of the optical system used in the
pulse radiolysis studies . . . . . . . . . . . .

Cell used for pulse radiolysis.studies . . . . .
Effect upon the V-band of increasing the_concen-
tration of sodium ions in the reaction e + Na+

—_+ V_band o o I n I o o I o I o o o o o o I o 0

Computer fit of the V—band in the presence of
excess cesium. . . . . . . . . . . . . . . . . .

Absorbance of the V-band as a function of the
concentration of sodium ions . . . . . . . . . .

viii

Page

50

52
55
57
59
41
45

44
47

55

54

56

58

65

64

66

LIST OF P

PKWRE

A
-

‘

2

l7.

73.

3.

W

“Q.

2

(\3

We

(\3

(\J

I\)
O)
O

S.

Abs<
eth}
inte
banc

Vari
ceni
yell
band

Kine
deca

Typi
studj
9rOW*
band

Kinet
of t}
fitte

Osci]
SOIVE
the E

fitte

TYPic
CESiL
Pure

Spect

Comps
tiOn
Potas

Fit t

LIST OF FIGURES-—continued

FIGURE

17.

18.

19.

20.

21.

22.

25.

24.

25.

26.

27.

28.

Absorption spectrum of the anthracenide ion in
ethylenediamine and positions and relative
intensities of the anthracenide ion absorption
bands in THF. . . . . . . . . . . . . . . . . . .

Variation of the optical spectrum of the anthra—
cenide ion with time showing the decrease of the
yellow band and the increase of the anthracenide
band C D O O O I O O O O O I O O O I l O O C I 0 0

Kinetics of growth of the anthracenide ion and of
decay of the intermediate (yellow) band . . . . .

Typical oscilloscope trace obtained during the
study of the reaction e + Na+ __,.V—band. Top:
growth of the V—band; Bottom: decay of the IR—
band 0 O O O O O I O O I O I O C O O O D O O C I .

Kinetics studies of the growth of the V-band and
of the decay of the IR-band. Each curve is
fitted by a second-order equation . . . . . . . .

Oscilloscope trace showing the growth of the
solvated electron in basic ethylenediamine after
the pulse 0 O O D O O O O I O O O I I O O O I O 0

Growth of the V-band and decay of the IR—band
fitted with the same three parameters . . . . . .

Typical fit of a spectrum of potassium and
cesium in ethylenediamine and the spectrum of a
pure cesium solution. . . . . . . . . . . . . . .

Spectrum obtained by pulse-radiolysis in an
attempt to study the reaction e + K+ . . . . . .

Comparison of the spectrum of a pure sodium solu—
tion and of a solution which also contains
potassium ions. . . . . . . . . . . . . . . . . .

Reaction of sodium with water in ethylenediamine.
Fit to a first-order meChaniSm. o o o o o o o a 0

Plot of log k 5 versus log [H20] for the reaction
of sodium witfi water in ethylenediamine . . . . .

ix

Page

69

7O

71

75

74

78

85

87

92

94

97

100

LIST OF FIGC

FIGURE

29.

30.

51.

34.

36

Absorp
liquid

Absorp'
ethyle:

Absorp'
water-j

Solvate
mixture

Variati
POSiti:
electr;

Variati
Positic
Electra
tures.

Optical
Ether i

Variati'
mixture

 

 

LIST OF FIGURES-—continued
FIGURE Page

29. Absorption spectrum of the solvated electron in
liquid ammonia at -15°C. . . . . . . . . . . . . 101

50. Absorption spectrum of the solvated electron in
ethylenediamine. . . . . . . . . . . . . . . . . 102

51. Absorption spectrum of the solvated electron in
water—ammonia mixtures . . . . . . . . . . . . . 104

52. Solvated electron band—shape in water—ammonia
mixtures I I I I I I I I I I I I I I I I I I I I 105

55. Variation with solvent composition of the peak
position and the half-width of the solvated
electron spectrum in ammonia-water mixture . . . 108

54. Variation with solvent composition of the peak
position and the half—width of the solvated
electron spectrum in ethylenediamine-water mix-
tures. . . . . . . . . . . . . . . . . . . . . . 109

55. Optical spectra of metals in THF and in diethyl
ether in the presence of "crown" . . . . . . . . 114

56. Variation with composition of the molar absorp—
tivity of the solvated electron in ammonia-water
mixtures I I I I I I I I I I I I I I I I I I I I 122

Soluti:

 

studied for
that in dilL
fiectrons a:
sis tEChniq.
water (47),
Stable SOlu
EJrOduced by
hlmost Sol
permit some

The ne
of contrOvE
that the 0E
solvated e]

these Solut

I. INTRODUCTION

Solutions of the alkali metals in ammonia have been
studied for more than a century (1,2,5). Kraus (6) suggested
that in dilute solutions, the metal dissociated into solvated
electrons and solvated cations. The advent of pulse—radioly-
sis techniques and the discovery of the solvated electron in
water (47), increased the interest in both stable and un-
stable solutions of solvated electrons. Solvated electrons
produced by pulse radiolysis have only a transient existence
in most solvents, but the life—times are long enough to
permit some of their physical properties to be measured.

The nature of metal—ammonia solutions is still a subject
of controversy. Nevertheless, there is general agreement
that the optical absorption band can be attributed to the
solvated electron. In order to explain other properties of
these solutions however, it is also necessary to postulate
the existence of loosely—bound aggregates.

The optical spectra of metal-amine solutions are more
complicated than those of metal-ammonia solutions. Three
bands have been observed, with maxima at 1500 nm (IR—band),
at 660 nm (V-band), and at about 850-1050 nm (R-band) (44).

The shapes and positions of the first two bands are

independent
to solvated

and in acc:

Hurle
caused by
tributed t
son of UM
I-in sol
attribute

The
to estabj
ethylenec
equilibr
followirl

(2.)
its m01£

an0 1V9(

By Such
ions De

the V~b

Of this

independent of the metal. The IR-band has been attributed
to solvated electrons by analogy with metal—ammonia solutions
and in accord with the pulse radiolysis results of Dalton

g a_1. (50) .

Hurley 23 El- (54) demonstrated that the V-band was
caused by the presence of sodium. Matalon §t_gl. (55) at-
tributed the V-band of sodium to the species Na- by compari—
son of the spectrum of the V—species with the spectrum of
I— in solution. The R-band for the other metals was also
attributed to the corresponding alkali anions.

The goal of the research described in this thesis was
to establish the nature of the absorbing species in metal-
ethylenediamine solutions, and to study the reactions and
equilibria of these species. To attain this goal, the
following studies were carried out:

(1) The nature of the V-band was studied by measuring
its molar absorptivity and oscillator strength. The method

involved the use of the reaction:
-_ +
e +.Na ——+' V-band.

By such studies, it was possible to decide how many sodium
ions per electron are involved in species responsible for

the V-band. By using pulse radiolysis techniques the rate

of this reaction was also studied.

 

The rea
diamine has
sodium hydro

(2) The
in metal-eth'
addition of *
followed by .
SPectrum. T]
they are fur‘
by ionic Str:

(3) The
water and in
USIng pulSe J
to an equatic
tained. This
absorptiVity
compoSition.

(4) 30mE

bil-

are nOrrna l 11?

The reaction of sodium solutions with water in ethylene—
diamine has been further investigated with the role of
sodium hydroxide being studied.

(2) The equilibria existing between the absorbing species
in metal-ethylenediamine solutions have been studied by the
addition of various amounts of salt to metal solutions,
followed by a measurement of the change in the optical
spectrum. These equilibria are themselves fairly complex and
they are further complicated by ion-pairing equilibria and
by ionic strength effects.

(5) The spectrum of the solvated electron in ammonia—
water and in ethylenediamine-water mixtures was measured by
using pulse radiolysis techniques. The band shape was fitted
to an equation whose form applies to all of the spectra ob-
tained. This permitted estimates to be made of the molar
absorptivity of the solvated electron as a function of solvent
composition.

(4) Some preliminary experiments relating to the solu—
bilization of the alkali metals in solvents in which they

are normally insoluble were reported.

 

 

Alkali
in liquid 2

solutions 1

II. HISTORICAL

2.1. Metal-Ammonia Chemistry

Alkali and alkaline earth metals can be dissolved freely
in liquid ammonia without chemical reaction. The resulting
solutions have been regarded both as scientific curiosities
and as subjects for serious scientific investigation for most
of the century since their discovery (1). They exhibit a
blue or bronze color and sometimes a phase separation,
depending upon concentration and temperature. The dilute
blue solutions are electrolytic while the concentrated solu—
tions behave as liquid metals. The intermediate region
exhibits a metal-non-metal transition. The properties of
these solutions were reviewed extensively during the
"Colloque Weyl" I and II (2,5) and in several review articles
(4,5). It is our purpose to discuss here only the properties

of dilute solutions.

2.1.1. Properties of Dilute Solutions
(< 10' M) .

Kraus (6) proposed that metals dissolved reversibly in

ammonia to give atoms and ions in equilibrium according to:

+ _
M -T——+ M + e (1)

The reactio

 

is thermody;
by taking p
catalyze th
shown to be
(7,8). Con
as the conc
Species occ

In a I

3f d1 lute 5

Th
ba
on
st
9r.

te

as
So]
tio

and

The reaction of the metal with the solvent:

M + NH3 _*: MNHg + 1/2 H2 (2)

is thermodynamically favorable, but it can be made very slow
by taking pains to avoid any trace of certain materials which
catalyze the reaction with solvent. This reaction has been
shown to be reversible under high pressures of hydrogen
(7,8). Complete dissociation requires very dilute solutions;
as the concentration increases, association to aggregate
species occurs.
In a recent review, Dye (9) classifies the properties
of dilute solutions in four categories.
a) Null results: properties independent of the metal
and of the concentration. The most important null
result is provided by the optical spectrum (10,11,12).
The spectrum consists of a single broad absorption
band whose position is independent of the metal and
only slightly concentration dependent. The band is
strongly asymmetric with a long tail on the high
energy side. This shape is independent of metal,
temperature, and concentration.
Some other properties must also be classified
as I'null results." The partial molar volume of the
solute (15,14,15) is nearly independent of concentra-
tion in the dilute region. Solvent NMR studies (16)

and line width of the EPR absorption (17,18,19) show

b

C

d

v

V

V

that electron relaxation is independent of concentra—

tion in this concentration range.

Cation-electron interaction: Conductance (20,21)

and transference number (22) measurements show a
concentration dependence of the cation conductance.
The behavior of the conductance of dilute metal-
ammonia solutions is similar to that of salts in
liquid ammonia. The conductance decrease is explained
in terms of ion pair formation.

Cation NMR studies (25,24,25) also show the
effect of cation-electron interactions. The chemical
shifts are both concentration- and temperature—

dependent.

Electron—electron interaction: The magnetic suscepti—
bility (26,27,28) decreases markedly as the concentra—
tion increases. It also decreases as the temperature
is decreased. This has been attributed to the

formation of diamagnetic species.

Non-specific conceptration effects: These properties
depend upon concentration but relate to the average
properties of the solute species rather than to
specific interactions. These properties cannot be
used to develop a model for the solutions but are

appropriate to test it.

Zn

ta

~\u

.o.
AC

Activity coefficients (29) in dilute solutions
give an indication of the extent of reactions involv-
ing the solvated electron.

The enthalpy of solution is strongly concentra—
tion and temperature dependent (50,14) and seems to
correlate with susceptibility.

Transport numbers (22) indicate that most of
the current is carried by negatively charged species
and that the fraction carried by such species in—

creases with concentration.

2.1.2. Models for Metal-Ammonia Solutions

 

Any model proposed for these solutions should explain
all of the properties without too much reliance upon acciden-
tal cancellation of effects.

Two kinds of models can be considered; those based on
a physical picture on one hand, and those based only on

stoichiometry on the other.

2.1.2.1. Physical Models
The model proposed by Kraus (equation (1)) for the solu—

tion of metals, combined with the significant volume expansion
accompanying the dissolution of metals led to the cavity
model for the solvated electron.

a) Cavity Model: This model postulates that in the

case of infinitely dilute solutions, the electron is

removed from the metal cation and is located in a
cavity in the liquid. The volume expansion data
suggest that the electron creates a hole in the sol—
vent. This model has been extensively used to
interpret the optical spectrum.

099 (51) used this model to explain the optical
spectrum. He considered the electron to be trapped
in a “spherical box" surrounded by an infinite po-
tential barrier. He calculated values for the
solvation energy and position of the absorption maxi-
mum. His results gave a value of the position of the
absorption maximum of 5,000 cm-l compared to the ex—
perimental value of 6,500 cm'l.

A more quantitative formulation of the cavity
model was carried out by Jortner (52). He supposed
the electron to move in a cavity of radius R = 5.2 to
5.4 R. The solvent around the cavity is polarized by
the electron, producing.a potential, V(r), given by:

2
( -%) r<R

O

V(r)

II
I
xrn

1
an

r 600 60

V(r) _§: 1 1 ) r > R

where 600 is the high frequency, and so the low fre-
quency dielectric constant.

Jortner showed that a transition from the lowest
3 to the lowest p level in the potential well of the

cavity could account for the optical absorption.

.‘iIIII.

b

V

The value of the cavity radius required to fit the
observed optical band position is 5.4 3. This value
also accounts for the volume expansion. Jortner,
Rice and Wilson (55) attempted to improve this model
with some SCF calculations but the agreement between
calculated and experimental values worsened. This
model is useful only in the limiting case of very

dilute solutions.

Cluster model: This model was first introduced by
Coulter (54) and later expanded by Becker, Lindquist,
and Alder (55). This model considers that in dilute
solution, the electron is removed from the vicinity
of the cation. The electron polarizes the dipoles

of the ammonia molecules so that they are oriented
with their positive extremities preferentially turned
towards the electron. The metal ion is also solvated
in a similar way. The effect of the polarization of
the ammonia molecules by the cation is to make the
hydrogen extremities more positive, thereby increas—
ing the affinity of these protons for the electron.
Such a unit, consisting of a metal cation solvated

by ammonia molecules upon which the electron is
delocalized, is called a monomer. Becker, Lindquist
and Alder further postulated that the diamagnetism

resulted from the formation of dimers, M2.

   

AV

r.

 

10

2.1.2.2. Models based on stoichiometry

In order to describe the concentration dependence of
the properties of metal-ammonia solutions, some association
of species and equilibria between these species must be
introduced. Douthit and Dye (10) introduced the ion pair

+

M e_ to explain the optical spectrum of metal-ammonia

am ' am
solutions. In such pairing, the electron would stay sur-
rounded by the same solvation sheath and the optical spectrum
would stay unchanged when the concentration is increased.
Dye, Sankuer and Smith (22) used two equilibria (which

had the same stoichiometry as the model of Becker, Lindquist

and Alder) to account for their transference number results.

