ABSTRACT
THE KINETICS OF THE REACTION BETWEEN THE

ALKALI METALS AND WATER
IN ETHYLENEDIAMINE

BY

Earl M. Hansen

Since the first direct observation of the hydrated
electron in 1962, there has been a great deal of interest
shown in the rates of reaction of the solvated electron (1).

The rate of the reaction of the hydrated electron with water

eaq + H20 ——> H + OH (1)

has been measured using the technique of pulsed radiolysis
and has a rate constant of 16 M“1 sec’1 (2). Dewald (3) and
Feldman (4), using solutions of the alkali metals (mainly
cesium) in ethylenediamine. measured the rate of reaction of
the solvated electron with water in ethylenediamine.

In the work reported here, the stopped-flow system
described by Feldman (4) was slightly modified. The glass
stopcocks were replaced with Fischer-Porter greaseless stOp-
cocks and the glass syringes and plungers were replaced with

Hamilton gas tight syringes and plungers having Teflon tips.

Earl M. Hansen

Provision was made for cooling the photomultiplier tubes to
decrease the thermionic noise, thus increasing the signal

to noise ratio. An improved data analysis system, utilizing
a Varian C—1024 Time Averaging Computer is also described.

The results of this investigation show that the reac-
tion of sodium with water is second order in water at water
concentrations greater than 1 g, and the decay of the 660 nm
absorption band (V-band) is nearly first order in the absorb-
ance. The reactions of potassium, rubidium and cesium with
water are all apparently first order in water, but the decay
of the optical absorption during the reaction is not simply
first- or second-order in the absorbance.

The data for the reaction of potassium, rubidium and
cesium with water are treated in terms of a mechanism involv-
ing an equilibrium among the species present (solvated elec-
trons, electron-paired Species and "ammonia-like" aggregates)
with the slow step being the reaction of any one or all of
the reducing species with water. The results are consistent
with current models for metal-amine solutions. Improvement
in the internal consistency of rate constants is due to im-
proved kinetic control.

The mechanism for the reaction in ethylenediamine is
shown to be different from that which is suggested for the

same reaction in liquid ammonia (5).

Earl M. Hansen
The rates of the reactions:
+ .
Cs solutions (1280 nm) + Na —-$>V—Spec1es (660 nm) + Cs+ (2)

+
Rb solutions (890 nm, 1280 nm) + K. ——9*K solutions (850 nm,

1280 nm) + Rb+ (3)

were also investigated. These reactions are extremely fast
(t§_<:10’3 sec) and the results of these studies are of a
qualitative nature. The importance of these results in rela-
tion to the mechanism described above is discussed.

The mechanism of the formation of molecular hydrogen
during the reaction of the alkali metals with water in ethylene-
diamine has also been investigated. It is found that not more
than 2% of the hydrogen formed in this reaction comes from
the d-position of the solvent. Other possible mechanisms for
molecular hydrogen formation are discussed.

The purple color observed in decomposed rubidium ethylene-
diamine solution is shown to be due to pyrazine anion. The
mechanism of its formation is unknown but may be important to

the chemistry of metal-amine solutions.

REFERENCES

1) J. K. Thomas, Rad. Res. Rev., 1, 185 (1968).

2) E. J. Hart, S. Gordon and E. M. Fielden, J. Phys. Chem.,
lg, 150 (1966).

5) R. R. Dewald, Ph. D. Thesis, Michigan State University,
East Lansing, Michigan, 1965.

Earl M. Hansen

4) L. H. Feldman, Ph. D. Thesis, Michigan State University,
East Lansing, Michigan, 1966.

5) R. R. Dewald and R. V. Tsina, Chem. Commun., 647 (1968).

THE KINETICS OF THE REACTION BETWEEN THE
ALKALI METALS AND WATER

IN ETHYLENEDIAMINE

BY

Earl MI Hansen

A THESIS

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

DOCTOR OF PHILOSOPHY

Department of Chemistry

1970

c; c :2 7 35:5”
Qty/‘7O

To Colleen

ii

ACKNOWLEDGMENTS

The author wishes to eXpress his sincere appreciation
to Professor James L. Dye for his patience, guidance and
encouragement throughout the course of this work.

He also wishes to acknowledge the help of Dr. Vincent
A. Nicely and Dr. John Bartelt for help with the computer
programs used.

Financial assistance from the United States Atomic
Energy Commission is gratefully acknowledged.

 

iii

TABLE OF CONTENTS

Page

I. INTRODUCTION . . . . . . . . . . . . . . . . . . . 1
II. HISTORICAL . . . . . - . . . . . . . . . . . . . . 5
A. Metal-Ammonia Chemistry . . . . . . . . . . . 5

B. Metal-Amine Chemistry . . . . . . . . . . . . 11

C. Radiation Chemistry . . . . . . . . . . . . . 15

III. EXPERIMENTAL . . . . . . . . . . . . . . . . . . . 21
A. General Laboratory Procedures . . . . . . . . 21

1. Glassware Cleaning Procedures. . . . . . 21

2. Vacuum Techniques. . . . . . . . . . . . 21

B. Solvent Purification. . . . . . . . . . . . . 22

C. Metal Purification. . . . . . . . . . . . . . 27

D. Solute Purification . . . . . . . . . . . . . 28

E. Covering Gas Purification . . . . . . . . . . 30

F. Solution Preparation. . . . . . . . . . . . . 50

1. Metal Solution Preparation . . . . . . . 50

2. Water Solution Preparation . . . . . . . 54

5. Salt Solution Preparation. . . . . . . . 55

G. Stopped—Flow System . . . . . . . . . . . . . 35

H. The Rapid-Scan System . . . . . . . . . . . . 45

I. Data Analysis . . . . . . . . . . . . . . . . 46

J. Conductance Measurements. . . . . . . . . . . 50

K. Tritium EXperiments . . . . . . . . . . . . . 52

IV. RESULTS AND DISCUSSION . . . . . . . . . . . . . . 54
A. Introduction. . . . . . . . . . . . . . . . . 54

B. Alkali Metals Plus Water. . . . . . . . . . . 76

1. Cesium . . . . . . . . . . . . . . . . . 76

2. Sodium . . . . . . . . . . . . . . . . . 81

5. Rubidium and Potassium . . . . . . . . . 92

C. Band Interconversion Reactions. . . . . . . . 106

1. Cesium plUS'Na+. . . . . . . . . . . . . 106
2. Rubidium plus_K+ . . . . . . . . . . . . 108

iv

TABLE OF CONTENTS-—continued Page

D. Summary . . . . . . . . . . . . . . . . . . . 114
E. Suggestions for Future Work . . . . . . . . . 11S

LIST OF REFERENCES. . . . . . . . . . . . . . . . . . 117
APPENDICES. . . . . . . . . . . . . . . . . . . . . . 111

A. A Detailed Derivation of the Rate Equation
for the MeChanism Described in Section IV . . 125

B. Description of Computer Program for Analyzing
Data. . . . . . . . . . . . . . . . . . . . . 155

C. Observation of Pyrazine Anion in Decomposed
.Rubidium-Ethylenediamine Solutions. . . . . . 158

LIST OF TABLES

TABLE

I. Comparison of Experimental and Theoretical
Values for Some PrOperties of the Ammoniated
Electron. . . . . . . . . . . . . . . . . . .

II. PrOperties of the Hydrated Electron . . . . .

III. Results from Tritium Experiment to Check Origin

of Molecular Hydrogen in Reaction of Cesium
with Water in Ethylenediamine . . . . . . . .

IV. Conductance of Cesium, Sodium and Potassium
Hydroxides in "Wet" Ethylenediamine . . . . .

V. Values of kM' and ke- Calculated from the Best

Fit of Equation 59 to the Data Obtained for the

Reaction of Cesium with Water in Ethylene-
diamine . . . . . . . . . . . . . . . . . . .

VI. Values of kM- Calculated from the Best Fit of

Equation 40 to the Data Obtained for the Reac-

tion of Cesium with Water in Ethylenediamine.

VII. Values of the Rate Constant for the Reaction of

Sodium with Water in Ethylenediamine. . . . .

VIII. Values of kM— Calculated for the Reaction of

Potassium with Water in Ethylenediamine Calcu-

lated Using Equation 59 . . . . . . . . . . .

IX. Values of kM‘ Calculated from the Best Fit of

Equation 40 to the Data Obtained for the Reac-

tion of Rubidium with Water in Ethylenediamine.

vi

Page

18

55

62

80

82

89

96

102

LIST OF FIGURES

FIGURE

10.

11.
12.

15.

First distillation train used for purifying
ethylenediamine. . . . . . . . . . . . . . . .

Vessel used for freeze purification of
ethYIenediaInj-neo O O O O O O O O I O O O O O 0

.Second distillation train used for purifying

ethylenediamine. . . . . . . . . . . . . . . .

Vessel used to prepare metal solutions used in
the kinetic studies. . . . . . . . . . . . . .

Apparatus used for preparing metal solutions
used in the initial kinetic studies of this
work [from Dewald (89)]. . . . . . . . . . . .
StOpped—flow system. . . . . . . . . . . . . .

Block diagram of rapid-scan system . . . . . .

Jig assembly used for the drilling of the
quartz flow cells. . . . . . . . . . . . . . .

a--Cross section of the four-jet mixing cell
showing the nearly tangential entry of the four
jets, b—-Finished flow cell. . . . . . . . . .

Typical oscilloscope trace used for data
analysis in the initial studies of this work .