M + e_ --* M - e (5)
2M+ ' -——* M (4)
o e ‘_-’ 2

The presence of a species M2 is difficult to reconcile with
the null results provided by the optical spectrum. The
optical spectrum follows Beer's law and this implies that M2
is an absorbing species; but the spectral shape does not
change with concentration and therefore M2 must have the same
spectral shape as e- but twice the molar absorptivity. Gold,
Jolly and Pitzer (56) proposed that (4) should be replaced
by

2M . e -—-> (14+ . e')2 (5)

where (M+ - e_)2 is a quadrupolar aggregate in which each

component retains its solvation shell.

11

These models give reasonable agreement for a few proper-
ties at a time,but cannot be used to explain all of the prop—
erties of metal—ammonia solutions. In particular if we try
to get equilibrium constants from conductivity measurements
and also from magnetic susceptibility measurements, serious
discrepancies between these constants appear.

To resolve these discrepancies, Arnold and Patterson (57)
assumed the existence of two diamagnetic species. They chose
a species M_ consisting of an electron trapped in the field
of an M center. The prime requirement on this M- is that it
is diamagnetic and negatively charged. The following equi—

libria were used:

M+ + e_ -—§1+ M (6)
2M —K-7—’ M2 (7)
M + e" is» m' (e)

The values of the three equilibrium constants were obtained
by fitting conductance, transference data and paramagnetic
susceptibilities. A remarkable fit of the experimental data
was obtained.

Golden, Guttman and Tuttle (58) used a very similar
model. The main difference was that they replaced the M2
species by the ion-pair (M+ - M_) and the "monomer" M by
(M+ - 8-) (where S— is a solvent anion or the solvated

electron). Introducing a species A— to represent either S-

 

F5"-

12

or M_, they were able to reduce the number of equilibria to

two, given by

M+ + as“ Kfi M" + as (9)
M+ + A" *—K1_9—> M+ - A— (10)
The originality of this model arose from the fact that K10
was evaluated using Fuoss' theory of ion—pair dissociation.
The constant K9 was then used as the only adjustable para—
meter. Good agreement was obtained for vapor pressures,
Knight shifts, conductances and optical spectra.

Recent conductance measurements by Dewald (21) showed
that the previous conductance values at very low concentra-
tions were in error. This new set of results showed that the
conductance data could be explained by the standard electro-
lyte theory with only one ion—pairing equilibrium.

The main difficulty in finding a correct set of equilibria
for the metal-ammonia solutions comes from the fact that mag-
netic and conductimetric data do not give the same equilibrium
constants. At least five species are needed to explain the
properties of these solutions: e_, the solvated electron;
M+, the metal ion; M, the metal atom, monomer or ion-pair;
M—, the metal anion or ion triple; and M2 the metal dimer or
ion quadrupole.. Currently, these species are generally
regarded as aggregates of solvated electrons and metal—ions,

each species keeping its own solvation layer and therefore

I‘A
by

Le

th

15

not being strongly perturbed by what is happening outside its
layer. This approach helps to explain the invariance of the
optical spectrum and the other null results. Dye (9) has
attempted to fit all of the available data to a set of
stoichiometric equations. In order to reconcile magnetic and
conductimetric data, he postulated that magnetic interactions
leading to a singlet state occurred, on the average over long
distances such that deviations from normal ionic interactions

caused by the spin pairing process are relatively small.

2.2. Metal-Amine Chemistry

Alkali metals are less soluble in the aliphatic amines
than in ammonia. While solutions of metallic character can
be formed in ammonia, with concentrations of the order of
several moles per liter, solubilities in amines are of the

order of 10-3 M even in the most favorable cases.

2.2.1. Properties of Metal-Amine Solutions

The first studies of these solutions were done with
methylamine by Gibson and Argo (59) who recorded the optical
spectrum only in the visible region. One peak was observed
with all of the metals and it was concluded by these authors
that solutions in methylamine were similar to those in
ammonia, with the difference that the peak was shifted to

higher energies.

 

f“

In

D)

n)

p“

14

The complete optical spectrum of alkali metals in
methylamine was first recorded by Blades and Hodgins (40).
Instead of a single peak as in ammonia, several bands were
observed. Since then, a number of workers have studied the
spectra of metal-amine solutions. Characteristic positions
of the absorption maxima for metal solutions in several
amines are summarized in Table I. From this table it can be
seen that there are in general three bands depending upon
the metal used, and that all of the amines present the same
features. The band occurring at wavelengths around 650 nm
is independent of the metal used and has been called the
V—band. The band at about 1500 nm is also metal-independent
and is called the IR-band. The position of the intermediate
band is metal-dependent, this band is called the R-band.

The nature of the species responsible for these differ-
ent bands has been a subject of controversy for a long time.
The discovery of hyperfine splitting by the metal nucleus in
methylamine and ethylamine solutions (45,46) demonstrates
the presence of species of stoichiometry M involving a metal

nucleus.

2.2.2. Models for Metal-Amine Solutions

a

v

Infrared band: This absorption band is independent
of the metal used and its position and shape is very
similar to the band observed with metal-ammonia

solution. Furthermore, only the solutions exhibiting

.-

Iiill.‘
.

15

.mocmnu0mnm HHmEm
*

*

 

 

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as am omm mz
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made 9.: 0mm 0mm ”3 M
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00 E: an EC
mocoumumm a > m «H Hana: pcmsaom

 

 

mGOMHSHom unmadlamuwz «0 ocean coHumuomQ< man no sOwuHmom may we ammEEsm

.H wanma

 

 

‘b

v

16

anIR—band are paramagnetic. The IR-band is attrib—
uted to the same types of species as those which
exist in metal-ammonia solutions; that is the
absorption is caused by solvated electrons which

may, however exist in aggregate species. Further
strengthening of this assignment comes from the
pulse radiolysis studies (50). From the time of

the first spectroscopic evidence for the formation
of hydrated electrons (47), it has been assumed that
solvated electrons produced by the radiolysis of
water and other solvents are analogous to those
formed when alkali metals are dissolved in liquid
ammonia and amines. Compton and co—workers (48)
showed that the spectrum obtained by pulse radioly—
sis of anhydrous ammonia was similar to that of
metal solutions. On the other hand Anbar and Hart
(49) reported an absorption maximum at 920 nm for the
transient obtained in ethylenediamine. Dalton _g._;.
(50) showed that this result was an instrumental
artifact:and that the shape of the absorption curve
they obtained was close to that of the IR—band for
solution of metals in ethylenediamine. The lack of
fast infrared detectors at the time prevented a study

of the spectrum up to the wavelength of the maximum.

Visible (V) and reg (R) bands: These two bands are

not observed in metal-ammonia solutions and a number

 

17

of interpretations have been proposed for them.

Blades and Hodgins (40) attributed the different
bands to electrons trapped in different sites. In
their model, the IR-band was due to an electron
trapped into an ammonia-like cavity, i.e., an
electron surrounded by the amino groups of the amine,
and the V-band was due to aliphatic traps, i.e.,
cavities in which the amino groups have been replaced
by methyl groups. The R—band was assigned to a
third kind of trapping site which was presumed_to be
a mixture of the two preceding ones.

Fowles, McGregor and Symons (51) based their
model upon magnetic considerations. Since the
V-band was diamagnetic and seemed fairly independent
of the metal, the diamagnetic species e2: was pro—
posed for the V-band.

One very puzzling feature, observed by most
investigators, was that in solutions exhibiting both
V— and R—bands, the relative intensities of these
two bands were absolutely irreproducible. Studies
of the decay of the V- and R-bands in different
laboratories gave different answers. Ottolenghi g; 3;.
(52) observed that the R—band decayed by a first
order mechanism at a rate equal to twice the decay
rate of the V-band and that the decay of the EPR

signal due to monomers matched the decay of the

18

Vsband. The V-band was therefore attributed to
monomeric species and the R—band to dimeric species.
On the other hand,Dye,and Dewald (55) observed a one—
to-one decay of the V- and R—bands and observed some
slow band interconversions for solutions of lithium
in ethylenediamine. The R-band, being metal de—
pendent, was attributed to the covalent dimer
analogous to that observed in the gas phase. The
peak position gave a good correlation with the
transition 12“ <—— 129 for dimers in the gas phase.
These transitions occur at 860 nm for K2 and at 940
nm for C32 (54). The species responsible for the
V-band had to be metal-independent and be able to
convert slowly to another species. This ruled out
the possibility of using ion-paired species for
which the equilibria would undoubtedly be fast.

A species involving an electron trapped in the field
of a molecular ion M2+ was proposed.

A major breakthrough occurred in 1968, when
Hurley, Golden and Tuttle (55) reported that solu—
tions of potassium in ethylamine prepared in a quartz
apparatus did not show any V-band. Solutions of
potassium previously prepared in Pyrex always showed
a V-band. Flame analysis of the residue after solvent
evaporation showed a correlation between the presence

of the V-band and the presence of sodium. From this

19

it seemed certain that the V-band was due to sodium
contamination from the Pyrex glass. This explained
part of the discrepancies in the measurements of
optical spectra.

Recently, Matalon gt_al. (56) attributed the
V-band to the species Na—. This assignment was
based on properties of the spectrum of the V-band
that paralleled those of I— in solution. The
spectrum of I- in solution has an absorption band
in the ultraviolet (S5250 nm) that does not corres-
pond to any of the bands in the gas phase. It has
been postulated that this band is caused by a charge-
transfer-to-solvent (ctts) transition. Let us
review briefly some of the characteristic properties
of a ctts band.

The position (in energy units) of the absorption
peak shifts linearly with the temperature to higher
energies.

The positions of the peaks for two anions in
a variety of solvents are in a linear relation to
one another.

Matalon §t_gl.(55) used solutions of sodium in
ethylamine and ethylamine-ammonia mixtures to verify
that the above relations also applied to metal-amine

absorption bands.

 

-w‘a.lIII---------------------————-——-——————-————-
20

The theory of ctts absorption was introduced by
Frank and Platzman (57). Symons and co-workers (58),
and Stein and Treinin (59) made further refinements.
The calculations predict that the position of the

maximum of absorption is given by the relation:

 

2
hvmax = Ip - Lx + E; (2 + 2Dop _ gs)
_ E: (1 _ 1..) _ Ifflég. .1. _ i.)2
Zfie DOp 2 h Dop DS
in which
Ip = electron affinity of the ion.
Re = radius of the excited state.
DS = static dielectric constant.
op = optical dielectric constant.
Lx = heat of solvation of the ion.

ro = radius of the cavity.

r0 can be related to the crystallographic radius by
a multiplicative factor. For most of the anions
in solution, a plot of hvmax — Ip versus 1/rcryst
gives a straight line.

Matalon 95 ii! calculated the radii of the
alkali anions using Slater's formula (60) rM- =
2rM - rM+ . They used electron affinities obtained

from molecular beam experiments. The plot of

hvmax - Ip versus 1/r _ gave a stra1ght l1ne.

   

A

21

They concluded that both the V- and the R—bands were
due to ctts transitions of alkali anions M_, this
anion being in equilibrium with solvated electrons.
The presence of a V—band then implies the existence

of Na- in solution.

The results of the past few years simplify the picture
of metal-amine solutions a great deal,since only two types
of absorption bands are involved instead of three. The
V—band is simply the sodium R-band.

The species, existing in metal-amine solution, responsible
for the IR-band are probably similar to the species in metal-
ammonia solutions. It seems that the main difference resides
in the fact that in amines associated species tend to be more
stable than in ammonia. It is also to be remembered that most
of these species exist as ion pairs; even more so than in
ammonia. Hansen (67) in order to explain the rate of reaction
of solvated electrons with water in ethylenediamine postulated
that electrons paired to form diamagnetic species in a manner

similar to the pairing in ammonia.

2.5. Metal-Ether Solutions

Blue solutions of alkali metals in ether solvents were
first reported in 1957 (61). These solutions are paramagnetic
and have been compared to solutions in ethylamine. Cafasso

and Sundheim (62) reported the positions of the optical

 

U?
22

absorption bands, which corresponded to the V— and R-bands in
amines.

Glarum and Marshall (65) recently described some
photolysis experiments of solution in dimethoxyethane. In
these studies they monitored the EPR signal of the solvated
electron as a function of the wavelength of the irradiating
light. The curve giving the intensity of the EPR signal as
a function of the wavelength of the incident light resembles
closely the absorption spectrum of these solutions. This
suggests that the absorption of light is coincident with,

or followed by, electron ejection.

2.4. Rationale for Thesis Research

The assignment of a species of stoichiometry M— to the
V- and R-bands is based only on some similarities with ctts
bands and the observation that the species responsible for
these bands gives no ESR signal. The optical studies were
done by comparing the position of the I_ and M_ band in a
very limited set of solvents (ethylamine-ammonia mixtures).
This work deals with studies of stoichiometry and

kinetics of the reaction

m Na+ + ne_ ——+'V-band.

For this we needed to determine the molar absorptivities of
the V—band and the solvated electron. The nature of the

solvated electron was investigated by studying spectral shapes

I

~U.

25

of the solvated electron band in the solvent mixtures water—
ammonia and water-ethylenediamine. From these data we hoped
to be able to determine the species responsible for each
band with more certainty than before.

We also studied the equilibria existing in solution when
several bands are present. The particular reaction investi—

gated was

- +
(e )solv + K —> R-band

+ . .
K was chosen because 1ts R-band 13 well separated from the

 

IR-band. ‘ U.“
Throughout this study we were interested in band shapes,

absorptivities and oscillator strengths. Because of the

interpretations made on the basis of oscillator strength,

the definition and nature of this function are considered

here in some detail.

2.5. Theoretical Background: Oscillator Strength

A quantity of interest when studying optical spectra is

the integrated molar absorptivity.

v1:,
A= f e(v) d(v) (1)
v
a
The amount of energy in the frequency range Va to Vb which

is absorbed by the sample per unit volume per unit time is

given by

A _

24

 

~’ I.C.A.=‘I.C. fvb e(v) dv (2)
V

a
where
C a concentration
I = intensity of light.
The energy absorbed per unit volume per unit time due to a
certain frequency Vkfi associated with the transition k —+ fl

is given by the expression:

CN
Bk—on 9(sz) hvkz lboo ° (5)

where N0 = Avogadro's number.

hvkz = energy absorbed per molecule undergoing a
transition k—efi.

B] 1 = Einstein transition-probability coefficient of
absorption.

p(vk£) = radiation density due to radiation of frequency
V .
R!
If we assume that the absorption occurs over a narrow range
of frequencies, vk2 can be identified with the maximum of
the absorption curve. We then equate (2) and (5) and solve

for A to obtain

Bk-vfl Pivkz) N0 hvkfl

\A 3P 1000 I (4)

By definition

Bk—->£ = 3%L l.‘*“k£|2

I (v) = cp(v)

 

 

25

where lupkfl '18 the transition moment and c is the speed of

light. We then obtain:

A =27Tl‘i/k2l2hN0 (5)

theor VkE

 

2
5000 h' c

If the transition moment can be calculated one can predict
the integrated absorption coefficient once vkfl is known.
Let us first consider the case of an heteronuclear mole—

cule. In the approximation of the harmonic oscillator its

dipole moment can be written, for displacement x as
um)=m +€m x
x x=0 '

For transitions from the level v=0 to v=1 we have

IE0¥|'=<¢1|LL0+ (%E)x=oxl¢o> (6)

where W0 and W1 are wave functions for the two states of the

harmonic oscillator.

 

 

2_ h- a 2
[501 I — 4me Vol (5£°x=0 (7)
Combining (7) with (5) we get:
A= "N0 €52 m)
x x=0

5000 umC

The classical theory of interaction of light with bound
electrons considers that the electron is bound to the nuclear
framework by a Hooke's law type of force. We will therefore

apply the results obtained for the harmonic oscillator to the

 

OS

i‘itii

int

26

case of electrons.

_ W N 5 2 5 2 d 2
A ‘ 5000 u: c [(63%)X=O + (3%);50 + (35%: :l (9)

 

As a reasonable approximation we replace the reduced mass
Pm by m the mass of the electron. As a further approximation

we set

a 2 _ B 2 _ a 2 _
(35:50 ‘ (5%)y=o ‘ (352% ' e2
e = charge of the electron.

The integrated coefficient now becomes:

= .IlEn.§E.
Amodel 1000 me (10)

The ratio of the experimental integrated absorption coefficient

to the intensity expected from an equivalent harmonic

oscillator is called the oscillator strength and is defined by
A

f = £9?— = 4.55x10‘9f d7) d7 (11)
eXP Amodel

where V is in wavenumbers.
A purely theoretical value can be obtained for the
oscillator strength if the experimental value Aexp is re-

placed by A given by (5)

theor

8w2 m c

f ’31—?— ”k) WEI 2 (12’

theor =

The oscillator strength of a transition is a measure of the

intensity of that transition. For intense transition, and

to

27

for one electron systems, f is usually of the order of unity.

Kuhn and Thomas (82) have shown that

2 f = N (15)
n run

where fmn is the oscillator strength for a transition from
the state m to the state n. The sum is taken over all final
states n; N is the total number of electrons in the system.
This is known as the f—sum rule or the Kuhn-Thomas sum rule.
It can be shown (64) that transitions to upper states have

positive fmn's; those to lower states have negative f’s.

 

Q)

U:

W]

1!?

'w'a:

III. EXPERIMENTAL

5.1. General Techniques
5.1.1. Glassware Cleaning

All glassware was cleaned in two steps. The first
involved the use of an HF cleaner (55% HNOa, 5% HF, 2% acid
soluble detergent, 60%'water) followed by a thorough rinsing
with conductance water. The second step was a washing with
aqua regia prepared ig_§itu, The glassware was then rinsed
at least ten times with boiling conductance water and dried
in an oven.

All parts of the stopped-flow apparatus were cleaned in
the same way before assembling the system. Between each run,
the flow system was washed by flowing freshly prepared aqua
regia through it. This was followed by rinsing. The system
'was dried by evacuation.'

The vessels destined to contain ethylenediamine were

rinsed several times with anhydrous liquid ammonia.

5.1.2. Vacuum Techniques
All of our work was done using standard high vacuum

techniques. The Pyrex vacuum lines were evacuated using

28

 

USE

lin

RG7

Gia

(N
O
m
C

29

dual-stage mechanical pumps and two-stage oil diffusion

pumps. The use of Dow Corning 704 diffusion pump fluid
allowed us to reach pressures as low as 10"6 torr without
liquid nitrogen traps. Liquid nitrogen cooled traps were
used whenever ethylenediamine or ammonia were in the vacuum
line. The pressure measurements were made with a Veeco

RG75P glass ionization gauge tube and a RGLL6 control circuit.
Glass stopcocks were of the high vacuum type; they were
greased with "Dow Corning High Vacuum" silicone grease.
Teflon needle-valve stopcocks were also extensively used

(Fisher-Porter, Delmar-Urry).

5.2. Metal Purification

 

Metals of the highest purity available were used. They
were always distilled several times prior to use.

Na: J. T. Baker, Co. (99.99%)

Rb: Fairmount Chemical Co.

K: J. T. Baker, Co. (99.99%)

Cs: A gift from the-Dow Chemical Co.

5.2.1. Storage of Smallyguantities of
Alkali Metals.

Sodium and Potassium: Small pieces of metal were cut
from.the center of a larger piece and covered with n-
hexane. These pieces were introduced into a 40 mm OD vessel
containing some lengths of 4 mm OD tubing which had been

sealed at one end (Figure 1). The system was evacuated and

 

 

50

T High vacuum

 

~&- Helium

‘ supply
5}

'WTS 40/50
I

1‘ . [r [ W40 mm OD

 

 

 

 

90 cm

 

 

 

 

 

WV/«Sodium or Potassium
metal

 

 

 

 

 

 

 

Figul’e 1. Apparatus for the preparation of storage tubes
for sodium or potassium.

51

the metal was melted. When all gas—evolution stopped, a
slight pressure of helium was applied over the molten metal
to force it into the small tubing. In this way, small
samples of metal free of oxides could be obtained by cutting
a small piece of glass tubing.

Eggium’and Rubidium: Cesium and rubidium burn very
easily in air. These metals were originally contained in
glass ampoules of 50 to 40 grams of metal each. These large
ampoules were first divided into smaller ones containing only
a few grams by the method described by Dewald (66). To get
even smaller samples of metal, the apparatus shown in Figure
2 was used. The ampoule containing the metal was scored with
a glass-cutting knife and the metal was cooled by immersing
the ampoule in liquid nitrogen. The ampoule was then broken
and introduced into A. Tube A was quickly sealed and
pumped. The metal was then melted and distilled into B under
high vacuum. Constrictions C and D were then sealed off.

The metals could then be melted into the long tube and the

quantity needed taken by sealing a length of tubing.

5.2.2. Breakable Metal Ampoules

It was found very convenient for the preparation of
metal solutions. to have the pure metals enclosed in an
ampoule equipped with a breakseal. In this way the solvent
could be degassed without being in contact with the metal.

The procedure used to distillmetal into this ampoule was the

punpinkv Firs-F; CF—L

52

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BC
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55

same as that described previously. The apparatus is shown

in Figure 2(b).

5.2.5. Analysis of the Alkali Metals

The alkali metals, sodium and potassium were analyzed
by both emission and absorption flame photometry. These
studies were made by using a Beckman DB Flame Photometer
and/or a Jarrell-Ash Atomic Absorption Flame Photometer.
The alkali metals were analyzed after they had been intro-
duced into a dilute aqueous solution of hydrochloric acid.
Standard solutions for potassium and sodium were prepared.
A stock solution containing 1g/l equivalent of potassium or
sodium was prepared. All the other more dilute standard
solutions were prepared by volumetric dilution from the stock
solution, never by successive dilutions. The concentration
of the unknown was determined by interpolation between two
standard solutions.

The potassium was analyzed for the presence of sodium
in this way. The potassium coming from the manufacturer did
not show any detectable trace of sodium. After distillation
of potassium metal in Pyrex with a flame containing no oxygen,
no sodium was detected. Distillation of potassium with an
taxy-gas flame produced a measurable amount of sodium in the

<iistillate. In a typical experiment the molar ratio Na/K

was 0.50.

54

5.5. Solvent Purification

Ethylenediamine of 99% stated purity was obtained as
a gift from the Dow Chemical Co. The solvent was first put
under vacuum in a 5 liter: vessel over barium oxide for a few
days. A magnetic stirrer was used to insure good mixing of
the liquid and the solid. Ethylenediamine was then trans-
ferred into an evacuated freeze purification vessel through
a medium porosity glass frit. The freeze purification vessel
is shown in Figure 5. The solvent was slowly frozen in a
refrigerator whose temperature was kept near 0°C. During the
freezing process, a low voltage was applied to the central
heater to establish stirring by convection. The freezing
process required from two to three days under those condi-
tions. After freezing, the central core was melted and
discarded.

After 5 cycles it was found that this ethylenediamine
could be distilled onto a potassium film to form stable blue
solutions. However ethylenediamine prepared in this way
could not be-mixed with a dilute metal solution without
decomposition. One more step was added to the purification
of the solvent. (It involved the formation of a blue solution
twith Na-K alloy, followed by a distillation from this solu—
tion. Solvent prepared in this way usually gave very stable

solutiOns.

55

Teflon stopcock

 

 

 

 

 

= , ‘$““-‘~— 15 mm Fischer-Porter
'oint
\ J

 

 

_/,./:Heater

To vacuum

1

CJ ' L1
Teflon 'lr
stopcock '————d' 7
_I

Figure 5. Freeze—purification apparatus.

 

 

 

 

 

 

 

 

 

 

 

56

5.4. Solution Preparation

A typical vessel for the preparation of solutions is

shown in Figure 4.

5.4.1. Metal Solutions

The metal was introduced into a side arm of the vessel
in an ampoule equipped with a breakseal.. Ethylenediamine
was distilled into the vessel under vacuum by using a dry
ice-isopropanol bath. The solvent was then degassed by
successive freeze-pump—thaw cycles until no detectable change
in pressure occurred. The freezing was done with a dry ice—
isopropanol bath rather thanvfiifliliquid nitrogen, because
there is a phase transition in solid ethylenediamine below
-80°C which causes the solid to expand and to break the vessel.
.After degassing, the solvent was again frozen, the breakseal
‘broken with the magnet, and the metal distilled. A pressure
of about 100 torr of purified helium was applied and the
vessel was separated from the vacuum line. The frozen ethylene-
diamine was then thawed with warm water and a blue solution

formed immediately.

5.4.2. Salt Solutions

Analytical reagent grade salts were used. Quantities
.larger than 100 mg were weighed; smaller quantities were
cjbtained by measuring the volume of a water solution which

cxsntained a known concentration of these salts. The salts

Magnet

72/~ar||

 

 

9

 

Met a1 ampou 1e

Figure 4.

 

57

’//¢/’

Teflon stopcock
I—

 

 

1.

Solution make-up vessel.

58

were dried by pumping at 10"6 torr for a few days. After
evacuation, anhydrous ammonia was condensed onto the salt
and distilled away several times to complete the drying

process.

5.5. Absorption Spectra

5.5.1. Spectrgphotometer

The principal component of the spectrophotometer shown
schematically in Figure 5, is a Perkin-Elmer Model 108
Rapid-Scan Monochromator. This and the associatedelectronics
have been described by Dye and Feldman (65). We will review
briefly the different components. The monochromatic light
beam leaving the monochromator is divided by a beam splitter
and focused on the sample and reference cells. The two light
beams are received on two RCA 7102 or 6199 photomultipliers.
The anode currents of the photomultipliers are sent to a
transducer circuit (Philbrick—Nexus PL1P) which takes the
logarithm of the ratio of the two intensity values. Opera-
tional amplifiers (Philbrick-Nexus P25A and P65AU) are used
to produce an output voltage of about one volt per absorbance
unit. The absorbance signal is recorded in analog form on
a 4 channel: Ampex SP500 FM Tape Recorder. One channel is
used to record the scan synchronization signal from the mono-
chromator. The Spectrophotometer can be assembled either on

a stopped flow appratus or with a thermostated cell

59

 

 

 

 

 

 

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compartment. The cell holders accept either square optical

cells or round ESR tubes.

5.5.2. Variable Path Length Cell

A cell whose path length could be varied under vacuum
was built. It is shown in Figure 6. It consisted of a 1 cm
path length quartz cell with a square cross-section connected
to a 16 mm cylindrical quartz or Pyrex tubing. In this cell,
a quartz insert could be raised or lowered with an external
magnet. This insert was built with three steps so that by
raising or lowering the cell in the light beam or by com-
pletely removing the insert, four path lengths were obtained:
10.0, 1.0, 0.5 and 0.1 mm. Various side arms were fixed
onto the quartz or Pyrex part so that dilutions could be made
by distillation. This did not work well because the vapor
pressure of ethylenediamine is too low to permit fast distil-
lations, and the smallest trace of hydrogen from decomposi—

tion stops this distillation completely.

5.5.5. Stopped—flow System

The stopped-flow system used in this work is similar
to those described by Dewald (66), Feldman (67), and Hansen
(68). Only one concentration of metal could be used per run
ibut a variety of solutes could be used, and dilutions could
be made. The system down to the waste vessel was equipped
(with Teflon stopcocks and Fischer-Porter "Solv-Seal" joints.

(holy the minimum number of joints was used in order to

Graded seal

agnet encased in
Pyrex

 

 

 

 

\L'

 

\ "
\ \-
. K
. \
. .‘

 

 

 

 

 

 

 

 

Graded seal

\

 

 

‘7—
;

Quartz insert

 

 

 

 

 

 

 

~ /// 9.9 mm.
' 9.7 mm
Quartz ///////
optical “2+5 cm
cell J /////// 9.0 mm.
6— 14/

 

 

 

 

 

 

 

 

Figure 6. Variable path length cell for optical
spectra.

42

prevent leaks. A schematic view of this system is shown

in Figure 7. The syringes were equipped with Teflon plungers
on which lips had been machined to give a vacuum—tight liquid
seal. The syringes used first were "gas tight" syringes

from Hamilton. In the course of this work, however, it
became necessary to have special syringes constructed. These
syringes were made of precision bore tubing (Trubore 8700—60,
Ace Glass Inc.). Teflon plungers were machined to fit these
new syringes.

As shown in Figure 8, in order to eliminate air leakage
from the syringes, a back-pumping of the seal was installed.
(This modification was suggested by Dr. V. A. Nicely.)

A side arm was sealed at the mid—point of the syringe, taking.
care not to distort the barrel, and the Teflon plunger was
equipped with two pairs of seals, above and below the con-
nection, so that this section could be constantly evacuated
during the motion of the plungers.

The mixing cell was a quartz four-jet: mixing cell.

This type of cell gives a mixing time of the order of 2 milli-
seconds. Details of the construction are given by Hansen

(68).