Block diagram of the CAT data analysis system.

Apparatus used to measure the conductances of
the alkali metal hydroxides in ethylenediamine

Shape of the IR-band as a function of the ini-
tial water concentration and the extent of
reaction during the reaction of cesium with
water in ethylenediamine . . . . . . . . . . .

vii

Page

25

25

26

29

51

56

57

41

42

47

49

51

56

LIST OF FIGURES--continued

FIGURE

14.

15.

16.

17.

18.

19.

20.

21.

22.

25.

24.

25.

Decay of the 890 nm absorption of a rubidium
solution during reaction with water in ethylene—
diamine. Also shown is the behavior of
log(Abs.) and 1/(Abs.) for this push. . . . . .

Plot of specific conductance gs, hydroxide
concentration for cesium hydroxide in "wet"
ethylenediamine . . . . . . . . . . . . . . . .

Plot of initial absorbance gs, push number for
the reaction of cesium, sodium and rubidium
with water, in ethylenediamine. . . . . . . . .

Comparison of observed decay of the absorbance
with that given by the best fit of Equation 59
for the reaction of cesium with water in

ethylenediamine . . . . . . . . . . . . . . . .

Fit of Equation 59 to observed decay at absorb-
ance for reaction of cesium with water when a
long tail is observed . . . . . . . . . . . . .

Plot of kM_, calculated from Equation 40, ver-
sus water concentration for the reaction of
cesium with water in ethylenediamine. . . . . .

Decay of 660 nm band of sodium during the reac-
tion with water . . . . . . . . . . . . . . . .

Plot of logKE. log (water concentration) for
the reaction of sodium with water in ethylene-
diamine. The line drawn has a slope of two . .

Band shape and position of the 660 nm band of
sodium as a function of the initial water con-
centration and the extent of reaction . . . . .

Typical Spectrum observed for potassium in
ethylenediamine, showing the presence of a
V-band in addition to the R- and IR-bands . . .

Plot of log (Abs.) versus time for the reaction
of potassium with water in ethylenediamine. . .

Typical spectrum of rubidium solutions used in
this work . . . . . . . . . . . . . . . . . . .

viii

Page

58

64

75

78

79

84

86

87

88

94

95

98

LIST OF FIGURES-~continued

FIGURE

26.

27.

Page

Typical decay of the rubidium spectrum during
the reaction with water. The decay of both
the R— and IR-bands can be seen. . . . . . . . 99

R-band obtained by subtraction of cesium,
IR-band from the rubidium spectrum observed in
the kinetic studies. Before the subtraction
was performed, the absorbances of the two

' Spectra were normalized at 1100 nm . . . . . . 104

28.

29.

50.

51.

52.

Comparison of the R-band shape from Figure 27

with that obtained by subtraction of Spectrum

near the end of the reaction with water from

the spectrum observed at the beginning of the
reaction . . . . . . . . . . . , . . . . . . . 105

Spectrum observed after mixing a solution of
sodium bromide and cesium in ethylenediamine . 107

Optical Spectrum observed before and after

mixing a solution of rubidium and potassium

bromide in ethylenediamine. Curve A is the

spectrum observed before mixing and Curve B

that observed after the push . . . . . . . . . 109

Operational block diagram of program KENANAL . 154

EPR spectrum of the pyrazine anion formed in
decomposed rubidium-ethylenediamine solutions. 140

ix

I. INTRODUCTION

The existence of ammoniated electrons as the colored
species in alkali metal-ammonia solutions was first sug-
gested by Kraus in 1908 (27). However, only recently has
the existence of the solvated electron in other media been
demonstrated (67). Since the discovery of the optical absorp-
tion of the hydrated electron by Hart and Boag in 1962 (67),
over 600 reactions of this Species have been characterized
(69).

The prOperties of metal-ammonia and metal-amine solutions
have been studied by a number of investigators and will be
discussed in Chapter II. Dewald, Dye, Eigen and DeMaeyer
(97) first examined the reactions of "stable" solvated elec-
trons with water by studying the reaction of a dilute cesium
solution with water in ethylenediamine using the stopped-flow
technique. Feldman (90) continued these studies and suggested
that the reaction proceeds via two parallel pseudo-first-
order processes with rate constants of ZQMfl sec-1 and SMfl
sec-1. However, the rate constants measured by Feldman
Showed a large amount of scatter.

In this research, the earlier studies of Dewald and

Feldman were extended. However, the use of a rapid scanning

monochromator and a better data analyzing system Showed that
the reactions of cesium, rubidium, and potassium solutions
with water in ethylenediamine probably do not proceed through
parallel first order reactions. Instead the kinetic behavior
appears to be complex.

New experimental results, not available to the previous
investigators, have drastically altered the interpretation of
the behavior of metal-amine solutions. A major goal of this
work has been the formulation of a reaction mechanism which
is consistent with all available information about metal-

amine solutions.

II. HISTORICAL

A. Metal—Ammonia Chemistry

When alkali or alkaline earth metals are dissolved in
liquid ammonia, primary aliphatic amines or certain ethers,
metastable blue solutions are formed, with no net chemical
reaction. The characteristic blue color of these solutions
was first observed in 1864 by Weyl (1), who called them
"metal-ammoniums."

Since solutions of alkali metals in these solvents are
metastable, extreme care must be exercised to ensure proper
cleanliness and purity of materials. Impurities such as
water, carbon dioxide, transition metals and surface contami-
nants are thought to catalyze the decomposition reaction

with the solvent,
+ ___L +
M NH3 MHNg £32 (1)

and can lead to inconclusive results. Kirschke and Jolly (2)
and more recently, Schindewolf (5) have shown that the re-
verse of Reaction 1 can be made to occur to a Slight extent
under the proper conditions.

The unusual chemical and physical properties of dilute

solutions of alkali metals in liquid ammonia have stimulated

5

the interest of a large number of investigators and have
been studied by a variety of exPerimental methods. These
investigations have been extensively reviewed elsewhere
(4—11) and will not be discussed in detail here.

In the course of the investigations of the properties
of dilute metal-ammonia solutions, several models have been
suggested to account for the observed prOperties. Unfortu-
nately, each of these models is able to account for a few,
but not all of the observed prOpertieS. Any model which is
proposed for dilute metal-ammonia solutions, must be able to
account for the following experimental observations:

1. A large volume expansion occurs when alkali metals
are dissolved in‘liquid ammonia (12,15,14,15). The
report by some investigators (12,14) of a pronounced
minimum in the volume expansion of sodium and potas-
sium solutions in liquid ammonia seems to be incor-
rect (15). However, if this minimum is real, it
also must be accounted for by any proposed model.

2. All solutions have a single, broad, unstructured,
asymmetric Optical absorption band which peaks near
1500 nm. This absorption obeys Beer's Law from 400
to 1520 nm. up to metal concentrations as high as
0.05M_with a molar extinction coefficient of approxi-
mately 4 x 104 Mflcm"1 (16-18).

5. The molar magnetic susceptibility decreases markedly

as the concentration is increased which suggests the

presence of a diamagnetic species in solution (19-21).

4. The electrical conductance and transference data
Show that the negative Species in solution carries
approximately 80% of the current in dilute solutions
and nearly 100% in more concentrated solutions (22,
25). However, the observed mobility of the solvated
electron in dilute metal—ammonia solutions is not
high enough to be characteristic of a free electron
(22).

5. Knight shifts for nitrogen and sodium nuclei as well
as proton chemical shifts are observed in sodium—
ammonia solutions (24,25). .The EPR Spectrum of metal—
ammonia solutions consists of a single narrow line
(21).

Before discussing the various aspects of the models which
have been proposed for metal-ammonia solutions, it will be
useful to examine, in a qualitative way, the various Species
which are suggested by the above experimental observations.

-Since the conductance data indicate that the major cur-
rent carrier is negatively charged and the EPR data indicate
the presence of unpaired electron Spins, the major Species
present in metal-ammonia solutions is probably the solvated
(ammoniated) electron. The conductance data also suggest
the presence of a non-conducting species in solution. The
most likely stoichiometry of this Species is M, and it is
probably an ion pair formed by the interaction of a solvated

metal cation and a solvated electron (26).

As mentioned above, the magnetic susceptibility data
suggest the presence of a diamagnetic Species in addition
to the M unit and the solvated electron. This Species could
be two electrons in the same cavity with their spins paired.
However, Optical and volumetric data suggest the presence of
ion-paired Species such as M— (e- - M+ - e—) and M2 (M+ - M-).
The models discussed below include some or all of these
species. However, none of these models adequately describes
all of the observed physical and chemical prOperties of metal-
ammonia solutions.

The first model for metal-ammonia solutions was that
suggested by C. A. Kraus (27). He proposed that solvated
metal ions and solvated electrons as well as undissociated
metal atoms were present in dilute metal-ammonia solutions.
In 1946, 099 (28) postulated that the solvated electron
occupies a spherical cavity in which it is trapped by the
surrounding ammonia molecules. Assuming the electrons to be
confined in this cavity by an infinite potential well created
by the surrounding solvent molecules, Ogg estimated the
cavity radius and the enthalpy of solution of the solvated
electron. The cavity radius calculated in this manner was
'too large (102) and the calculated heat of solution was
smaller than the experimental value.

.The original cavity model of 099 has been refined and
improved by a number of investigators (29—55). The most

extensive treatment of a refined cavity model is due to

Jortner (55). Jortner has applied this treatment to solvated
electrons in liquid ammonia and in other solvents.