Stopping plate

4-Jet mixing
chamber and

optical cell

High

vacuum —'>

Metal
solution- a

Syringes

A'A
w

Figure 7.

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Figure 8.
flow system.

5.6.1.

a)

45

5.6. Data Analysis

Calibrations

Wavelength calibration: The sweep of the optical

frequencies by the monochromator is nearly a sinu—

soidal function of time. Electronic circuitry which
was designed to give a display linear in wavelength
was supplied with the instrument, but this proved to
be unreliable. Therefore a slotted disc was con-
structed which permitted light to reach a photodiode
once each cycle. In this way a synchronization pulse
was produced at the beginning of each scan. The
wavelength calibration was done with respect to this
reference pulse.

The wavelength calibration could be done in
either of two ways:

(i) The monochromator is equipped with two micro-
meters that permit reproducible adjustments of
the position of the center of scan and of the
scan width. These settings can be calibrated
with respect to absorption lines of glass filters.
The knowledge of these values and of the rota—
tion speed of the mirror is sufficient to cali-

brate the wavelength scale.

(ii) The second method (which was actually used in

this work) involved the recording of a known

46

spectrum under the same conditions as the un-
known. In this way, the unknown spectrum could
be calibrated by comparison. A computer program,
described in the next section, was written to do

this calculation.

b) Absorbance calibration: The path length of the
optical cell was measured by comparing the absorbance
of a solution of potassium permanganate measured with
our system, and with a UNICAM SP800 in a standardized
cell. The absorbance signal which we measured ap-
peared as an output voltage. To obtain the absolute
absorbance, the signal obtained by using standard
neutral density filters (Oriel Optics Inc.) was

recorded and used for calibration.

5.6.2. Data Analysis with a CAT

Most of the data consisted of spectra that did not change
over long periods of time. The main purpose of the analysis
was to obtain spectral shape and absorbances. Data stored
on magnetic tape were analyzed and put into digital form by
using a time averaging computer (CAT) Varian C 1024.
Figure 9 shows a block diagram of the circuit used for analy-
sis.

Description of the Analysis.

The signal from a blank channel of the tape recorder

and the signal carrying the spectrum were fed to a

47

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48

differential amplifier in order that the noise from the tape
recorder could be minimized. The output of the differential
amplifier was sent to the input of the CAT and to an oscil-
loscope. .The synchronization signal triggered the time base
of the oscilloscope. The gate signal from the oscilloscope
triggered the CAT and a time delay circuit. The delayed
pulse triggered a waveform generator (Wavetek, Co.) which
gave from 1 to 256 periods of a square wave. Each period of
the square Wave was then used to advance the channels of the
CAT. -Each period of the square wave advanced one channel.
By changing the time delay, the frequency of the square wave
and the number of periods, it was possible to analyze any
part of the spectrum.

The data stored in the CAT memory were then plotted on
an X-Y recorder or punched directly on cards.

It is to be noted that the oscilloscope was used only
for monitoring purposes. All of the measurements were made
from the output of the CAT.

5.6.5. Typical Measurements Made During
9.329.
1. The amplifiers of the tape recorder were calibrated
to give a known amplification ratio (usually 1:1).
2. The base line was recorded.
5. The spectra of the neutral density filters were

measured.

49

4. The spectrum of a didymium or holmium glass filter

was recorded to give the wavelength information.

5. The metal solution was
and its absorbance was
6. The metal solution was
mixture was stable the
Steps 2 through 4 were

ing the run.

introduced into the system
measured.

mixed with solvent. If the
run could be continued.

repeated several times dur-

5.7 Computer Treatment of the Spectra

5.7.1. Linearization of the Energy Scale

If we assume that the dispersion of the prism of the

spectrophotometer is linear over the region of interest and

that the rotating mirror turns

then we can write

at a constant angular velocity,

P=Asin [w(wt+f+0.5)] +13

with

P = wavenumber at the point in question.

-1

A = width of the scan in cm .

—l

B = center of the scan in cm .

w = angular velocity of the mirror.

t = time of rotation from arbitrary zero.

f’= phase factor.

To obtain the values of the above parameters, it was conven-

ient to fit this equation to a calibration spectrum.

50

The spectrum (both the forward and the reverse scan) of
the didymium glass filter was recorded. The following
quantities were then measured from an-X—Y recording of the

calibration spectrum.

P (I) = wavenumber of the Ith calibration point.
X (I) = fraction of total scan at the Ith point.
t (I) = channel number at which the Ith calibration

point is stored.

The values of w and )pwere obtained by using the relation:
X = wot + Y1 The values of A and B were calculated by fitting
with a least-square method P and t to the equation giving P.
After the calibration was completed, the wavenumber corre-
sponding to any channel number could be calculated.

All of the spectra studied in'a given run were analyzed
under exactly the same conditions as the calibration spectrum

and punched on cards.

5.7.2 Calibration of Absorbance

The absorbance curves obtained with the neutral density
filters were analyzed at the same time as the spectra of metal
solutions. For each channel number, a power series was calcu—
lated which related the true absorbance to the number of

counts from the CAT. In this way the spectrum could be trans—

formed to real absorbances.

51

5.7.5. Band-Shape Analysis

In order to analyze a spectrum consisting of V-, R—,
and IR—bands together it was necessary to know the positions
and band shapes of these bands and, if possible, to assign*
equations which describe these bands. All of the bands are
asymmetric with a long absorption tail towards the high
energy side. A combination of a Gaussian band shape and a
Lorentzian band shape was used. The procedure used involved

fitting the data to the following equations:

for I; <1 :7

 

 

 

max
é- —- 5" imax 2
A (v) = A(vmaX)-exp [ -O.69515 ( A—G ) ]
i
for v 2 vmax
A(V) = A(Vmax)
'3'- 3max 2
1 + < I?
i
with
A (7) = absorbance at the wavenumber
Vmax = wavenumber at the max1mum-
Avg = half-width at half-height for the Gaussian
side.
53L = half-width at half—height for the Lorentzian
2' side.

A non linear least-square program was used to fit these equa-

tions to the data (69). This program adjusted four parameters

52

._ _. A._G A....L
A(V ), Vmax, vi. and Vé’ .

The results of this fit are shown in Figures 10 and 11 for
cesium in ethylenediamine and sodium in ethylenediamine.

It is not possible to obtain only the R-band of potas-
sium so we had to assume that the R-band followed the same
form of equation as did the V- and IR-bands.

With one equation for each of the bands, a program was
written (Program SPFIT) that fitted any composite spectrum
to a sum of V—, R- and IR-bandsby least-squares. It is to be
noted that the program SPFIT did not adjust the banddwidths.
These were obtained from spectra of the pure components.

The fits obtained with this program will be given in the

Results section.

5.8. Pulse RadiOlysis Experiments
Two kinds of experiments were performed, spectral
determinations and kinetic studies. Neither of these re-

quired precise dosimetry.

5.8.1. The Accelerator

These experiments (70) were performed at the Ohio State
University with a Varian V—7715A linear electron accelerator.
Electrons were generated with energies of 5-4 MeV, with a
pulse current of about 550 mA. The pulse width was varied,
from 0.1 to 1.2 u sec. The average dose of radiation re—
ceived by the solution was about 6 x 106 eV/g for a 0.1 u sec

pulse.

55

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55

5.8.2. Optical System

A block diagram of the optical detection system is shown
in Figure 12. The light beam from a 500 W-Osram Xenon lamp,
type XBO450W, was split, after passing through the cell, by
a partially silvered mirror. The two light beams entered
two grating monochromators (Bausch and Lomb, Type 55-86-25,
f/5.5). This set-up allowed two wavelengths to be monitored
simultaneously. The detectors used in this work were of two
kinds depending on the type of studies.

(i) For the spectral studies a liquid-nitrogen cooled
indium-antimonide detector, type A10X (Barnes
Engineering, Inc.) was used. An RCA 7102 photo-
multiplier was used in the other beam as a reference
wavelength monitor in point—by-point spectral
scanning.

For effective use of the indium antimonide
detector it was found desirable to pulse the lamp
to Obtain a higher output. In the high intensity
pulsed mode a current pulse of 150 A is added to
the normal continuous current of 20 A. The result—
ing increase in intensity is about 25—40 times that
of the steady state operation depending on the wave-
length. The duration of the light flash is several
milliseconds, with a usable constant intensity,
portion of 0.15 msec synchronized with the electron

pulse.

56

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57

(ii) For the kinetics studies two wavelengths were
monitored: 600 nm with a 1P25 photomultiplier and
1020 nm with an RCA 7102 photomultiplier. The out-
put of both detectors were displayed on a dual
beam oscilloscope and pictures of the traces were

taken.

5.8.5. Reaction Cells

The optical-irradiation cells were made of high-purity
silica. They were connected to a sample handling device in
which samples of material to be added to the solvent were
contained in sealed, evacuated glass bulbs which could be
successively broken ip_§ipp_to change the composition of the
system. This sample system is shown in Figure 15.

This technique was very useful since all solutes addi—

tions were made to the same sample of solvent.

58

 

Figure 15. Cell used for pulse radiolysis
studies.

 

 

 

IV . RESULTS

In this section the band at 660 nm will be referred to
as the V-band, the band at 850 nm as the R-band and the band

at 1500 nm as the IR—band.

4.1. Sodium Solutions
4.1.1. Influence of Sodium Ions Upgn
theyV-band

Hurley, Golden and Tuttle (55) concluded that the V-band
observed in potassium amine solutions resulted from the
exchange of potassium ions with sodium from Pyrex glass.
A series of experiments was done here to test these conclu-
sions. We established in section III that distillation of
potassium through Pyrex did not cause contamination of the
distillate by sodium provided that a cool flame was used.

When a Pyrex cell was filled with anhydrous ethylene—
diamine, allowed to stand for several hours, and then emptied
by distillation, no sodium could be detected in an aqueous
leach. When an identical cell was filled with a solution of
potassium in ethylenediamine, with no excess metal present,
allowed to stand for one hour, and then emptied by distilla-

tion, the molar ratio of Na/K was 0.15 (it should be noted,

59

Ir

60

however that only 1.7 x 10'6 gram atoms of potassium were
used). By using a quartz optical cell of path length 1.0

cm attached to a Pyrex apparatus, it was found that distil-
lation of the metal through Pyrex, and contact of the solu-
tion with Pyrex gave essentially only the V—band. Analysis
of the solution gave an Na/K ratio of 0.5, with enough total
sodium to account for the V—band.

A solution prepared in an all quartz apparatus showed
only the R-band. Analysis of the solution showed no detect—
able sodium. In another experiment, when a solution prepared
in quartz and containing only the R-band, came in contact with
Pyrex, a V-band developed immediately.

The difficulties involved in the production of stable
dilute solutions prevented us from getting reliable values
of the concentrations of species responsible for each of the
absorption bands. Concentrations of alkali-metals as low as
those we were using could only be determined by flame
photometry and even then only the *total concentration of
the particular metal could be measured.

It was also noted in these experiments that a solution
of cesium could be prepared in a Pyrex vessel without giving
any trace of a V-band. This agrees with previous observa-
tions in this laboratory (66,68).

4.1.2. Molar Absorptivity of Sodium-
Ethylelediamine Solutions

The instability of metal—amine solutions has prevented

61

the determination of the concentration of active metals by
the usual analytical techniques. None of the techniques
which involve analysis for the alkali metal permit dis-
tinction between the metal present as decomposition product,
and as active metal. Direct determination of the concentra—
tion of metal solutions can be done by reacting the solu—
tions with an acid (H20 or NH4+) and measuring the volume

of hydrogen evolved (66).
e-(or M) + H20 ——> OH” + 1/2 H2 (+ M+)

This method requires large volumesof solution and/or rela—
tively high concentrations in order to obtain a volume of
hydrogen large enough to permit accurate measurement.

The optical spectrum of a sodium solution in ethylene-
diamine consists of a single band centered at 660 nm (15,200
cm-l) with little or no absorption in the infrared region.

This indicates that the equilibrium
V-band —-—>i IR—band

lies very far to the left. The results described later also

indicate that the reaction
e_(IR—band) + Na+ -—+‘ V-band

occurs very rapidly-
The reaction of sodium ions with a source of solvated

electrons, such as a cesium solution, proceeds quantitatively

62

to give the V-band presumably by the reaction

m Na+-X— + n Csfe- -—-9- V-band
(IR—band)

By keeping the initial concentration of the solvated electrons
greater than that of sodium ions, the dependence of the
absorbance of the V-band upon the concentration of sodium
ions added could be determined.

Some typical spectra are shown in Figure 14 in which we
have shown the effects of various amounts of sodium ion.
It is to be noted that the IR-band does not follow the varia-
tions of the V-band. This is because of the decomposition of
the cesium solution. The data were analyzed by using the
program SPFIT to separate the absorbance due to the V-band
from the absorbance due to the remaining IR-band. A typical
fit of the data is shown in Figure 15. The results are shown
in Tableiflt. The absorbances have been corrected to a path-
length of 1 mm. A plot of the absorbance of the V-band
versus the concentration of sodium ions added is shown in
Figure 16. These data can be fitted by least squares to a
straight line of slope 8.2.1 0.5 x 103 M‘l. This yields a
molar absorptivity of 8.2.: 0.5 x 104 M" cm“; based upon
added sodium. The data obtained when sodium ions were in
excess have not been included. In this case, the absorbance
is proportional to the concentration of the cesium solution

at the time of the experiment. This concentration can vary

65

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coHumuusmosoo

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64

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Table II. Absorbance of the V—band Produced by Addition of
Sodium Ions to a Cesium Solution

65

 

 

 

[Na+] A Standard
M x 105 deviation
2.15 0.25 0.02
2.50 0.195 0.02
5.15 0.22 0.02
4.50 0.41 0.04
6.50 0.556 0.07
9.45 0.85 0.07
10.75 0.94 0.07
12.60 0.89 0.05
14.60 1.25 0.08
18.90 1.82 0.10
18.90 2.11 0.05
22.00 1.79 0.12
57.85 2.65 0.15
44.00 5.86 0.40

 

66

 

 

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0

. Run 5-25-70
A Run .12-02-69

 

l l l l

 

4.0”fl
'U i-I.
c
m
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> 5.0“
m
n
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ma
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m
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o ._
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100'—

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Figure 16.

10.0 20.0 50.0 40.0

[Na+] (M x 105)

Absorbance of the V-band as a function
of the concentration of sodium ions.

67

because of decomposition. Therefore the amount of V-band
obtained in such experiments is not reproducible. It was
just such non-reproducibility of metal solution concentra—
tions which led us to use the present method in the first
place.
4.1.5. Reaction of the V-band Species

with Anthracene

From the results of pulse radiolysis of solutions of
aromatic compounds in alcohols, it was known that the electron
transfer reaction to give the negative radical ions was very
fast (70). It was thought that the reaction of the V-band
species with anthracene would also be very fast. Previous
observations indicated that anthracenide ion was very stable
in ethylenediamine, and did not even react with water (68).
Furthermore, these observations showed that the radical anion
was very rapidly formed when cesium solutions were mixed with
solutions of anthracene.

When a sodium solution, of concentration 2.5 x 10“ M,
was allowed to contact a crystal of anthracene, the solution
turned to a bright yellow color very rapidly. The optical
spectrum of this solution in a 1 mm cell did not show any
spectrum characteristic of the anthracenide but, rather,
exhibited a new band at 457 nm. A small peak of anthracenide
was observed when the pathlength was increased to 1.0 cm.
After a few hours it was noted that the solution gradually

became greener. -An optical spectrum recorded 24 hours later

68

showed the characteristic spectrum of anthracenide as well
as the peak at 457 nm. At this time, both peaks were of
the same magnitude. This spectrum did not change further
with time. The spectrum is shown in Figure 17; the positions
of the peaks of anthracenide in tetrahydrofuran (75) and
their intensities have also been reported. The solvent was
then distilled back over sodium to regenerate a blue sodium
solution. This solution was put back into contact with
antracene and anthracenide. The optical spectrum of the
resulting solution was recorded as a function of time.
A decay of the band at 457 nm was observed together with a
growth of the anthracenide peak. An isosbestic at 550 nm was
observed. Experimental difficulties prevented us from obtain—
ing the beginning of the reaction. The spectra observed
during the reaction are shown in Figure 18. Both the growth
and the decay follow second order kinetics as shown in Figure
19.
4.1.4. Kinetics of the Reaction of Sodium

Ions with the Solvatethlectrons

The formation of the V-band by the reaction:
— +
m e + n Na —-->- V-band

can be studied very conveniently by pulse radiolysis. Each
pulse of electrons was used to obtain two sets of kinetic
data: the growth of the V—band, monitored at 600 nm (16,600

cm‘l), and the simultaneous decay of the e- band (IR-band)

69

 

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70

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71

 

Growth of the anthracenide band

 

 

 

 

 

 

 

 

60 P
50..
40*—
.8 /
50 - ’///’Q
can
I.¢ 20 57/’/0
J
10 -
l 1 L_ l l
2 4 6 8 10
Time (min)
Decay of the intermediate band
-10 :-\0\
O\\\\\
’t 20
1* ' o
d \\\\\\\\\\\\\
-30..
l l l l L
2 4 6 8 10
Time (min)
Figure 19. Kinetics of growth of the anthracenide ion and

of decay of the intermediate (yellow) band.

72

monitored at 1020 nm (9,800 cm'l). A set of typical traces
is shown in Figure 20. Both the growth of the V-band and
the decay of the IR-band follow second order kinetics.
within experimental error. A typical pair of curves is
shown in Figure 21, together with the fit of these curves to
a second order mechanism using 5 parameters: A0 and Ag),
absorbances at time zero and infinity; and k the rate
constant. Each pair of curves gives us some informations
about the relative absorbances of the two species. In Table
III, we have listed the values of the initial absorbance of
the IR-band and of the final absorbance of the V-band. It
is to be noted that the ratio of these two absorbances is a'
constant whose value is 1.88.: 0.28.

In order to reduce the number of adjustable parameters
needed to fit the data, each set of curves was fitted simul—

taneously to the same kinetic equation.

Analysis of Kinetic Results
For reasons of clarity we are going to assume here some
of the results that will be established later. Namely, we

postulate that the stoichiometry of the reaction is:

Na+ + 2e— -——9- Na (1)

and that the two absorbing species are e-(IR—band) and

Na- (V-band).

 

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75

Table III. Reaction e- + Na+'-—)-V-band. -Relation Between
the Absorbance of the IR-band at the Beginning
of the Reaction to that of V-band at the End

 

 

 

 

Identification ANa_(600,a3) Ae_(1020,o) 5%:£%$gégjg)

5.69.81 0.462 0.251 2.00
82 0.426 0.205 2.10
86 0.215 0.086 2.50
87 0.156 0.079 1.97
88 0.812 0.528 2.47
89 0.715 0.545 2.07
90 0.666 0.554 1.99
91 0.691 0.580 1.82
102 0.644 0.569 1.74
105 0.624 0.567 1.70
107 0.851 0.561 1.51
109 0.118 0.068 1.72
112 0.177 0.090 1.96
115 0.757 0.491 1.54
114 0.617 0.564 1.69
115 0.975 0.528 1.84
116 1.159 0.781 1.46
117 1.095 0.555 2.05
120 0.251 0.154 1.87
121 0.259 0.151 1.71

 

 

76

The absorbance at any wavelength is given by:
A(x, t) = eNa-(x)~b-[Na ] + ee_(k)-b.[e-] (2)

in which €Na_(k) and ee_(k) are the molar absorptivities at
the wavelength A and b is the pathlength. Furthermore we
assume that after a very long time the only absorbing species
is Na-. In Table IV, we have listed the values of ANa_(600,a>)
and Ax£m(1020,oo) and their ratio. This ratio does not change
appreciably with hundred—fold change in the concentration of

the sodium ion. This substantiates the assumption that:
A(k.a>) = eNa_(A) ° [Na ]00 (5)
The presumed stoichiometry of reaction (1) gives

[Na’loo = %- re")O <4)

or

[Na—1 = %-( [e’] — [e’] >

The above relation is useful only if we can determine the
initial time of the reaction. When basic ethylenediamine

was subjected to pulse radiolysis, a growth of the electron
band was observed for 5-10 microseconds after the end of the
electron pulse, as shown in Figure 22. This growth prevented
the determination of the exact initial time of the reaction
with Na+. Therefore, the initial electron concentrations

and the zero of time were used as parameters in the

77

 

 

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78

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79

investigation of the kinetics of decay of the IR-band and
growth of the V-band.

The growth of the V—band and the decay of the IR-band
represent the kinetics of the same reaction. It was pos-
sible to fit each pair of data sets to the same kinetic
equation. The parameters used are: A(1020,o), the initial
absorbance of the IR-band;1§, the initial time at the pre-
sumed zero of time; 6 _(:020).b' where k is the pseudo-second
order rate constant; :nd.A(600,a>), the final absorbance of
the V-band. By using this method of analysis, it is possible
to fit the data with four parameters instead of six used
when each curve was fit individually.

The rate of the reaction (1) was found to follow the

equation

_£%E§:L_ = ..§E%E§i:l = — 2k[e—]2 [5]

:93 which k is the pseudo-second-order rate constant. By
\uaing the relations (2). (5), (4), and (5), it is possible
to write equations in terms of absorbances and molar absorp—
tivities.

e (600)

_._ Na“

A(6°°' t) ’ 2 €3-110203 '

H

.A(1020, o) +

 

 

 

 

€e_(600) _ 1. €Na_(600)
_, ee_(1020) 2 ee_(1020)
1 2 k (t +73)

 

 

A(1020, o) + €e_(1020).b

80

and
eNa_(1020) 6Na_(600)

 

 

 

 

 

 

 

_ .1
1 _ $-. €Na_(1020) eNa_(600)
2 eNa_(600) €e_(1OZOT
1 + 2 k (t +7)
A(1020, o) ee—(10205- b

Some of these ratios can be simplified, but they are written

in this way so that the known quantities appear explicitly.
. . eNa_(1020) €e_(1020) .
The quantities eNa‘1600) and €e_(600) are obtained

 

 

directly from spectra of sodium and cesium solutions in

eNa_(600)
ethylenediamine, respectively. The quantity 6 (102077 is
e‘

obtained from Table III.

“600' OD) _ 6Na_(600).b.[Na-]m
311020, oI' ’ €e_(1020).b.[e']o

 

From.relation (4) we obtain:

A(600, oo) _ 1 eua-(600)

A(1020, 07" E’ ee:T1020)

which yields:

eNa_(600)

€e_(1020) = 5.76.: 0.55

 

The results obtained by adjusting three parameters to each
set of decay-growth curves are shown in Table V, in which
we have listed the sodium ion concentration, the initial

absorbance of the electron band and the value of the rate

81

 

 

 

Table V. .Kinetic Analysis of the Reaction Na+ + 2e- —1>Na-
[Na+] A(1020,o) k/e(1020) Standard Deviation
M cm.sec-lx 10"4 cm.sec‘1x 10"
0.00554 0.297 8.12 0.22
0.265 8.12 0.20
0.125 8.08 0.29
0.105 7.28 0.24
0.497 8.16 0.52
0.485 7.52 0.24
0.448 7.52 0.22
0.475 6.80 0.19
0.018* 0.228 12.6 0.64
0.211 8.72 0.98
0.275 10.77 0.84
0.297 12.5 0.45
0.206 15.1 0.81
0.506 12.6 0.68
0.180 8.76 0.47
0.228 12.6 0.64
0.022 0.405 10.8 0.21
0.406 11.2 0.27
0.562 9.7 0.10
0.084 9.7 0.19
0.065* 0.156 10.74 1.51
0.215 10.14 2.00
0.177 14.0 2.7
0.260 10.6 1.66
0.086 0.127 14.16 0.57
0.116 11.92 0.52
0.411 10.84 0.57
0.575 10.48 0.11
0.564 10.24 0.16
0.1211* 0.156 8.8 0.70
0.254 7.88 1.54
0.500 8.8 0.82
0.215 8.7 0.96
0.457 7.56 5.2

continued

82

Table V—-continued

 

 

 

[Na+] A(1020,o) k/€(1020) Standard Deviation
M cm.sec’IX”10" cm.sec'lx 10“
0.2179 0.662 12.0 0.51
0.602 10.6 0.28
0.585 9.76 0.21
0.165 10.56 0.65
0.172 9.60 0.16
0.5424 0.256 12.44 0.50
0.185 10.24 0.15
0.157 10.76 0.14
0.545 9.76 0.08
0.558 9.24 0.10
0.411 9.28 0.11
0.474 8.84 0.18
0.455 9.56 0.12
0.420 8.72 0.14
0.506 9.24 0.15
0.648 10.12 0.29
0.611 8.72 0.19
0.754 9.40 0.24
0.691 10.00 0.25
0.541 8.92 0.15

 

*-

,_v

= different run

85

constant with its standard deviation. The parameter

A(600 co) ENa‘(600)

A 1020’0 which appears in the ratio 68-11020; was not
adjusted in our study. A typical fit of the data is shown

in Figure 25. These results were used to obtain the averages
given in Table‘VI. It can be seen that the pseudo-second-
order rate constant is independent of the concentration of

sodium ions over the concentration range studied.

4.2. Equilibria in Metal-Ethylenediamine Solutions

4.2.1. Equilibrium, R-band ——>,= IR—band
in Potassium Solutions

The absorption spectra of solutions of potassium in
ethylenediamine showed two bands. One was characteristic of
the solvated electron, and the other was metal dependent.
By analogy with sodium solutions,and in accordance with the
conclusions of Matalon §E_§_. (56) and of Glarum and
Marshall (65), we considered the metal-dependent band to be
characteristic of the species K—. Since the two bands exist
together, it is logical to postulate that we have an equi-
librium that can be written

rK'l 7K-

[ca-172 '. [1817 ° Ve-Z- “no“

 

 

.. + _.
2e +K-—>‘EK (6)K5=

or

= _ - 3’ "
‘— [e2] .[K 1 7.; . 4K.

 

 

where K5 and K7 are the equilibrium constants.

84

. + — -
Table VI. Reaction Na + 2e —->-’ Na . Average Values of
the Rate Constant

 

 

+

 

Na k/e Standard deviation

M cm.sec"l cm.sec'1
0.0055 7.88 x 104 0.57 x 104
0.0180 11.88 x 104 0.82 x 104
0.0220 10.56 x 104 0.45 x 104
0.0850 11.57 x 104 1.02 x 104
0.0880 11.52 x 104 0.80 x 104
0.1211 8.51 x 104 0.55 x 104
0.2179 10.52 x 104 0.47 x 104

0.5424 9.88 x 104 0.24 x 104

 

85

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86

This equilibrium was investigated by using the same tech—
nique as in the study of sodium solutions. A cesium solu-
tion was used as the source of solvated electrons, and was
mixed with a solution of a potassium salt of known concen-
tration. This reaction is faster than the mixing time so
that study of its kinetics by stopped—flow methods is not
possible. Because the reactions (6) and (7) give an equi-
librium position which is not too far to the right, it is
possible to generate various amounts of the K--band with
the same starting cesium solution. .The study of this reac-
tion was made more difficult than the corresponding study
of the sodium ion reaction by two effects:

(i) Potassium solutions are much more reactive than

sodium solutions.

(ii) The amount of R—band generated could not be de-
termined easily during a run and it was necessary
to wait for the computer analysis of the spectrum
to know if the results were valid.

The potassium solution was generated in a quartz mixing
chamber so that sodium exchange after mixing was not an
important factor. The spectra obtained after mixing were
analyzed by the pregram SPFIT which gave the contribution
of each band to the spectrum. A typical fit is shown in
Figure 24.

. The results for two different runs are shown in Table

VII, which gives the absorbance of the starting cesium

87

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0404 .04 00402 40 000
:04 x us .04 x u: 04 x z
m =0 4 m .M 4 m0 040 0040 4 +0 00440044440004

 

 

pamalm .4lll.+M + pamaan mm4osym E544a444svm. .HH> magma

89

 

 

 

NN.0 H. 0.0 H. "msam>
44.4 0.0 00040>¢.
mm.m 00.0 mmm.0 004.0 n.m
n4.m 00.04 4mm.0 004.0 0.0 044.0 N.m
04.0 04.44 mma.0 NhN.0 0.4
nm.m >0.N4 444.0 ¢¢N.0 4.4
04.0 00.04 0m4.0 th.0 0.0 000.0 0.4
00.0 00.04 04.0 000.0 0.0
N0.m 00.04 00.0 000.0 4.0
40.0 mm.4 004.0 mm4.0 0.0 0400.0 0.0
0004.44 40080000 40 000
IOH 44 IS IOH x I: O.“ x E
m
0% d N .M a Md MH< OMHd N +M aowymuwmwychH

 

 

wmscflyaoollHH> manna

90

solution: AIRO' the concentration of potassium-ions: [K+]°,

and the absorbances of the R-band and of the IR—band in the

final solution: AR’ R

The value K' is taken as

and AI respectively.

A A0
K' = R 2 . IR
(AIR) [16F] o

and K" as

A . [K+] °

The reasons for the calculations of these pseudo-equilibrium
constants will be explained in the Discussion section. It
is to be noted that the values of K' and K" are fairly
constant for both runs.