The treatment of Jortner involves application of Landau's
polaron theory (54). In this type of treatment, the electron
is considered to be trapped in a cavity by the polarization
forces of the solvent. .The electrostatic potential which
results from this polarization is assumed to be constant with-
in the cavity and continuous beyond the cavity boundary.

This treatment does not restrict the electronic wave function
to the cavity but allows the charge distribution to extend
beyond the cavity boundary. Using this approach, Jortner
obtained reasonable agreement with the eXperimental values
for the heat of solution and optical transition energy of
metal-ammonia solutions (see Table I). Jortner, Rice and
Wilson (55) refined this type of calculation by using a self
consistent field treatment but obtained no improvement in the
agreement with existing experimental data. In fact, the
agreement actually worsened.

The cluster, or BLA model has also enjoyed considerable
popularity. The basis for this model was originally sug—
gested by Coulter (57) and was later expanded by Becker,
Lindquist and Alder (56). According to the cluster model,
the species in dilute solutions are the metal cation and a
solvated electron. As the metal concentration is increased,
these two species are thought to associate into "monomer"

units according to

TABLE I

COMPARISON OF EXPERIMENTAL AND THEORETICAL VALUES
FOR SOME PROPERTIES OF THE AMMONIATED ELECTRON

 

 

 

Optical
Cavity Heat of Transition
Radius Solution Energy Oscillator
Reference Used (eV) (eV) Strength
Jortner 5.2 1.60 0.81 0.65
(35)
JRW (55) 5.2 0.92 0.95 0.70
Land and
O'Reilly 5.05 5.4 1.02 0.98
(45)
Exp't. -- 1.710.? 0.80 0.72

(55)

 

+ — K1
M + e --4> M (2)

am am ‘——— am

At higher metal concentrations, the model allows for the
association of two monomer units to form a dimer according to

K2

ZMam ——¥ (M2)am (3)

This dimer is thought to be held together principally by
exchange forces. The "cluster" or "BLA" model was used with
some success in fitting conductivity and magnetic suscepti-
bility data (58,59).

Douthit and Dye (16) and Gold, Jolly and Pitzer (26),
have suggested that the monomer unit of the "cluster" model
is actually an ion pair between a solvated metal cation and
a solvated electron. These authors also suggested that the
metal ion and solvated electron forming such an ion pair
retain their individual characteristics. The "BLA" dimer
is pictured as a quadrupolar assembly of two solvated elec-
trons and two metal cations. Using these modifications,
Gold, Jolly and Pitzer obtained qualitative agreement with
volumetric, optical and Knight shift data.

In Spite of the apparent agreement, the set of equi-
librium constants for Reactions 2 and 5 calculated from
conductivity data do not agree with those calculated from
magnetic data. The agreement can be improved somewhat by
the introduction of a third equilibrium and another species
(M') , .

-———=- M + e (4)

10

Arnold and Patterson (59,40) and Golden, Guttman and
Tuttle (41) have suggested a model which includes the species
of the "cluster" model, but adds M- as an additional species.
The models of these authors consider M- to be a diamagnetic
species.

Arnold and Patterson calculated the equilibrium con-
stants K;, K2, and K3 using conductivity, magnetic suscepti-
bility and transference number data. Although these calcu-
lations give reasonably good agreement with experiment, the
calculation involves the use of three adjustable parameters
to fit the data. .No assumptions about the detailed nature
of the various species are made in the treatment of Arnold
and Patterson.

The model of Golden, Guttman and Tuttle also assumes M—
as an additional Species and further assumes the dimeric
species, M2, to be an ion pair between a solvated metal cation
and a solvated metal anion (M+ - M-). .These investigators
used only one adjustable parameter in fitting this model and
obtained reasonable agreement with optical, Knight shift
and vapor pressure data. However, JOlly (42) has pointed
out that the correlation with optical data may be in error.

Recently, Dye (100) has attempted to correlate all of
the experimental data for dilute metal-ammonia solutions
with the stoichiometries implied by the above models.

The new conductance data of Dewald and Roberts (101), which

showed the earlier data to be in error in the dilute region,

11

were used in this correlation. Dye concluded that the use
of distinct species of stoichiometry M+, e-, M, M- and M2
with concentrations determined by equilibrium constants was
inconsistent with the available data. He suggested that
electron—electron interactions were long range in nature
and could not be described by equilibria among distinct

"species."

B. Metal-Amine Chemistry

Metal-amine solutions are more complicated than metal-
ammonia solutions. It appears that in addition to the sol-
vated electron and "loosely bound" aggregate "species" which
may be present in metal—ammonia solutions, new Species, which
more directly involve the alkali metal, are present in metal-
amine solutions. Optical and EPR studies (44—48) indicate
that the species in metal-amine solutions which contain the
alkali metal are more than simple ion pairs.

The optical spectra of solutions of alkali metals in
ethylenediamine Show one to three absorption bands (44).

One of these bands appears in the visible at about 660 nm
(V-band), one in the near infrared region at 850 nm to 1050
nm (R-band), and one in the infrared (IR-band) at 1280 nm.
The V-band has been observed in ethylenediamine solutions

of sodium, lithium, potassium and occasionally rubidium and
cesium. The position and shape of the V-band are independent

of the metal. The R—band is observed in solutions of

12

potassium (850 nm), rubidium (890 nm) and cesium (1050 nm)
in ethylenediamine. Solutions of all the metals except
sodium exhibit the IR-band. The shape and position of the
infrared band are independent of the metal used.

Pulse radiolysis studies of amines (49) show the presence
of a transient which has a broad optical absorption in the
infrared region. The correlation of this fact with conduc-
tivity and solubility studies in ethylenediamine have led to
the assignment of the IR—band to the solvated electron and
its loose "ammonia-like" aggregates (see Part A, this Section).

The V-band and the non-reproducibility associated with
its study has been a most troubling phenomenon (50-55).

It now appears that the V-band puzzle has been solved.
Hurley, Tuttle and Golden (54), have recently investigated
the V-band observed in solutions of potassium in ethylamine.
Analysis of metal solutions prepared in Pyrex vessels Showed
the presence of enough sodium to account for the V—band ob-
served in the optical Spectrum. They also found that solu-
tions prepared in fused Silica vessels exhibited no V—band
and contained no sodium. DeBacker (55) has recently con-
firmed these observations for potassium solutions in ethylene-
diamine. It now seems likely that the V-band is character-
istic only of sodium solutions and that the observation of

a V-band in other metal-amine solutions indicates the pres-
ence of sodium in the solution. Although the exact mechanism

for the contamination of the solutions by sodium from Pyrex

15

glass is unknown, the metal solutions and/Or the solvent,
evidently leach sodium or sodium ions from the glass surface
or take part in ion exchange phenomena. Although these ex-
periments have revealed the origin of the V—band in metal-
amine solutions, the detailed nature Of the sodium species
responsible for the V-band is still unknown.

The exact nature of the R-band remains a mystery. It
has been observed that the magnitude of the R-band decreases
relative to that Of the Iwaand as the solution is diluted
or decomposed (56). This implies that the species responsi-
ble for the R—band can dissociate. Also, since the position
of the R-band is metal dependent, it seems reasonable that
the species responsible for this band contains the metal
cation.

Dye and Dewald (56) suggested that the R-species is a
solvated alkali metal dimer, similar to those found in the
gas phase. They also suggested that the Optical absorption
arises from a lzu <--123 transition. However, now that it
has been shown that the V-band is due to the presence of
sodium, it is likely that the species responsible for the
R-band is of the same type as that which is responsible for
the V-band observed in sodium solutions and in other metal
solutions contaminated by sodium ions. Since the lnh *F—}Z+
transition is also an allowed transition which is easily
Observed for the gaseous alkali metal dimers, the absence of

a second absorption band in sodium solutions makes it

14

unlikely that the species responsible for the R-band is the
solvated diatomic molecule, (M2). Because of the strong

metal dependence of the R-band, it probably does not origi-

nate from a simple ion pair such as M ° e or e . M+ . e .
Recently Matalon, Golden and Ottolenghi (102) have con-
cluded that the V-band (and hence also the R-bands) can be
attributed to a species M-. They reached this conclusion
by comparing the shift of the Optical absorption with solvent
and temperature to that of the charge-transfer—to-solvent
(CTTS) band Of 1.. They also showed that the variation of
the peak position with metal is consistent with that expected
on the basis Of reasonable radii for the alkali metal anions.

The conductivity data of Dewald and Dye (50) and of
Dewald and Roberts (105) Show that the species responsible
for the V—band in sodium solutions in ethylenediamine and
in methylamine is very different from the solvated electron.
Indeed, the small variation of equivalent conductance with
concentration is unlike the behavior Of any known system in
solvents of such low dielectric constant.

EPR studies of metal-amine solutions Show the presence
Of nuclear hyperfine Splitting by the alkali metal nucleus
(45-48). These studies have Shown that a monomer Species
of stoichiometry M exists in some metal-amine solutions but
only as a minor constituent (48). These workers (45-48)
have also Shown that the hyperfine Splitting exhibited by
metal-amine solutions is strongly dependent on the solvent

and the temperature.

15

In summary, it appears that metal-amine solutions are
indeed more complex than metal-ammonia solutions. Two dif-
ferent Optical absorptions are Observed. One (IR-band) has
been assigned to the solvated electron and its"ammonia-like"
aggregates such as (M+-e-), (e- - M+ - e-) and (M+ . M-).
The exact nature of the other Optical absorption (R-band) is
still unknown. It may be due to an alkali metal dimer or a

metal anion which is not simply an ion pair. It could also

be the absorption of a completely different Species.