A control experiment was performed in which the blue cesi—
um solution Used for the run was analyzed for total cesium
content by flame photometry. The effect of adding a cesium
salt solution to the solution of potassium salt, before
mixing it with the cesium metal solution, was studied.

This run was characterized by very poor stability of the
solution after mixing with a solution of either the potassium
salt or of the cesium salt although the cesium solution was
stable by itself.

The absorbance of the cesium solution used in this run
was about 0.6 at the maximum, which, with a molar absorptiv-
ity of 2 x 10‘ M'locm‘l (defined in the next section),

implied a concentration of cesium of 5 x 10“ M. However,

91

the analysis of the cesium residue yielded a concentration
of about 2 x 10'3 M in cesium ions. Upon analysis of the
data, it was noted that the absorbance of the R-band was
only of the order of 0.05 absorbance units. Given the very
poor stability of these solutions, these values are unre—
liable and, no useful information concerning the equilibrium
constants could be obtained.
4.2.2. Attemp¥Hto Stu_y the Reaction

e" +K -—+ R-band bygpulse

Radiolysis

This study was attempted in the same way as the study

of the reaction of sodium ions with electrons. The solutions
were prepared similarly but no growth of a band in the
region of 850 nm was observed upon irradiation. The spectrum
obtained was mapped at different times during the decay.
These spectra,shown.in Figure 25,do not show any variation
of the band shape with time. Therefore, no kinetic studies

of this reaction were possible.

. . . +
4.2.5. Equilibrium V—band + K -—+vR—band
The purpose of this study was to see whether the equi-
librium
+
V—band 1——9- IR-band + Na

or

+ - +
V—band + K '1->' R—band +‘Na

could be shifted to the right. We added a massive excess of

92

 

 

A = End of the pulse

0 = After 20 usec
U = After 40 usec

 

4.
A
A(600)
5
2
1
Figure 25.

A
60
U A
6A
D
[39A
0
BA
0A
B
[X
8
1 l 1 1 1
10 11 12 15 14

Wavenumber (cm-1 x 10‘3)

Spectrum obtained by pulse radiolysis in an
attempt to study the reaction e' + K .

 

95

potassium iodide to a solution of sodium in ethylenediamine.
No drastic changes in the spectrum occurred during the reac-
tion. In particular, no band in the neighborhood of the

R—band appeared by the reaction
+ +
V—band + K -—-> R-band + Na

‘———

We show, in Figure 26, the spectra obtained with and without
addition of potassium salt. Both spectra have been normal—
ized to the maximum of absorbance of the V-band.

The effect of the addition of potassium solution whose
concentration was 1000 times greater than that of the sodium
solution was a slight change in the absorbance towards the
infrared. In order to verify that this was not an instru-
mental effect, some experiments were done in which the potas-
sium salt solution was7mixed with a concentrated sodium salt
solution. 'As shown in Table VIII, for pushes of series 5 and
8, when sodium ion was present in excess, almost no absorption

in the infrared was detected.

4.5. Reaction of Sodium-ethylenediamine
Solutions with Water: ‘Hydroxide'Effect

This reaction was studied extensively by Feldman (67)
and by Hansen (68). In this work, the effect of various
concentrations of sodium hydroxide on the rate constant for

this reaction was tested.

94

 

.0004 854000yom 0040yaoo 0040 am4a3 :04y5400 0 40 0:0
004y5400 554000 musm 0 mo Esuyommm may no 0004400800 .04 mysm4m

40104 x 4:800 mymaezam>03

 

04 04 ma 44 m4 Nd 44 04
_ a _ T _ _ 4, _
.lm.0
0m000 I.
:04 854000yom ay43 u N 4
:04y5400 854000 mysm u H 1:4.0
x020-
4 1 I0...
[0.0

 

 

 

 

 

95

+
Table VIII. Equilibrium Studies K + V-band

 

 

 

 

+
Identifica— [K ] A A
tion M IR AR V

5.5 0.125 0.108 0.056 0.255

5.4 0.145 0.050 0.579

5.5 0.129 0.051 0.292

5.6 0.156 0.050 0.575

5.7 0.146 0.019 0.548

5.2 04125 0.0 0.020 0.297

5.5 [Na ] added 0.0 0.015 0.554

5.4 0.012 0.010 0.524

6.5 0.1875 0.044 0.00 0.610

6.4 0.042 0.641

6.5 0.042 0.646

7.5 0.575 0.159 0.00 0.451

7.4 0.165 0.00 0.554

7.5 0.149 0.01 0.574

8.7 0 575 0.026 0.00 0.481

[Na‘] added

 

96

“As was the case for reactions with water in ethylene-
diamine, the reactions in the presence of sodium hydroxide
follow first order kinetics with respect to the V-band.

The decay curves of absorbance as a function of time can be

fit to the equation

where A0 = absorbance at the beginning

 

Aq3= absorbance at infinite time.

Three parameters were used to fit the curves: A0, Am) and
k the pseudo-first-order rate constant. A typical fit is
shown in Figure 27. In all of the cases studied, Au, was
of the order of 0.01 A0.

The pseudo-first-order rate constants, kps’ are listed
in Table IX, together with the water and sodium hydroxide
concentrations. In Figure 28 log kps is plotted versus
log [H20], the slopeof the straight line has been obtained

by least-squares and is 5.2.: 0.15.

4.4. Optical Spectrum of the Solvated Electron
in Water—Ammonia Mixtures and in
Water-Ethylenediamine Mixtures
The spectra of the solvated electron in water-ammonia
rmthures and in water-ethylenediamine mixtures were obtained

iby pulse radiolysis. As shown in Figures 29 and 50, the

spectra.obtained in pure ammonia and ethylenediamine by pulse

97

.Em4amammfi HmUHo y044m 0 0y y4m

 

 

.ma4E04Umcm4maym a4 ymy03.ay43 854000 40 :04yu0mm .hm mysm4m
Aummv mE4B
m.0 . who . 4.0
AY/IO
%
O//.O
///O I N.0
/O/

0
/Jo 7.4.0
1.0.0

40ycmE4Hmmxm u 0
Umy045040o u
2 40.4 n 4000.

2 004 x 0.0 u 4.00.
0.Nd :04y0o444yam0H

 

 

 

0.0

0.4

XMEAN

98

Table IX. Reaction Na- + H20; Hydroxide Effect

 

 

 

Identifi- [H20] [NaOH] k Standard
cation ps Deviation
M M sec-1 sec'1
18.5 1.90 5.5 x 10-3 0.574 0.010
18.4 0.625 0.008
18.5 0.519 0.008
18.6 0.507 0.004
18.7 0.557 0.006
17.5 2.16 1.75 x 10-3 0.982 0.021
17.4 1.114 0.015
17.6 0.690 0.005
17.7 0.754 0.004
17.8 0.645 0.004
19.4 2.45 0.00 0.642 0.004
19.5 0.642 0.005
19.6 0.585 0.004
19.7 0.594 0.006
20.5 2.79 2.92 x 10‘3 1.445 0.055
20.6 1.195 0.007
20.7 1.210 0.012
20.8 1.455 0.051
15.5 5.54 8.75 x 10-~3 6.71 0.20
15.4 5.07 0.05
15.5 6.50 0.18
15.6 5.55 0.05
12.4 4.01 5.5 x 10-3 8.95 0.15
12.5 10.68 0.09
412.6 10.21 0.07
12.7 9.84 0.11
11.5 4.20 4.58 x 10-3 15.67 0.07
11.6 14.77 0.09
11.7 15.59 0.11
14.4 4.41 2.92 x 10-8 9.77 0.08
14.5 9.56 0.08
14.6 10.01 0.26
14.8 9.18 0.05

continued

99

Table IX-—continued

 

 

 

Identifi- [H20] [NaOH] k Standard

cation ps Deviation
M M sec-1 sec-1
16.4 4.75 9.7 x 10" 9.50 0.06
16.5 9.51 0.25
16.6 15.80 0.50
16.7 11.90 0.20
16.8 11.80 0.50
16.9 10.00 0.10
10.8 4.86 0.00 11.17 0.12

10.9 11.17 0.09

 

100

 

 

 

 

 

100 r
b x = Our results
- E = E. M. Hansen (68)
10 -—
C
:1 -
l
U u-
0
4"}
m b
o.
.2
1 L—
r-
F
r-
1 L 1 7 J I l
1 1.5 2 5 4 5 6 8
[H20] (M)

Figure 28. Plot of log (k ) versus log [H20] for the reac-
tion of sodium with water in ethylenediamine.

101

.Uomdl um MHGQEEM
Uflsvfla a“ couuooam Umum>aom mnu mo Esuuommm coflumHOmnd .mm muomflm

AMIOH x HIEUV Hmnfiscw>m3
dd 0d m m b m m

<'

 

 

0.0

fl

_ V _ _ _ _ w

l.m.o

Nflf

 

mwmwaowumu madam u o

I .oo

 

coquHOm Eswmmmuom I.III

 

 

102

 

.mcHEMAo
Imcwamnum CH couuowam Umum>aom mnu mo Esnuommm 20aumnomn< .om musmflm

Amloa x HIEUV Hmnfiscw>m3

3 ma ma 3 om m m .6
_ ._ _ _ 1 _ _ _ o. o

 

mammaowomu 0masm

 

coflusaom Eswmmo 0.6

 

 

 

105

radiolysis were the same as those obtained for solution of
metals in these solvents. As we have shown in Section 5.7.5,
these spectra can be fit by a combination of a Gaussian and
Lorentzian band shape. As shown in Figure 51, as the concen-
tration of water increases, the position of the maximum
shifts to higher energies and the band broadens markedly.
All of the spectra obtained have the Gaussian-Lorentzian line
shape. In Figure 52 we have plotted on a normalized energy
scale such a Gaussian-Lorentzian band shape, together with
the experimental points obtained for a variety of ammonia
mole fractions.

A method of treating the data was sought which would
permit error estimates to be made for both peak positions
and half-widths. The procedure chosen involved fitting the
data with a shape function by using a damped non-linear
least-squares program (69) which provided estimates of the
standard deviations of the parameters. The function used
was a combination of a Gaussian on the low energy side and
a Lorentzian on the high energy side. This procedure yielded
excellent representations of the spectra.

The peak position and half width for ammonia-water and
ethylenediamine-water mixtures are given in Tables X and XI.
Figures 55 and 54 show the variation of the position of the

maximum and of the band-width with water concentration.

104

0 I m 0 s O _ y 0
mm.“ on mzxé .mmm oummzxuam .mmw ouomzxuo «ONE whom B .252 musm I

.mmusuxfle macoEEMIH0um3 aw couuowam Umum>HOm on» no Esuuommm cofiumuomn< .am musmam

finned x AIEUV mHmQEDcm>mz

ma Z. 3 ma 5...“ ma ma «.8 3 m m p m
1

w 4 fl _ _ _ _ 1
/

 

  
  

ILN.O

m.o

w.o

m.o

“WV/v

m.o

>.o

m.o

.m.o

0.6

 

 

 

105

 

1.0L-

 

AMax 0.6—-

0.5—-
0.2—-

O.1_.

 

   

 

 

Figure 52.

Symbol XNH3
O .051
A .159
+ .285
x U .655
Q X 1.000
\:
'i/o
3
C]
A/
A.
0.
Lorentzian
E]
Gaussian +
l l l I l l l
-004 -002 000 002 004 006 0.8 1.0
v_f vMax
vMax

Solvated electron band-shape in ammonia-water

mixtures.

106

Table X.. Solvated Electron Absorption Band Position and Half-
width For Ammonia-Water Mixtures

 

 

 

Mole Position Width at

Fraction of the Standard Half-» Standard

of Water Maximum Deviation Height Deviation

cm'l cm-l cm’l cm‘1

0.0 6500 5100
0.144 6550 210 5410 710
0.215 6970 700 5700 200
0.558 7180 90 4470 560
0.567 7470 40 5710 60
0.421 7650 110 4000 160
0.421 7620 140 4200 200
0.489 8250 70 4950 100
0.496 8500 270 5550 420
0.555 8900 120 5800 400
0.594 9570 240 6520 440
0.594 9570 50 5850 100
0.717 11090 100 6580 210
0.752 11820 80 7250 150
0.759 12170 250 6550 600
0.841 12950 70 6780 80
0.862 12900 80 7120 170
0.929 15570 110. 6950 150
0.949 15470 100 7100 200
1.000 15640 70 7210 110

 

107

Table XI. Solvated Electron Absorption Band Position and
Half Width for Ethylenediamine-Water Mixtures

 

 

 

Mole Position Width at

Fraction of the Standard Half- Standard

of Water Maximum Deviation Height Deviation

cm‘l cm‘l cm'l cm'1

0.0 7560 145 7070 555
0.265 8860 140 7950 560
0.424 9540 210 7050 550
0.424 9590 200 7260 550
0.524 10160 250 6600 560
0.557 10170 70 7210 100
0.605 11000 100 7000 155
0.655 11400 100 6916 150
0.702 12460 150 6750 .150
0.757 15020 170 6815 180
0.820 15840 250 7140 220
0.865 15700 160 7000 190
1.000 15640 70 7200 .100

 

 

108

14h- O = Peak position —i

13__ O I Half—width ,erf

12 - 3;) _,
/

11-— O ._

10-— ‘-

_Wavenumber (cm‘1 x 10‘3)

 

 

 

1 1 1 1 1 1 1

v

1..

oLzl-.1

0 .1 .2 .5 .4 .5 .6 .7 .8 .9
Mole Fraction of Water

Figure 55. Variation with solvent composition of the peak
position and the half—width of the solvated
electron spectrum in ammonia-water mixtures.

 

11-—

10..

109

Half-width § 0

Peak position
o/

0
II

 

Wavenumber (cm-1 x 10-3)

 

Figure

54.

 

1 1 1 1 1 1 1 1
.2 .5 .4 .5 .6 .7 .8 .9

Mole Fraction of Water

Variation with solvent composition of the
peak position and the half-width of the
solvated electron spectrum in ethylene—
diaminedwater mixtures.

 

110

4.5. Preliminary Ingestigation of
Cyclohexyl-lB-crown-6
It has been reported (72) that some cyclic polyethers

are able to complex strongly the alkali-metal cations. The
compound we used is: 2,5,11,12-dicyclohexyl, 1,4,7,10,15,16-
hexaoxacyclooctadecane, to which the trivial name cyclohexyl—
18-crown-6 has been given (75). The structure of this com-
pound is shown below. We will refer to this compound as

"crown".

4.5.1. Ethylenediamine Soiutions

We first establishedth‘ata solution of "crown" did not
react with a solution of solvated electron by mixing a
cesium solution in ethylenediamine with a solution of "crown".

A solution consisting of a mixture of sodium ions with
an excess of "crown", was mixed with a cesium solution. When
this reaction was allowed to occur a short time after the so-
lution of "crown“ and sodium ions was prepared, the reaction
with cesium proceeded as usual giving the V-band. The crown-

sodium ion solution was then allowed to stand for about ten

 

111

minutes and then mixed with the cesium solution. It was noted
that the V-band was much smaller than before. The same
experiment was repeated at different times with the same
crown-sodium ion solution. At longer times it was observed
that the reaction with the cesium solution gave less V-band.
The complexation reaction between sodium ions and "crown"
therefore seemed to be slow. We attempted to see if this re—
action could be followed by conductimetric methods.

A solution of sodium bromide in ethylenediamine (10"3 M)
was prepared in a conductance cell. When the value of the
conductance, measured with a Wayne—Kerr bridge, was constant,
a weighed amount of "crown“ was added to the solution to
give equimolar concentration. The conductance was then
measured as a function of time. A slight increase in con-
ductance was observed during the solubilization of the "crown"
(5 minutes) after which the conductance stayed stable. A
large excess of."crown" was then added with the same result.

The same experiment was attempted with solutions of
potassium iodide. A solution of "crown" (10'3 M) was pre-
pared in a conductance cell. .A weighed amount of potassium
iodide was added to give a concentration of 10'3 M. The
conductance rose sharply just after the addition and stayed
stable thereafter. The same experiment was done with smaller
concentrations of KI (10“ M) with the same result.

The effect of "crown" upon a solution of sodium metal

in ethylenediamine was studied. We were interested to see

112

if the complexing of the sodium ion by the "crown" would shift

the equilibrium
+ 1
V-band-7——>' Na + IR-band

towards the formation of the IR-band. This study was done by
pouring a solution of sodium over some solid "crown". The
resulting spectrum was the same as the spectrum of pure
sodium solution and showed no IR-band. (After decomposition
of the solution, the solvent containing dissolved "crown" was
poured over metal. The spectrum of the resulting blue solu-

tion did not show any IR-band.

4.5.2. Other Solvents

Noting that the stabilization of the cations should in-
crease the solubility of metals (as suggested by Dr. V. A.
Nicely), we studied the effect of adding "crown" to tetra-
hydrofuran (THF) and diethyl ether, in the presence of a
mirror of potassium. Alkali metals alone are only very
slightly soluble in THF and not soluble in diethyl ether.
With both solvents, deep blue solutions were formed in the
presence of”crown.". Solutions of both potassium and cesium
in-THF formed readily at room temperatures and were stable
for several hours even in the absence of excess metal.
Solutions stored at -780C for several days showed no visible
signs of decomposition. In order to dissolve potassium and

cesium in diethyl ether it was necessary to first cool the

 

system (-78°C was the temperature used). Once formed, the
blue solutions in this solvent were stable at room tempera-
ture for five to ten minutes and for hours at -78°C.

The optical spectrum of each of these solutions was
recorded at room temperature and is shown in Figure 55.
No other absorption bands could be detected in the infrared
as far as we could go before the cut-off of the solvent
(1.5 u for THF and 2.4 u for diethyl ether in a 1.0 cm path
length cell). The EPR signal of these solutions consists of
a single line corresponding to the solvated electron line.
In diethyl ether at 25°C, in addition to the single line
(C 9’10”? M), a weak four-line pattern (C’_‘:’10‘a M, A =
11. G.) was observed for potassium solutions. No such four-
line pattern was observed in THF solutions. The single
line observed in THF could be observed down to the freezing
point of the solvent. In contrast, in diethyl ether the
single line disappeared below 0°C. In both solvents at low
temperatures (-60°C and below), a weak seven line pattern
was observed. The splitting values and relative intensities
indicated that this absorption was probably due to the
benzenide anion (74). This identification was strengthened
by adding small amounts of benzene to a similar solution of
potassium in THF in the presence of "crown". This resulted

in an intensification of the seven—line pattern.

 

 

114

.=C3OHU= mo mocmmmum may Gd
Honum Hmsumflo Ucm mma ca mamume mo mnuommm Hwowumo .mm musmflm

AmIOH x «IEUV HmQEscm>m3

om ma 3 3 «a 3 m
. _ 1 _ _ I _

XMZ‘

4

 

 

 

 

 

V . DISCUSSION

5.1. Oscillator Strengths and Molar Absorptivities

The main difficulty in the estimation of the oscillator

strength, resides in the evaluation of the area under the

 

absorption curve. We have shown in Section 5.7.5, that

each of the absorption bands (V, R or IR) could be fit by

an equation consisting of a Gaussian band shape for the low
energy side and of a Lorentzian band for the high energy side.

The area under a Gaussian cUrve is given by

AG = 2 x 1.0645 . AVG . y (1)
§ In

and under a Lorentzian curve by

AL=2x1.57.AvL.y (2)
g m

where AVG and AVL are the half-width at half-height for
Gaussian and Lorentzian curves respectively and ym is the

maximum amplitude.

5.1.1. Solutions in Ethylenediamine
a) Sodium solutions
The method used to determine the molar absorptivity of

sodium solutiorsby using the reaction

IR-band -+ x Na+ —->- V-band (5)

115

 

 

116

yields different values of the molar absorptivity of sodium
depending upon the number of sodium ions involved in the
formation of the V—band. The value of the molar absorptivity
of sodium solutions is 8.2 i 0.5 x 10‘ M"J'-cm"1 assuming one
sodium atom in the V-band.

Using A%: = 1720 cm'1 and Av: = 2280 cm"? obtained from
sodium spectra, an oscillator strength of 1.9 i_0.2 is calcu-
lated. According to the f—sum rule, the sum of the oscillator
strengths from a state m to all of the possible other states
is equal to the number of electrons in the state m.

An oscillator strength of about 2, obtained when we consider
one sodium atom per V-species, indicates that two electrons
are involved in the transition. Furthermore (64,75), it is
known that the sum of the oscillator strengths for the one—
electron transitions of the sodium atom ig_y§gug_is very

close to unity, and the transition 53 -—>-5p accounts for

0.94 of this value. This indicates that the core electrons
are not involved in the sodium spectrum to any significant
extent. Therefore a species Na_ with two electrons in a 55
state is compatible with an oscillator strength of 2.

A species Na- is isoelectronic with the Mg atom. The reported
value of the oscillator strength for the transition 51$ 9 5‘P
of the magnesium atom is 1.745 (76). If two sodium ions were
involved in the formation of the V-band, the molar absorptiv—
ity would become twice what it was before, i.e., 1.6 x 105

-1 1

M ocm- and the oscillator strength would be nearly four.

 

117

In this case, according to the f-sum rule, four electrons
are needed. There is no direct evidence that a species
such as Nag can give an oscillator strength of four.

If the determination of molar absorptivity were to be
done by dissolving sodium, and if decomposition effects
could be ignored, a value of half that which we found should

be expected since the solubilization reaction is

ZNa—->Na+ + Na (4)

However, this method would not offer any way of deciding
whether the V species is Na- or N32.
b) Solvated electron in ethylenediamine

During the study by pulse radiolysis, of the reaction
_ + -
2e + Na -—-> Na (5)

we have determined the ratio

ANa-(600)

~Aé:110207 = 1.88.i 0.28

 

where ANa_(600) refers to the final absorbance of the Na—
band at 600 nm and Ae_(1020) refers to the initial absorbance
of the solvated electron at 1020 nm.

Using the stoichiometry of the above equation we get

ANa-(600) ENa_(600)

 

 

 

- e —(600)
= . [Na ] = $_ Na
4641020) Ga. (10207 “'"m—[e 1° 2 ea. (102W

€Na_(600) can be obtained from the value of EN

the shape of the V-band

_(Max) and
a

 

 

118

= 4 -1, —1
6Na_(600) 5.95 x 10 M cm
so that

ee_(1020) = 1.58 x 104 M-1.cm-l.

By using the band shape of the solvated electron we can get

the molar absorptivity at the maximum

€e_(1560) = 2.0 :t 0.5 X 104 Mfl.cm-l.

 

By using the band parameters of cesium-ethylenediamine solu—
tions Av: = 2500 cm-1 and Av; = 4760 cm-1 we find an

oscillator strength

f = 0.88 i 0.12

If two sodium ions were involved in the V-band, the molar

absorptivity of the solvated electron would have to be

ee_ = 4.0 x 104 M-J'.cm'l

and the oscillator strength would be
f = 1.76

From the results of section 4.4 we know that the band shape
of the spectrum of solvated electron in ethylelediamine-water
mixtures does not change with water concentration. Therefore,
we postulate that the oscillator strength does not vary
appreciably with the concentration in solvent mixtures.

Since the band-width does not change when we go from water to

ethylenediamine, the integrated molar absorbance is a

119

constant. Therefore the same molar absorptivity is expected
for the electron in water and in ethylenediamine. The value
of the molar absorptivity of the electron in water has been
measured by Fielden and Hart (77) and has the value

Ee—(Hzo) = 1.85.i 0.2 x 104 M'I-Cm'l. This value is the same
within experimental error as the value of 2.0.: 0.5 x 10‘

M"1 x cm'1 obtained for the solvated electron in ethylene—
diamine. The value of 4.0 x 10‘ M'1 x cm“:L that would be
obtained if two sodium ions were involved in forming the
V-species is twice too large for this kind of comparison.

This strengthens the assignment of Na- as the species
responsible for the V-band rather than, for example, a species
of stoichiometry Nag.

c) Molar absorptivity of the R-band of potassium solu-
tions

Let us assume that the R-band observed for solutions
of potassium in ethylenediamine is due to K—. Let us further
assume that the oscillator strength of this band is the
same as for Na-. This assumption permits an estimate of
the molar absorptivity of K- to be made. By using Avg_=
1720 cm‘1 and Avg_= 2550 cm-1 the molar absorptivity is
7.6 x 104 M"1 x cm’l. This value is only an estimate so no
standard deviation is given.

5.1.2. Solvated Electron in WaterrAmmonia
Mixtures
The oscillator strength of the solvated electron in

water can be determined by using the spectrum reported by

1 'P

120

Matheson (78) and the molar absorptivity of Fielden and
Hart (77). The value obtained is f = 0.81. This value may
have a large error attached to it because of possible errors
in the peak shape. The area under the curve was obtained
from the only published spectrum (78) in which g%%%%% = 1.45,
while more recent measurements yield a value of 1.7 for this I
ratio.(77).

The oscillator strength and molar absorptivity of the
solvated electron in liquid ammonia have been reported by a “
number of workers. The most recent results are those of
Lagowski (12) for very dilute metal-solutions. The value
obtained for the molar absorptivity is 4.8 :1: 0.2 x 104

M‘l-cm'l

which is in accord with the values published previ-
ously (10). The oscillator strength calculated by Lagowski
is 0.64.: 0.04. This value is much lower than previously
published values. However, this value was calculated using
a formula (80) valid only for Gaussian absorption curves.

As we have seen this is not the case for metal—ammonia solu-
tions. Using Avg = 1275 cm'1 and Av: = 1975 cm"1 we obtain_
f = 0.92.: 0.1. We postulate that in water-ammonia mixture,
the oscillator strength of the solvated electron will vary
linearly from the value 0.81 in pure water to the value

0.92 in pure ammonia. We note furthermore that these values
are actually equal within the limits of error. This assump-
tion enables us to calculate the molar absorptivities of

the solvated electron in solvent mixtures. The results are

shown in Table XII and in Figure 56.

 

121

Table XII. Molar Absorptivities of the Solvated Electron
in Water-Ammonia Mixtures

 

 

 

Mole Fraction Molar
of Water Absorptivity

M'l.cm-l
1.00 18,500
0.949 18,100
0.950 19,900
0.862 19,800
0.841 21,200
0.759 22,500
0.752 20,500
0.717 22,000
0.594 24,500
0.594 22,500
0.555 26,900
0.496 26,700
0.489 29,200
0.421 55,200
0.567 41,000
0.558 54,000
0.144 45,600

 

 

 

122

.mwusuxae Hobo?
IMAGOEEm CH couuomam Uwum>aom msu mo >uw>wumnomnm
HMHOE msu mo cofluwmomeoo ucw>aom £uw3 coflumwum>

Hmum3 mo cowuomum 0H0:
o.d m.o m.o $.o N.o

.mm whomwm

 

_ _ _ _ _ _ _ _

 

 

125

5.1.5. Conclusions

Our results are summarized in Table XIII.

The oscillator strength of the solvated electron is
close to unity in all of the solvent systems we have studied.
This indicates that the absorbing species is a single elec-
tron. It also indicates that we should not expect another
strong absorption band for the solvated electron. The value

of two for the oscillator strength of the V—band and the

 

value of 8.2 x 10‘ M-lcm-l for the molar absorptivity are
consistent with the assignment of Na-ias the species responsi-
ble for the V-band.

Our results do not give any indication as to the nature
of the transition causing the V-band. They are not at
variance with the interpretation of Matalon gt_§l, (56) who
consider this band to be caused by a charge-transfer-to-

solvent.

5.2. Equilibria in Metal-Ethylenediamine Solutions

The optical spectrum of metal-ammonia solutions consists
of a single band which follows Beer's law over a wide range
of concentrations. However, it is known from conductance and
magnetic susceptibility measurements (28) that even in the
dilute region, a substantial fraction of the dissolved metal
is present as ion pairs and diamagnetic aggregates which
might be represented as (e-)2, e--M+.e—, (M+-e-)2 or higher-

order aggregates.

Table XIII.

124

Summary of Molar Absorptivities

and Oscillator

 

 

 

Strengths
Species/Solvent e f
M-1.cm-l

Na-/EDA 8.2 :1: 0.5 x 104 1.9 :1: 0.2
K-/EDA* 7.5 x 104 1.9

e—/EDA 2.0 i 0.5 x 104 0.88 _-l: 0.12
e-/NH3 4.8 1 0.2 x 104 0.92 i 0.1
{/1120 1.85 i 0.2 x 104 0.81

 

*
Estimated values.
EDA = ethylenediamine.

 

 

 

125

We have established that in metal-ethylenediamine solu-
tions the species e- and M- are present. We also know that
in a solvent of dielectric constant as low as ethylenediamine,
extensive ion pairing must occur. In order to fit the
kinetics of the reaction of cesium solutions with water,
Hansen (68) had to postulate that in cesium solutions some

equilibria of the type

paramagnetic-7-—+1diamagnetic

also existed.