C. Radiation Chemistry

The chemical reactions which result from the action Of
ionizing radiation on matter have been studied for about
seventy years. Debierne (57) suggested in 1914 that free
radicals were responsible for the overall chemical effects
Observed in aqueous solutions of radium salts.

Lea (58) suggested in 1947 that electrons escaped from
the parent ions during the radiolysis of water. Stein in
1952 (59), and Platzman (60) in 1955 suggested that these
electrons could become solvated. Up until this time, it
was thought that the irradiation of water produced only H-
atoms and OH radicals as primary products and that the subse-
quent reactions of these species were responsible for the
overall chemical effects (61).

The first experimental evidence for the possible exist-

ence Of the hydrated electron came in 1959. Barr and Allen

16

(62) Showed that the H-atom produced during the radiolysis
of aqueous solutions containing hydrogen ions, oxygen and
hydrogen peroxide reacted faster with oxygen than with
hydrogen perOxide. However, the H-atoms produced in solu—
tions containing only oxygen and hydrogen peroxide reacted
equally fast with the oxygen and the hydrogen peroxide.

They suggested that one of these H—atom species was probably

atomic hydrogen and the other a basic or acidic form of the

H-atom, as expressed by the following:

+ +
- +

Further evidence for the existence of the hydrated elec-
tron came from several investigators (65-68). The most
direct evidence came from the kinetic salt-effect studies of
Czapski and Schwartz (65). They studied the effect of ionic
strength on the rate constant ratios for reaction Of the
reducing Species with H30+, 02 and N02- to that with H202.
These studies showed that the reducing species in neutral
and slightly acidic solutions has a unit negative charge.
These results were verified by Collinson, Dainton et al.
(66), who studied the ionic strength dependence of the rate
constant ratios Of the reaction of the reducing species with
Ag+ and acrylamide. Their studies showed that at a pH Of 4,
' the reducing Species has a unit negative charge, but that
in acidic solutions (pH = 2), it is uncharged. This sug-

gests that in acidic solutions the major reducing species is

17

probably the H-atom, rather than the solvated electron.

The first direct observation Of the hydrated electron
came in 1962 (67,68), when Hart and Boag Observed a broad
transient absorption band, with a maximum at about 7200 3,
after pulsing deaerated water with a beam of 1.8 MeV elec-
trons. The observed Spectrum was similar in Shape to the
absorption band Observed in metal-ammonia solutions and its
intensity was decreased by the addition of small amounts of
known electron scavengers such as N20 and H30+. Since this
"discovery" of the hydrated electron, a number of its proper-
ties have been measured. These are listed in Table II.

With the advent of linear accelerators, the technique
Of pulse radiolysis has been extensively used to study the
kinetics of hydrated electron reactions. The rates of over
600 different reactions involving the hydrated electron have
been studied (69). The reaction of the hydrated electron
with water,

_ k1 _
e +H20 ——* H + OH (6)

aq ‘TEI'
is important to the understanding of the nature Of the hy-
drated electron and in comparing its prOperties with those
of solvated electrons in other media. .The kinetics Of both
the forward (70) and reverse (71,72) rates Of Reaction 6
have been studied. The currently accepted value for k; is
16 M71 sec‘l, but Anbar has suggested that this may only be

the upper limit for this rate constant (75). The reverse

18

TABLE II

PROPERTIES OF THE HYDRATED ELECTRON

 

 

 

Quantity Value Ref.
x 7200 R 82
ma3 (1.72 eV)
Molar extinction coefficient at 7200 R 15,800 82
gn—lcm-l
Oscillator strength 0.65 85 V
Solvation energy rv40 84
kcal mole“l
Equivalent conductance 177 85
Ohm-1cm2
Partial molal volume -5.5 to 86
-1.1cc.mole'l
G(e; ), y—ray yield in neutral water 2.6 87
q ions/100 eV
té in pure water at pH = 7 250 usec 85
Diffusion constant 4.75 x 10’? 85
cmasec“
o - + .—. ,
E (eaq + Hsoaq ——> 2- H2 + H20) 3 2.67 v. 84
Calculated mean radius of charge 2.5-5.0 A 88
distribution
_ _
pK (eaq + H20 —-¥ H + OH) 9.7 84

 

19

rate constant, has a value of 2.2 x 107Mflsec‘l.

k(0H‘+ H)’
Using these rate constants, a pKa value of 9.7 has been calcu-
lated for the H-atom.

Of particular interest to the radiation chemist has been
the mechanism Of molecular hydrogen production in irradiated
water. It has been unambiguously demonstrated that most Of
the molecular hydrogen is not produced by the recombination

Of H-atoms but rather is produced directly by the bimolecular

reaction (74):

eaq + eaq H20i H2 + 20Haq (7)

Hydrated electrons can apparently also be generated in
solution without exposure to high energy radiation. Walker
(75,76) has recently found evidence for the presence of hy-
drated electrons in the reaction Of sodium amalgams with water
and also in the electrolysis of water.

Observations of the solvated electron in a number of
liquids other than water have also been reported. Ahrens, Sury-
anarayana and Willard(77)reported observing a reversible in-
crease in the electrical conductivity of liquid ammonia during
exposure to y—irradiation. An Optical Spectrum similar to
that observed in alkali metal-ammonia solutions has been Ob-
served in the pulse radiolysis of liquid ammonia (78) and
Ward (79) has recently reported rate constants for the re-

actions Of the solvated electron with a variety of solutes in

liquid ammonia. Sauer, Arai and Dorfman (80) investigated

20

the Optical spectra and measured the yields of solvated
electrons in several aliphatic alcohols. The existence of
solvated electrons in other solvents has also been discussed

by Dorfman (81).

III . EXPERIMENTAL

A. General Laboratory Procedures

1. Glassware Cleaning Procedure

 

All glassware was first rinsed in a hydrofluoric acid—
detergent cleaning solution (5% HF, 55% HNOg, 2% acid soluble
detergent, 60% distilled water). This was followed by at
least ten rinses with distilled water. The glassware was
then immersed in boiling aqua regia and then rised at least
ten times in doubly distilled conductance water. Vessels
which were to contain the metal solutions were subsequently
filled with conductance water and heated gently. For later
runs, this steaming process was followed by a washing with
anhydrous liquid ammonia. In these cases, all other solution
vessels were also washed with liquid ammonia prior to solu-

tion preparation.

2. Vacuum Techniques

High vacuum techniques were used wherever possible.
Pressures of 10‘5 torr were Obtained using either two-stage
mercury vapor diffusion pumps or two-stage Oil diffusion
pumps. Pressure measurements were made using a calibrated

Veeco RG75P ionization gauge with a Veeco RGLL—6 power supply.

21

22

Dow Corning high vacuum Silicone grease was used on all stOp-
cocks which came into contact with liquid. Apiezon W wax

was used on all joints and tapers. In later work Fischer-
Porter "quick Opening" Teflon valves and "Solv-Seal" Teflon
joints were used on the stopped—flow system and on all solu-
tion vessels and Delmar-Urry Teflon valves were used on the
freeze-purification vessels. Breakseals were used on solu-
tion vessels and on ampoules containing metal and solute

samples.

B. Solvent Purification

Ethylenediamine (Matheson, Coleman and Bell 98-100% or
Dow Chemical 98-100%) was purified in one of two ways. In
the first method, the ethylenediamine was first poured into
an evacuated five liter separatory funnel. It was slowly
frozen. A core was then melted from the center and this
portion was discarded. The remaining solvent was thawed and
slowly refrozen. This procedure was repeated at least six
times. The ethylenediamine was then poured into an evacuated
vessel which contained pieces of sodium and lithium (Figure 1,
Flask A). The resulting blue solution was degassed twice by
slowly freezing it with an ice-water bath. After degassing,
the solvent was vacuum distilled into Flask B which con-
tained a potassium mirror. Any hydrogen formed by the decompo-
sition reaction was periodically pumped Off. The solvent was

distilled into storage Flask C, covered with nitrogen and

25

.mcflemwpmsmamnum msH%MHHsm Mom Owns cflmuu SOHDMHHHumHU umnflm .d musmflm

mxmmHm Hmufiqlm

mmuwwm mz/r .s m
“n I an:

  

 

 

 

 

 

,/
QEDQ fl//////IEDSUM>
smmou Ocm.All _ ,(k .fil\\\\\ 30H: 06
may 08

.7

ca
mewfimflpwsmawnum

 

 

24

used as needed. It was discovered that this storage vessel
was not vacuum tight and another purification scheme was
devised.

The freeze-purification procedure was carried out as
described above with two exceptions. Instead of using a
separatory funnel with large greased stOpcocks, a five liter
round-bottom flask equipped with Delmar-Urry Teflon valves
was used (Figure 2). The freeze-purification procedure was
repeated at least eight times. Attempts to prepare a stable
metal solution using only the freeze-purified solvent were
unsuccessful. The distillation train was also redesigned
(Figure 5). The freeze—purified ethylenediamine was admit-
ted tO Flask A which contained sodium—potassium alloy with
an excess of potassium. The solvent was then distilled
through a coarse fritted glass filter into storage vessels
equipped with breakseals. .The purpose of the coarse glass
filter was to prevent any possible splash-carry-over of the
metal. The solvent was thoroughly degassed by repeated
freeze-pump-thaw cycles until the pressure after any two
consecutive cycles was less than 1 x 10"6 torr. These vessels
were then sealed Off under vacuum. The solvent in these
vessels was used as needed by breaking the breakseal with a
magnet encased in glass and the solvent distilled as needed.
Both of the above techniques are extremely Slow due to the
low volatility of the ethylenediamine and because hydrogen
formation from the decomposition reaction during the distil—

lation slowed the distillation considerably.
' .

25

I/~’—~1r:ha>To Variac

Delmar-Urry 4 mm
’k/// Teflon Valve

VK‘Fischer-Porter 2 mm

Teflon joint

 

 

 

F——:‘l
’ ‘7“Fischer—Porter 15 mm

Teflon joint

   

, lez-Heater

 

(F—¥TO trap and high
vacuum

 

 

 

 

Delmar-Urry 4 mm ) €23

Teflon valve ‘<&-§ 54/45

 

Fischer-Porter 2 mm

Teflon JOlnt Iai-Liter filter

§ 18/9 flask

Figure 2. Vessel used for freeze purification of ethylene-
diamine.

26

 

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mxmmHm mammmo> mmmuoum

. .gi ////
gun)

 

 

 

 

 

 

 

 

    

 

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sz xmz I
Hmuawm
.\LV .vIL muuwum W
OSHEmflpmcmmmnum mmumoo 1r

 

 

 

 

 

 

F WV

(

 

EDDUN>
smug os

27

An alternate procedure was tried with the hope Of elimi—
nating the distillation step. This consisted Of drying the
solvent with anhydrous calcium hydride for approximately 24
to 72 hours before the freeze-purification procedure. .The
freeze-purification was repeated as before using a cylindri-
cal five liter vessel equipped with Delmar-Urry Teflon
valves. Attempts to prepare stable metal solutions using
solvent purified in this way were also unsuccessful. However,
this method does Show promise in that the metal solutions
prepared using solvent purified in this way were more "stable"
than those prepared with solvent that had only been freeze-
purified. This method seems to be very efficient for remov-
ing the residual water which is the major impurity found in

the ethylenediamine.

C. Metal Purification

Alkali metals of the highest purity commercially avail-
able were Obtained from the following sources: Sodium, J.
T. Baker CO.; Potassium, Fisher Chemical CO.; Cesium, a gift
from the Dow Chemical CO.; and Rubidium, Fairmount Chemical
Company. The final metal purification was carried out in
two ways. In the first method, the metals were vacuum-
distilled twice and stored in sealed ampoules. (For solu-
tion preparation,‘these ampoules had to be broken and dropped
into a sidearm sealed to the metal solution makeup vessel.

This brief eXposure to the atmosphere led to difficulties in

28

degassing the metal prior to vacuum—distillation into the
metal solution makeup vessel. Several metal solutions
decomposed because of this problem. The second procedure
which eliminated this problem was then used. This method
involves vacuum—distillation Of the metal into ampoules
which were equipped with breakseals. These ampoules were
then sealed directly to the metal solution makeup vessels
(Figure 4). The breakseals were not broken until the vessel

had been evacuated to less than 1 x 10—5 torr.

D. Solute Purification

Water was purified in the following manner. Conductance
water was thoroughly degassed by repeated freeze—pump-thaw
cycles. It was then vacuum-distilled into weighed fragile
glass ampoules, or into weighed ampoules equipped with break—
seals. .These vessels were used as needed for solution prep-
aration.

Absolute methanol was placed in a vessel containing con—
centrated sulfuric acid and 4-5 grams Of 2—4-dinitro-phenyl—
hydrazine (105). The methanol was then distilled, keeping
the middle fraction. It was thoroughly degassed by repeated
freeze—pump-thaw cycles and vacuum-distilled into ampoules
equipped with breakseals and used as needed.

The reagent grade salts KBr and NaBr were recrystallized
three times from conductance water and then weighed into

breakseal ampoules. The salts were flamed under vacuum prior

29

 
    
  

Fischer-Porter
9 mm joint

6 mm high vacuum
stopcock ‘——€>

Constriction for

vacuum seal-off 5

Breakseal

 

 

Constriction for
vacuum seal-Off

Magnet encased
in glass -——1>.

Breakseal~——<>

Alkali metal—’7

 

 

Figure 4. Vessel used to prepare metal solutions used in
the kinetic studies.

50

to use. Rubidium chloride was used as the reagent grade salt
without further purification.

The metal hydroxides were prepared by vacuum-distilling
conductance water into a vessel which contained the appro-
priate metal mirror. Concentrated sodium and potassium
hydroxide solutions were made up using reagent grade chemicals

(0.77% carbonate) and conductance water.

E. Covering Gas Purification

In earlier preparations, nitrogen (Matheson, pre-purified)
was used as a covering gas. It was further purified by passing
it over copper turnings in a tube furnace, through an Ascarite
column and finally through a silica gel column at 770K.

It was then stored in two liter bulbs on the vacuum line. Some
problems were encountered with the metal solution preparation
using nitrogen as a cOvering gas and in later preparations,

helium purified as above was used as the covering gas.

F. Solution Preparation

1. Metal Solution Preparation

Two different methods were used to prepare metal solu-
tions. In the first method, the solutions were prepared
immediately prior to use. The apparatus used for this purpose
is illustrated in Figure 5. An ampoule containing the appro-
priate amount of metal was broken and drOpped into the side-

arm Of the metal solution preparation vessel. The sidearm

51

.mammVOHMBOQ EOHMH xHOB was» m0 mmflpsum
OHDOCflx HOHDHSH OLD ca poms mcoflusaom HmumE mafiummmum How Own: msumummm¢ .m musmflm

 

Hmmmm> COHDHmOQEoomQ

 

O mermw> coflumumamw coausaom Hmumz

o
<
\\\\\\ scan

-maaapman Hmume
How EHMIOOHm

     

mmmam SH
Ommmucw umcmmz \4

 

Hmmmm>

umm3 09
u
.
_
(fl
um¢mz cuaomvmwmuAV/J
ESDOMW 5mg: 08

 

 

 

 

52

was capped and the vessel evacuated and flamed until the
pressure stablized at less than 1 x 10—5 torr. The metal

was melted down and degassed and the sidearm was sealed at A.
The metal was then distilled into the vessel and the remain-
ing seal—Off made at B. Solvent was then poured under vacuum
into the vessel containing the metal mirror. In most cases
the blue solution formed immediately. (The solution was
stirred using the magnet sealed in glass and any hydrogen
produced was pumped Off. The solution was then covered with
nitrogen or helium and five to ten milliliters were run into
the waste compartment Of the analysis vessel. From twenty

to thirty milliliters Of the solution were then run into the
calibrated bulb of the analysis vessel and were analyzed at

a later time. The metal solution vessel was removed from the
vacuum line and attached to the stopped-flow system. The
metal concentration was determined by measuring the amount

of hydrogen collected from a solution decomposed with ammonium

bromide according to the reaction:

NH4Br + M —*JgHg + MBr +NH3

(en)

The second method used to prepare metal solutions did
not inyolve pouring the solvent from one vessel to another.
The metal samples were stored in ampoules equipped with a
breakseal. One of these ampoules, containing the apprOpriate
amount of metal, was sealed to the solution preparation

vessel (Figure 4). The vessel was attached to the vacuum

55

line and evacuated and flamed until the pressure stabilized
at less than 1 x 10'5 torr. Liquid ammonia was then con-
densed in the vessel. The ammonia was distilled back into a
storage vessel containing sodium-potassium alloy. The metal
solution preparation vessel was opened to the high vacuum
line until the pressure again stabilized at less than 1 x 10'5
torr. This procedure was repeated four more times. Thoroughly
degassed solvent was then vacuum-distilled into the solution
makeUp vessel at -78OC. When the desired amount Of solvent
had been added, the distillation was stopped and the frozen
solvent allowed to melt. A final degassing using a freeze-
pump-thaw cycle was carried out and the solvent was frozen at
-780C until the metal solution was prepared. Just prior to

a run the breakseal on the sidearm was broken, using the
magnet encased in glass, the metal was distilled into the
vessel containing the frozen solvent and the sidearm was
sealed Off. Helium purified as described above, was admitted
until a pressure of about 1 torr was Obtained. The vessel
was then sealed off, the solvent was melted using a warm
water bath and the solution was prepared by allowing the sol-
vent to contact the metal mirror. (In most cases, a blue
solution formed immediately (see Appendix C). The solution
was thoroughly mixed by tipping the vessel back and forth.
The vessel was then attached to the stopped—flow system, the
connecting tubes were evacuated and the remaining breakseal

was broken.

54

2. Water Solution Preparation

 

Water solutions were also prepared by two different
methods. In the first method, dilute (10"2 M) and inter—
mediate (V0.5 M) water solutions were prepared using fragile
ampoules which contained a known amount of water. Ampoules
containing the desired amount Of water were placed in 500
ml. round bottom flasks and these flasks were weighed. The
solution preparation vessels were then attached to the vacuum
line via storage Flask C (Figure 1) and evacuated until the
pressure stabilized at less than 1 x 10-5 torr. The fragile
ampoules were broken using a magnet sealed in glass and
solvent was added from storage Flask C and the solution was
thoroughly mixed using a magnet sealed in glass. Helium or
nitrogen was then added as a covering gas. The vessels were
disconnected from the vacuum line, reweighed to determine
the amount of solvent added and attached to the stOpped—flow
system. More concentrated (5 to 10 M) water solutions were
prepared by vacuum distilling an amount of degassed conduct-
ance water directly into a weighed and volumetrically cali-
brated preparation vessel. The vessel was then disconnected
from the vacuum line and reweighed to determine the amount Of
water added. The vessel was again connected tO the vacuum
line and ethylenediamine was added until the total volume
of solution reached a calibration mark on the preparation
vessel, so that the total volume Of solution was known.