In the studies of decomposition of metal solutions,
Dewald (66) noted that most of the decays were first-order
but that different bands reacted at different rates. In
particular, for potassium and rubidium solutions, the R-band
reacted faster than the IR-band. This suggests strongly that

the R-band consists of aggregated species.

5.2.1. Equilibrium IR-band + K+ ER-band
From the optical spectrum of potassium solutions in

ethylenediamine it is known that we have equilibria of the

type

- +
K -———+- 2e + K (7)
-‘——-
(R-band) (IR—band)
This is obviously an oversimplified view. To be more real-
istic, ion pairs have to be introduced and the equilibrium
involved in the reaction of Cs solutions with KX may be

written

 

 

I1. ,llf .

 

126

+ — + -
o —+ o
2Cs e Cs Cs (8)
_ .. + _ + _.
Cs+.Cs + K+-X 17—9' Cs -K + Cs -X (9)
+ — + — + — + —
Cs -K + K -x ——>E K .K + Cs -x (10)

All of these equilibria are probably important in determin-
ing the relative intensities of the R- and IR-bands.
Unfortunately, this leaves us with too many unknowns.
Therefore a few simplifying assumptions have to be made.
Equilibrium (8) plays only a minor role and only at high
concentrations.) In fact in none of our experiments could
the Cs- spectrum be detected. Equilibrium (9) will be ig-
nored since it is not detectable in the experiments unless
K+-K- has a different molar absorptivity than Cs+-K-, which
is unlikely.

Relation (10) can be rewritten
+ - + - + - + _
2 Cs -e + K .X jr—*' Cs -K + Cs .X (11)

which gives an equilibrium constant

+ +

- - 7 + - 7 + -
_ Cs .K . Cs .X . Cs .K - Cs -X
K ‘ [Cs .e-J . [K .x-] (12)

2
7Cs+.e' ° 7K+.X'

 

where 7A+ B- are the activity coefficients of the ion-paired
species A+.B-.
Equation (12) can be re-written

st+.K’
st+.e‘

K = K' (15)

 

121

where

[Cs+.K-] - [Cs+-x"1 (14)

K. [Cs*.e‘]2- [K+.X']

K' will be referred to as the pseudo-equilibrium constant
of reaction (11).
The concentrations in equation (14) can be obtained

easily. From Beer's law:

. - Ax- + - _ -
[CS .K ] - 2:35— ; [CS .e ] — €e_.b

 

The other two concentrations can be obtained from the conser-

vation equations:

[K+]O = [K+.X-] + [Cs+.K-] (15)

This can be approximated by

+0 +—

[K J = [K -X 1
since the concentration of potassium ion is much larger than
the concentration of species present as K-.

The conservation of the total cesium yields:
0 + _ _ + _
[CS+] = [Cs .e ] + [Cs+.K ] + [Cs .X ]

From the control experiment we know that the concentration
of cesium ions is much larger than the concentration of
solvated electrons (Cs+.e—). The concentration of cesium
salt present in the solution will be considered as constant
for any particular run. The following approximation will be

made

128

+ e-
[Cs Jtotal a €e_.b

That is the total concentration of cesium is proportional
to the initial absorbance of the cesium solution. This
introduces an unknown factor in the equilibrium constant.

The pseudo equilibrium constant is therefore:

 

 

0
AK" . _#‘Ae-
eK_.b ee_.b
K' 01 A 2 (16)
- +
e e b ° [K 10
e...

K' 0‘ E'— ° F. . [KW (16')

The second part of this ratio has been calculated in Section
4.2. This value is nearly constant showing that all of our
assumptions are reasonable.

Let us now consider the possibility of having aggregates
of high order than ion pairs. As shown at the beginning of
this Section this certainly occurs in ethylenediamine. The
problem becomes much more complicated. Let us try a very

simple model
e2+K ———->- K (17)

The equilibrium constant is written

_ 'Y-
[Klr- K (18)

K = _
IK+1 - [92 YK+-‘Ye=

and the pseudo-equilibrium constant is

 

 

129

u _ K- — fie: 1A1<_
K ’ —L‘l_*1e51 . 1K '1" ‘ e ' _Ae_-""’1K lo ‘19)

The second part of this ratio has been calculated and called
K" in section 4.2. For both runs this value is a constant.

At the present point there is no way of deciding whiCh
are the important equilibria. A realistic approach would
involve taking all possible equilibria into account,but the
complexity added by aggregates such as e: or M2 makes this
treatment impossible.

The average values obtained for the two pseudo—equilibrium

constants are:

K' = 1.42 x 102 M'l
K" = 1.57 x 102 M'1
The value of K" has been calculated by assuming ee3 = 2 x €e"

The similarity between the values of K' and K" is surprising
but we must remember that K' as defined contains an unknown
multiplicative factor and that therefore the similarity is
probably fortuitous.
5.2.2. Effect of Potassium Salt Uppn the
Spectrum 9f Sodgpm Soiutigpg

Sodium solutions do not show any appreciable absorption
in the infrared region. This indicates that the concentra-
tion of solvated electrons is very low. However, by analogy
with the solutions of other metals, it is postulated that

there is an equilibrium:

 

150

- + _
Na '"""""1 Na + 2e (20)

lying far to the left.

The addition of a potassium salt to such a solution

 

might give the reaction

+ — _ +
K +Na """"1 K +Na (21)

to give an R-band. However, this is not what is observed

 

experimentally. The experimental results show an increase
of the absorbance in the infrared when the potassium is.
mixed with a sodium solution. This increase disappears
when a sodium salt is added to the potassium salt prior to
the mixing with the sodium solution.
Several possibilities exist to explain these results.
(i) The addition of a massive excess of potassium ions
and of its counter-ion bromide or iodide makes

possible the equilibrium

Na_ + Br-‘ 2 Na+-Br + 2e (22)
in which the bromide ion replaces two electrons.
This is not in contradiction with the fact that in
presence of sodium bromide no effect is observed,
since then the massive excess of sodium ions would
shift the equilibrium (20) to the left regenerat-

ing the V—band. However, if the reaction (22)

were responsible for the observed effect, it is

(ii)

151

difficult to explain the absence of an.R-band
from K-.

The other possibility involves the change of the
properties of the medium occurring when a large
amount of salt is added to a solution. The equi—

librium constant for reaction (20) is:

K = [Na+]°[_fl? 7Na+ ° 7e-2
[Na‘] ' VNa-

Assuming 7Na+ = yNa‘ = 7e” = yi gives

[Nah-1612 , 2

K = [Na-1 7.:

In solutions of sodium, this equilibrium is diffi-
cult to measure because there is almost no solvated—
electron-band. From measurements of the spectrum
we can conclude that the absorbance of the IR-band
does not exceed 5% of the absorbance of the V-band
in pure sodium solution. When the potassium salt

is added, the intensity of the IR;band becomes

about 50%«of that of the V-band. With these esti-
mates let us try to evaluate what changes in actiVity
coefficients could lead to the observed increase

in the IR-band. .In the case of a pure sodium solu-
tion of unit absorbance, the equilibrium constant

satisfies the inequality

 

K 5 ee“ . (25)

 

In the presence of an excess of potassium ions,
if no new equilibria are involved
+ 0.5 2
o —— 1‘» I
[Na ] (5e‘ 2

K 1" ' y+ o
(1.0) _

 

eNa

. + . ' .
Assuming that [Na ] 15 the same in both cases, we get

'2
0.09 M _<_ 0.0025 7i

or

Y: '2' 6 y; .

The solutions we are dealing with are much too concentrated
to evaluate yi theoretically. However, the observed change
is in the expected direction, and if y: decreases by a factor
greater than six when salt is added to the solution, the
observed increase in the absorption in the infrared could
result. It is to be noted that ionic strength effects

would not be expected to influence reaction (21) significantly.

5.5. Kinetics of the Reaction M+ + e- ——+-M-

5.5.1. Sodium Ion Reaction
The rate constants that we have obtained for the reac—

tion

 

155

Na+ + 2e— ———)- Na- (24)

do not appear to depend upon the sodium ion concentration in
the concentration range 5 x 10—3 to 0.5 M, that we have
studied (except possibly for the lowest concentration used).
This is evidence that the mechanism does not correspond to

the rate expression:

_QJE_1_ = _ 2k[Na+].[e—]2

dt

Several mechanisms can be proposed to explain the absence

of sodium ion dependence. These mechanisms are based on the
ion-pairing concepts we have developed in the preceding
section.

a) We can consider a first slow step
e_ + e_ slow e: (25)

followed by the ionic reaction

e: + Na+ -£3§E>- Na— (26)

Such a mechanism gives the correct featrues of our reaction:
second order with respect to the electron concentration and
no dependence on the concentration of sodium ions.

b) Alternately we can consider that the first step

is a fast ion pairing equilibrium

Na+ + e- £E§E>- Na+.e- (27)

+ ,~ .. 'y + .-
= [Na 0e ] . Na .e
K tNa+1-[e-1 vNa+.ve- ‘28)

 

154

followed by the rate determining step

— + -
2Na+oe ————+- Na oNa (29)
slow

Since in our experiments the concentration of the sodium
ion was at least 5 orders of magnitude greater than the
electron concentration and was high enough to give nearly
complete ion-pairing at equilibrium, most of the electrons
would be present in the ion-pair Na+.e- if reaction (27)

is fast. Therefore, no dependence upon the sodium ion con—
centration would be expected.

These two mechanisms could be tested by lowering the
concentration of sodium ions. If no change is observed,
then the mechanism (a) is probable, in the other case
mechanism (b) seems more appropriate. Preliminary testing
of this effect are currently in progress at the Ohio State
University. The use of lower concentrations of sodium
introduces another difficulty, however: the equilibrium ratio
of the V-band to the IR-band becomes smaller so that changes
are difficult to detect.

Since no growth of an R-band was observed in the pulse
radiolysis of solutions of KBr in ethylenediamine, it would

be possible to add an excess of potassium salt to the solu-

tion to give

K+ + e- -r—+- K+.e_ (50)
Na+ + e- ——)- Na+6e_ (51)

P

155

The potassium salt being in excess with respect to the sodium
salt, most of the electrons would be tied up as K+.e- leaving
most of the sodium ions paired with the counter ion X—.

The sodium ions could then react by:
2 K+.e‘ + Na+.x" ———>K+.Na" + K+.x" . (52)

5.5.2. Potassium Ion Reaction

The reaction of electrons with potassium ions did not
occur under the conditions of the pulse radiolysis experiment.
In fact, we know from metal solution studies that we have an

equilibrium

K+ + 2e" —->F K“ (55)

we have evaluated a pseudo»equi1ibrium constant for the

reaction

+ - + - — + + -
2Cs.e + K.X j?“*’ K .Cs + Cs.X (12)

and we postulate that it is similar to

+ _ +- + — +—
2K .e +K.x —”.= K .K +K.X - (54)

The pseudo-equilibrium constant is
K+ K'
K' = W Q5 1.4 X 102 M.)-
At equilibrium, the concentration of K_ is given by

[K’] = K'- [K+.e-]2 .

 

156

In most of the pulse radiolysis experiments the concentration
of solvated electron was of the order of 10"5 to 10'6 M

so that [K'] :5 1.5 x 102 x 10'10 = 1.5 x 10-8 M.

At equilibrium then, the maximum absorbance of the R-band in

a 4 cm cell would be

AR = 4 x 7.5 x 104 x 1.5 x 10"8 = 4.5 x 10‘3

which is below the limits of detection. Therefore, the
observation that no R-band was formed in the pulse radiolysis

experiments is consistent with the studies of metal solutions.

5.4. Reactions of Sodium Solutions with
‘nger in"Ethylenediamine

Sodium solutions in ethylenediamine occupy a special
place by reason of their stability. The reaction of water
with sodium follows first order kinetics with respect to
the sodium. Feldman [67] observed that the pseudo-first
order rate constant did not change appreciably with water
concentration below 1 M. Above 1 M and up to 6 M our data
together with Hansen's‘data (68) indicate a dependence on
at least the third power of the water concentration.

The present data also indicate that there is no effect

of hydroxide concentration upon the reaction rate. This

rules out the presence of equilibria of the type

N'+H0—->- N-H++OH-
a 2 ‘ a.

157

in the rate-determining scheme.
No reasonable mechanism can be proposed that would
account for a rate expression of the type

d [Na‘l
dt

 

= -k [Na-]°[H20]3

'The apparent zero-order dependence upon water at low water
concentrations and the sudden increase in rate above 1 M,
suggest that these effects may be caused by a change in
solvent properties. At low concentrations of water, the
sodium anion is relatively stable and does not react with
water in less than a few seconds. When enough water is
added, the solvent properties might change such that Na—

becomes less stable and reacts with water via the intermediate

formation of solvated electrons.

5.5 Studies of the “‘Crown'I Compound

"Crown" appears to be an efficient complexing agent for

the sodium ion according to
+
Na + "Crown" ————>- Complex (55)

This conclusion is based upon the fact that the reaction

Complex + e- -—-4>* V—band

does not proceed.

 

 

158

Furthermore the reaction (55) seemed to require times
of the order of ten minutes or longer to occur to a signifi-
cant extent. However, the conductimetric results did not
show any effect when "crown" was added to a solution of
sodium or potassium ions in ethylenediamine. We cannot pro-
pose any reasonable explanation for these results. Either
the complexation results in ethylenediamine are in error,
or the conductivity of the complex is the same as the con-
ductivity of the corresponding solvated cations. This
problem could probably be elucidated by a study of sodium
NMR in ethylenediamine with and without the addition of
"crown".

The complexation of the metal cations by the “crown“ is
confirmed by the fact that in THF, potassium solutions
containing "crown" do not show hyperfine splitting by the
nucleus in contrast to solutions of potassium in THF in the

absence of "crown". This indicates that the equilibrium

+ _
M. -F-—>- M + e

is shifted to the right by the complexation equilibrium
+ i II II
M + crown ———)-Complex .

The optical spectra of metals such as cesium and potas-

sium in diethyl ether and in THF show only the R-band of

these metals (81). Presumably the solubility equilibrium

159

+ .-

is shifted to the right by the addition of "crown“. The
metal cation is complexed, and the metal anion gives rise
to the observed band.

The absence of effect of "crown" upon the spectrum of

sodium in ethylenediamine indicates that the equilibrium

M' + "crown"-7—+>1 complex + 2e—

lies far to the left in this solvent.

With the possibility that alkali metals can be dissolved
in a variety of solvents in which they are normally insolu-
able, it should be possible to further test the validity of
the assumption (56) that the observed transition is of the
ctts type. The ability to use a wide variety of solvents
should provide a better test than is obtained with ammonia—

amine mixtures.

 

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