Nitrogen or helium was added as a covering gas and the vessel

55

was disconnected from the vacuum line and attached to the
stopped-flow system.

The second method of water solution preparation involved
vacuum distilling degassed conductance water into weighed
ampoules equipped with breakseals. These ampoules were then
sealed Off and reweighed to determine the amount of water
added. One of these ampoules was then sealed to the solution
preparation vessel. The necessary amount of solvent was dis-
tilled in, the breakseal on the sidearm was broken and the
water and ethylenediamine were mixed. The rest of the pro-
cedure was the same as that for the metal solution prepara-

tion which is described above.

5. Salt Solution Preparation

The ampoules containing the salts which were purified
as described above, were sealed to solution preparation vessels.
The solution preparation procedure was the same as that for

metal and water solution preparation.

G. StOpped-FlOw System

The stopped-flow apparatus used in this work, illustrated
in Figures 6 and 7, is generally Similar to those described
by Dewald and Feldman (89,90). AS before, only one concentra—
tion of metal solution could be used, but up to three differ—
ent stock concentrations of solute could be used for each run.

ApprOpriate dilutions of these stock concentrations were made,

56

  

TO high
vacuum

    
 
 
 

k’

Water or salt
solutions

(I).

<—-Thermostatted
buret

Stopping block——>

 

l
g
\
‘
:

 

 

 

 
      

   

'J/IIIII

5+ To waste

7I Optical

   

 
 

 

    

 

 

‘
fi
7 cell 5‘ ‘3 iii. .<_.Thermostatted mixing
// To hig 5 ‘ vessel
Ax vacuum lchambe I'-

   
 
     
  
  

    
   

I.--

   

   
  

It): I 7111111111

Fischer-Porter 2mm Teflon
valves

   
 
  

All

IFIIEIE

Metal solution

I" '1‘, 'JI-

Thermostatted syringes

    

Pushing block

'llllln
A
"I. . Ill

Figure 6. Stopped-flow system.

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57

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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ummmm> oszHz
mumseoaomm OH I .mmozwmmmmos (J
zmoomst msmm
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omsom
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_
—
qqmo
.. . m 2m .
I H
, r l_l.
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II no H mm 8mm
moa<zommo \ pu.H Mm anomHo mmomoomm mzommomOHz
nozoz . . ooq mm<s 2m .
zaom OHmam I ammo .14
r: 1 33m- a 26—
mmxammm
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mmOOHms smoom

 

 

 

r1 A<20Hm 00A
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58

either by diluting any one of them with pure solvent or by
diluting one stock solution with another. These solutions
were thoroughly mixed in a thermostatted mixing vessel using

a Teflon coated magnet. The whole system could be evacuated
to less than 1 x 10‘5 torr. Flow was stopped when the plunger
of a third syringe reached a metal plate (see Figure 6).

Two types Of syringes and stopcocks were used on the
stopped—flow system during the course Of this work. Early
kinetic investigations employed glass syringes (Sure-Fit,
Richard Allan and CO., Evanston, Illinois) with glass plungers
as well as all glass stopcocks (H. S. Martin and CO.). The
major drawback to the use Of all glass syringes and stOpcocks
was that it was necessary to grease them (using Dow Corning
Silicone grease). Both ethylenediamine and the metal solutions
Slowly attacked the silicone grease and left deposits Of silica
throughout the flow system. These deposits could not be re—
moved and it is possible that they acted as sites for catalytic
decomposition. Since the metal solutions are metastable, the
elimination of all sites for rapid catalytic decomposition is
a necessity in any kinetic study.

A second problem encountered in the use of the greased
stOpcocks was that during the course of a run the Slow attack
Of the metal solution and solvent on the silicone grease made
the stOpcocks very difficult to turn. They Often had to be
regreased several times during the course Of a given run.

This regreasing procedure necessitated Opening the flow system

59

to the atmosphere. The possibility for contamination of the
flow system and also the possibility of breakage due to the
difficulty in turning the stopcocks led to the elimination
Of the glass stOpcocks and syringes.

A system of greaseless Teflon plungers, stopcocks and
high vacuum joints was constructed. The greaseless plungers
were made by mounting Teflon tips on plungers taken from
Hamilton glass syringes. These tips had lips machined on
them to insure a vacuum-tight liquid seal. Fischer-Porter
2 mm "Solv-Seal" joints were sealed via uranium glass graded
seals to the Hamilton syringe barrels. These joints employ
a Teflon insert with 2 Viton-A O-rings as a greaseless vacuum
seal. The stOpcocks were constructed using Fisher-Porter
4 mm quick Opening valves and 2 mm i. d. heavy walled capil-
lary tubing.

Four-jet mixing cells Of both Pyrex and quartz were used.
The Pyrex cells were constructed as previously described.
Quartz cells had been previously constructed commercially,
however, the cost of commercial fabrication of these cells was
very high and a cheaper, more efficient method was devised.
The starting materials were 7.7 cm lengths of heavy-walled
1 mm i. d. (Thermal American CO.) quartz capillaries which
were polished flat on two Sides (PreciSiOn Glass Products Co.,
Oreland, Pa.). The drilling of the inlets was accomplished
using an Airbrasive unit (White Dental Supply, Bloomfield

Hills, Mich.). This instrument utilizes a high speed stream

4O

helium gas containing finely divided alumina to drill the
holes. The lengths of capillary were mounted in a jig

which could be accurately positioned using an indexing head

in a horizontal drill (see Figure 8). Using this device,
holes were drilled which entered the central bore of the
capillary almost tangentially and at an angle Of about 1050

to it. The jig was rotated 900 between successive holes

until all four holes had been drilled. To prevent unwanted
drilling of the capillary wall opposite a hole being drilled,
a length of polyethylene medical tubing was inserted in the
central bore of the capillary tube while the inlet holes

were being drilled. This drilling procedure yielded a cone-
shaped hole, tapered from the outside surface of the capil-
lary to the central bore. A 0.5 mm diameter tungsten rod

was then coated with a mixture of mineral Oil and the abrasive
powder and used in a drill press to enlarge the holes to a
minimum diameter of 0.5 mm. TO complete the construction Of
the inlet tubes, the appropriate vacuum joints (Fischer—
Porter, 2 mm "Solv-Séal" joints) were sealed to these lengths
Of capillary (see Figure 9).

The syringes on the flow system were thermostatted by
means of Plexiglas jackets which were sealed with Viton-A
O-rings. The thermostatting fluid was a 50:50 mixture of
water and Prestone antifreeze and was circulated by means of

a Lab-Line Hi-Lo Tempmobile.

41

To helium SUpply and
Airbrasive unit

//

   

 

 

 

 

 

 

 

 

CD Drilling tip
; fixed at desired
/
/' ‘Ag’angle to quartz
Indexing a; capillary
Head ————%> E;

 

 

Quartz capillary

 

Figure 8. Jig assembly used for the drilling of
the quartz flow cells.

42

 

 

Optical
path ——_—).

 

 

 

 

 

 

 

 

Fischer-
Porter 2 mm a
quartz-—<> ‘
jOints

Figure 9. a--Oross section of the four-jet mixing cell
showing the nearly tangential entry Of the
four jets.

b--Finished flow cell.

45

H. The Rapid-Scan System

The main component of the Optical system illustrated in
Figure 7 is a Perkin-Elmer Model 108 Rapid-Scanning mono-
chromator. The Spectral scan of this instrument is generated
by a double pass Littrow system with a rotating tilted mirror.
It is capable of scanning a selected spectral region between
500 and 1100 nm with from 5 to 150 scans per second. The
scanning speed may be changed either by interchanging gears or
by a two-position switch on the instrument. The two-position
switch permits selection Of two scanning speeds for each set
of gears.

A trigger circuit consisting Of a small neon light, a
slotted wheel which rotates at the same speed as the rotating
mirror of the monochromator, and a cadmium sulfide photocell
was used to generate a trigger signal at the beginning Of
each scan. The intensity Of this trigger signal is a function
of the scanning speed and is adjusted by means Of a potenti—
ometer.

A Bausch and Lomb source employing a tungsten-iodine
lamp with a quartz envelope was used for this work. AS shown
in Figure 7, the light, after leaving the monochromator,
strikes a stacked mirror beam splitter (from a Bausch and
Lomb Spectronic 505 Spectrophotometer). The beams are then
focussed on the centers of the flow and reference cell (in
the case that a reference cell is used) and then passed

through two quartz lenses used for focussing the light into

44

the photomultiplier tubes (RCA 6199 or RCA 7102). These
phototubes were cooled to -50°C using a stream Of dry nitro-
gen that had been passed through a copper condenser immersed
in liquid nitrogen. This was done to reduce the thermionic
or "shot" noise and also to reduce the dark current of the
phototubes. The anode currents of the phototubes, balanced
as well as possible over the spectral range of interest,
were then fed into a logarithmic amplifier. This circuit,
using Philbrick operational amplifiers (PL1-P and P-25),
produces an output voltage which is prOportional to the
logarithm Of the ratio of the current from the reference
phototube (lg) to that of the sample phototube (I). This
voltage is then proportional to the absorbance.

The output of the rapid scanning monochromator is not
linear in wave number about the center of scan. Because Of
this fact, the Spectral range investigated in each run was
calibrated using a Didymium or a Holmium oxide glass filter.
Both of these filters have well-defined Optical spectra.

Each rotation of the mirror actually gives two scans of
the spectral region Of interest. One-half of the total scan
is simply the mirror image of the other half. It is impor-
tant that the two halves of the scan be symmetric if all the
spectral data are to be used reliably for kinetic studies.
The symmetry between the two halves of the scan is a function
Of the slit width, position Of the light source with respect

to the slit and the presence of stray light from the first

45

pass of the light beam through the Optical system of the
monochromator. The slit width and the position of the light
source were adjusted prior to each run to give the best
symmetry Of the Spectrum of the Didymium glass filter. The
instrument was checked for internal stray light and appro-
priate masking was used to eliminate it.

In early work using the rapid-scanning monochromator,
the linearity of the absorbance was not checked prior to
each run. The adherance of a permanganate solution to Beer's
law showed that the output voltage Of the Philbrick log-
arithmic amplifier was linear in absorbance up to an absorbance
of about 1.5, but that it became non-linear above this value.
For this reason, calibrated neutral density filters (Oriel
Co., Stamford, Conn.) with absorbances ranging in value from
0.5 to 5.0 absorbance units were used to check the system
during each Of the later runs. These filters were calibrated
in the wavelength range 400 to 1000 nm. Intermediate absorb-
ance values could be Obtained using two of these filters.
In this way, the absorbance range 0.5 to 5.0 was then cali-
brated using the ten readings 0.5, 0.5, 0.8, 1.0, 1.5, 1.5,
2.0, 2.5, 2.5, and 5.0. The details Of this calibration are
given in Appendix B, which deals with the computer programs
used in this work.

All pertinent data taken during the course of a run were
recorded on magnetic tape using an Ampex SP—500 FM tape
recorder equipped with 4 record/reproduce heads. All infor—

mation concerning solute concentrations, scanning Speed and

other

of th

first
from

Stora;
and 5;
nel o;
permi1
trigge
from 1

Of the

46

other instrumental settings was recorded on the audio channel

Of the tape recorder.

I. Data Analysis

Data analysis was carried out by two methods. In the
first method, the signal from the log circuit was played back
from the tape recorder into the positive input of a Type 564
Storage Oscilloscope with Types 2A65 Differential Amplifier
and 5B4 Time Base plug-in units. The output of a blank chan-
nel on the tape recorder was played into the negative input to
permit common—mode noise rejection. The oscilloscope was
triggered externally in the normal mode by the trigger signal
from the monochromator which was recorded in a third channel
Of the tape recorder.

The decay of the Spectrum was displayed on the oscillo-
scope in the storage mode and this display was photographed
by using a Polaroid camera and Type 146L transparency film.

A typical diSplay is shown in Figure 10. These photographs

were then enlarged and traced on graph paper and the absorbance-
time data were taken from these traces. The data were then
analyzed with the aid of a CDC 5600 computer. It is to be

noted here that since one looks at the decay of the absorp-

tion Spectrum with time, every scan recorded on tape cannot

be used in the kinetic analysis of a relatively slow reaction.
If one tries to use every scan, only the envelope of the

decay is Obtained.

47

 

 

Figure 10. Typical oscilloscope trace used for data
analysis in the initial studies of this
work.

Sin:
could no:
I

seemed tel
carried C
)
conversicl
a new dat
I

main com;
|
Average '1
used is s.
The I

the outpu'l
positive 5
signal fr:
as an imp;
fier. The
taneouSly

 

L.

Agate PUl

p..~

by the 545.

mayetek, 1

12+,

n:‘
is.

e triggz

48

Since in the above method, many Of the data recorded
could not be used, a more efficient data analysis system
seemed to be in order. Also, since final data reduction was
carried out with the aid of the computer, analog to digital
conversion of the data was desirable. To achieve these ends,
a new data analysis system was designed and assembled. The
main component Of this system is a Varian C-1024 Computer of
Average Transients (CAT). A block diagram Of the system
used is shown in Figure 11.

The signal from the tape recorder channel containing
the output of the log circuit was used as an input to the
positive side of a calibrated differential amplifier. The
signal from the blank channel of the tape recorder was used
as an input to the negative side Of this differential ampli-
fier. The output signal of this amplifier was then simul-
taneously fed into the positive input of the storage oscillo-
SCOpe and into the CAT.

The storage oscilloscope was triggered externally in
the normal mode by the trigger signal from the monochromator.
A gate pulse, generated at the end of each sweep of the oscil-
loscope,was input to a Tektronix type 545-A OscilloSCOpe
equipped with a time delay unit. A gate trigger generated
by the 545A OscillOSCOpe was input to a waveform generator
(Wavetek, Model 116, San Diego, Calif.). The length of time
between the signal input to the 545A Oscillosc0pe and the

gate trigger output of this scope could be varied by means

49

.Emummm mammamcm Hump ado map mo Emummwp MUOHm

mUZDmQM¢U

 

 

 

mmBDmSOU
DZHU<MM>¢
NSHB ONOHIU

MWQMOUWM MIN

 

 

 

MUZ¢>Q¢ mmmMQQ< Oflfi

4

 

 

 

MNBH>¢3

 

 

 

 

mmwmeB QWNdAMQ

r
‘

 

 

 

 

 

mmOUmQAQHUmO
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MWOOHmB madw

 

 

 

 

7

 

 

 

 

 

 

 

 

 

 

 

 

 

 

.aa magmas
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a mmoone-

)( tr aaonm mmomoomm
q<onm ea mm<s Sm
mHmHumz<

u +
. mmHqumz< —
mmoomoquomo .anszmmmmmHo mmxcmmm

moamosm «mm

 

 

 

 

 

 

 

of the 1
t0 exami
The
the desi
used to
the port.

CAT has a

reaction
to advanc
fed into
monitorin;
Havi:
into CAT,
tion 0r1 ar
The card P
an IBM k8}

 

me discus

1) that de I

 

50

of the time delay circuit within the scope. This corresponds
to examining a given portion of the recorded Spectrum.

The frequency of the waveform generator was adjusted to
the desired value. From 16 to 256 trigger cycles could be
used to analyze any given scan. This corresponds to defining
the portion of a given scan with 16 to 256 points. Since the
CAT has a total Of 1024 channels, a given kinetic trace can
consist Of up to 64 different absorbance values over the total
reaction time. The output of the waveform generator was used
to advance the address register of CAT. This signal was also
fed into the negative input of the storage oscillOSCOpe for
monitoring purposes.

Having read the absorbance data as a function of time
into CAT, in this manner, one can then display this informa-
tion on an X-Y recorder and/or punch it directly on cards.
The card punching was completely automatic and was done with
an IBM keypunch (type IBM 526) equipped with a Varian C-1001
coupler. The computer programs used to analyze these data

are discussed in detail in Appendix B.

J. Conductance Measurements

The alkali metal hydroxides used in these measurements
were prepared as described in the preceding Section D. The
conductance apparatus used in these measurements in essential-
ly that described by Keskey and Spleet (91). This apparatus

is shown in Figure 12. After each sample Of the hydroxide

 

Fischer-.
Effim Tefl:
valve

To high x

1 ml

 

 

51

  
  

Aqueous alkali metal
*‘—- hydroxide

qu<—-2 mm stopcock

Fischer—Porter
2mm Teflon-——a>.7'

valve °".
//fl

9 14/35

To high vacuum

     

   

1 ml Buret —-—->

 

 

 

 

 

 

 

 

 

l
s 45/50«+>\ Drip Spout

‘$_Leads for conductance
bridge

[1

Conductance cell

 

 

Figure 12. Apparatus used to measure the conductances Of
the alkali metal hydroxides in ethylenediamine.

 

solution
resistan
describe;
these co:

cell use:

For
labelled
was obtai
Chloride ,
diamine k"
SOlUtions
SClVent .
water 501;
a modifie;
perUCed “I
introduCedl
and this

hydrogen t

‘ I

 

was COHdenf

tilled Wi t I
(ca

3 measurc

52

solution was added, the solution was shaken until a constant
resistance reading was Obtained. Helium, purified as
described in this Sectiom,was used as the covering gas in

these conductance experiments. The cell constant for the

cell used was 0.25.

K. Tritium Experiments

For these experiments a 1 mCi sample of ethylenediamine
labelled at the d—position (HgN-CTg-CTg—NHg) was used. It
was obtained from New England Nuclear Corp. as the hydro-
chloride. This was first dissolved in 20 ml of pure ethylene-
diamine which was then distilled once prior to use. Cesium
solutions (7 ml samples) were prepared using this labelled
solvent. These metal solutions were mixed with concentrated
water solutions and the hydrogen produced was collected using
a modified Van Slyke apparatus. The volume of the hydrogen
produced was measured at atmospheric pressure. It was then
introduced into a vessel containing 1-2 9 of silver oxide

and this vessel was heated to 1000C for 1 hr to burn the

hydrogen to water via the reaction
0
A90 + H2 AM Ag + H20

A sidearm Of the vessel was then cooled to 770K and the water
was condensed. The vessel was then Opened and the sidearm
filled with scintillation liquid. The activity Of this liquid

was measured using a Tri—Carb Scintillation counter. Any

 

hydrogé
itself

any act
samples
Table I

cussed .

EXperi _
ment

 

55

hydrogen produced by decomposition of the metal solution
itself was also collected, burned to water and tested for
any activity. NO appreciable activity was observed in these
samples. The results of three such experiments are given in
Table III. The significance Of these results is also dis-

cussed in Section IV.

TABLE III

RESULTS FROM TRITIUM EXPERIMENT TO CHECK ORIGIN
OF MOLECULAR HYDROGEN IN REACTION OF CESIUM
WITH WATER IN ETHYLENEDIAMINE

 

 

Volume H2 Average Percent of
Experi— collected number total hydrogen
ment (ml) counts active
1 0.75 244 2.5
2 0.85 269 2.58

5 0.65 225 2.06

 

 

Th
in ethy
Feldman
follow :
reactior
peting P
graphica

Thi:
analyze 1
Observed
v‘band in
that the 1
ream; inde
rePort (5.
CC”tarniriat
conversioh
the glass

IV. RESULTS AND DISCUSSION

A. Introduction

The reactions of dilute metal solutions with water
in ethylenediamine were first studied by Dewald (89) and
Feldman (90). Feldman showed that the reaction rate did not
follow simple first-order kinetics. He suggested that the
reaction with water could be described in terms of two com-
peting pseudo-first-order reactions and analyzed his data
graphically on this basis.

This parallel first-order reaction scheme was used to
analyze the kinetic data for two reasons. First, Dewald had
observed a very slow (minutes) interconversion Of the IR- and
V-band in solutions of lithium in ethylenediamine, suggesting
that the two kinds of Species in metal-amine solutions could
react independently (89). If, as Hurley, Tuttle and Golden
report (54), the 660 nm absorption (V—band) is due to sodium
contamination from the Pyrex container, then the slow inter-
conversion of the Optical bands results from reaction with
the glass and not~from a homogeneous reaction. Studies in

the present work (to be described later) Of reactions of the

54

 

type
Cs

and

Rb

in ethyl
(13 > 10'
proves t]
cannot be
kinetics .
treatment
Em band (3

“one the

 

55

type
CS solution (1280 nm) + Na+ -—+-"V-species” (660 nm)

+ Cs+ (1)

and
Rb solution (890 nm, 1280 nm) + Na+ —-#-"V-species"

(660 nm) + Rb+ (2)

in ethylenediamine show that these reactions are fast
(té_>-10"3 sec ). This information, not available to Feldman,
proves that independent decay of the different Optical bands
cannot be the explanation Of the deviations from first order
kinetics. The second reason for the parallel first order
treatment was the conclusion reached by Feldman that the 1280
nm band decayed before the 1050 nm band when a dilute cesium
solution reacted with water in ethylenediamine (90a). This
is contrary to the order of decay expected for equilibrium
among the species (see Section II). However, re-examination
Of the gamg_kinetic data of Feldman using the CAT data analy-
sis system, shows that there is no change in shape of the
cesium Spectrum during reaction with water. Also, there is
no dependence Of the spectral shape on the initial water
concentration. These two Observations are illustrated in
Figure 15. Apparently, difficulties with the triggering
circuit Of the monochromator (see Section III, Part H) led
Feldman to an erroneous conclusion.

The consistency of the values Of RA Obtained from the

above analysis was not good and the scatter among rate

56

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AECVK

OOOH 00m 00m ooh com
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um 001:: (. quv (. sqv)

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o

 

 

 

 

 

constani
In some
kinetic
them ga\
Whe
optical
tained i
Feldman
tem wher
log(Abs.)
strictly
530 nm at
ing the r
the behav
kinetic p:
It is
ism for tt.
diamine is
for the sa
reactiOn 0
minutes to
actiOn Wit;

(as). If

 

diamine t'

57

constants was larger than the expected experimental error.
In some cases, oscillOSCOpe traces taken from different
kinetic pushes were nearly superimposable but analysis of
them gave rate constants which were not the same (90).

When it became obvious that independent decay of the
Optical absorptions could not occur, the kinetic traces Ob-
tained in the present study and also those of Dewald and
Feldman were carefully examined, with the aid of the CAT sys-
tem where possible. This analysis showed that plots of
log(Abs.)versus time are, in fact, smooth curves and have no
strictly linear portions. Figure 14 shows the decay of the
890 nm absorption of a rubidium-ethylenediamine solution dur-
ing the reaction with water. Also shown in this Figure is
the behavior of log(Abs.)and l/Abs. versus time for this
kinetic push.

It is necessary to ask at this point whether the mechan-
ism for the reaction of alkali metals with water in ethylene-
diamine is different from the mechanism which is Operative
for the same reaction in liquid ammonia. In ammonia, the
reaction of dilute metal solutions is Slow (half-times of
minutes to seconds at -54OC) and is thought to involve re-
action with the ammonium ion produced by solvent dissociation
(98). If this same mechanism were Operative in ethylene-
diamine, the necessary reactions would be:

k1 _

H20 + RNHg ——-¥ RNH3+ + OH (3)
k2

 

 

 

 

 

 

 

 

 

 

58

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mzu ma CBOSM Omad .osHEmHOwclonum CH umumB £DH3 COHDUMOH

 

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“SQV

 

followe

Cor
weak aci
Reaction
measured
(33a). :

IGpresent

(Sing the

d (R:

 

 

59
followed by

— +
e50l +RNH3 iii-r H + RNHg (4)

and

M+ + OH— 43-» MOH(s) (5)

Conductivity studies (91) Show that water acts as a
weak acid in ethylenediamine with K = kl/ka < 10—12 for
Reaction 5. The rate constant of Reaction 4 has been
measured in ethylenediamine (k3 = 1.7 x 105 M‘1 sec ‘1)
(90a). The rate of disappearance of the reducing Species,

represented by e can be written as:

sol.’
_d_dL:_l= k3 [e‘] [RNH3+] (6)

. . + .
Using the steady state apprOXimation for RNH3 gives

QIRNH3+1

dt = 0 = kilHaollRNHel - kalRNH3]SS[0H'1

+ (7)
- kale’JIRNHs 158

which yields

__ k H 0] [RNH ]
Imus. - fires . .3.-. an

 

Substituting this result into Equation 6 gives

_ d|e-| = k3k3|e-||H20||RNH2|
dt k2[OH‘] + kale-1 (9)

Measurement of the rate of reaction with water in a

ethylenediamine gives approximately

 

The dev

this is

However
that pre
In
-1
sec a

becomes

If the re
Concentra
in order
The e
in pure et
r“Drywall of

We It (3

 

 

60

—L——de: = ke— [e'] [H20] (10)

The deviation from pseudo-first-order behavior shows that
this is not described by the simple reaction
_ ke—
e +H20 —--> products (11)
However, a comparison of the approximate value of ke‘ with

that predicted by Equation 9 can be made.

In a typical run [9-] = 10-4 M, Using ke‘ §' 20 Mfl
sec'l' as Observed and [H20] = 6 M, the rate of reaction 11
becomes

- Qé%_l = 1.2 x 10"2 Msec"l (12)

If the reaction were forced to proceed through RNH3+, the
concentration Of the hydroxide ion would have to be very low
in order for the equilibrium to favor the formation Of RNH3+.
The alkali metal hydroxides are only Slightly soluble
in pure ethylenediamine with KSp = 10‘9 (91). Therefore,
removal Of OH_ by precipitation could keep its concentration
low. It can be assumed that the rate of recombination of
RNHs+ and OH— according to the reverse of Reaction 5 will
be close to the diffusion controlled limit, so that
kg 2 109 M‘1 sec"l .
The solubilities of sodium, potassium and cesium

hydroxides in "wet" ethylenediamine were measured conducti-

metrically as described in Section III. The results are

 

given in
all of t}
the solut
concentra
reached 1
tation we
became cl
increasir.
olutions
hydroxide
trations
by reacti
cannot be
denominat

If i-

 

 

 

61

given in Table IV and shown for cesium in Figure 15. With
all Of the above alkali metal hydroxides, the conductance of
the solution increased smoothly with increasing hydroxide
concentration. It was not until the hydroxide concentration
reached 10‘4 M_([H20]3’0.2 M) that any indication Of precipi-
tation was Observed. At this concentration, the solution
became cloudy and the conductance increased more slowly with
increasing hydroxide concentration. Therefore, in dilute
solutions Of water in ethylenediamine, the alkali metal
hydroxides are reasonably soluble. Since hydroxide concen-
trations as high as 10’4 M will be attained in these solutions
by reaction of the metals with water, and since hydroxide ion
cannot be removed by precipitation, the term k2[OH-] in the
denominator Of Equation S9 cannot be neglected. That this is
true, can be shown by the following argument:

If it is assumed that
kale—l >> k2[OH_l

Then from Equation 9

_ d[e—] _ k~k3[e-][H20][RNH2]

dt * k3[e'] = kilHeollRNHel (15)
and from Equation 12
" ile—J‘ = k1[H20] [RNHg] = 1.2 X 3.0-2 Ll SEC”:L (14:)

dt

Solving 14 for k; with [RNHg] = 16 M_and [H20] = 6 M, gives

k1 = 1.2 x 10‘4 M-1 sec-3- = 10‘4 M'1 sec-1‘

 

[0H

Cesium Hr

 

I III
I» 411:1,[7/ 7 EC .5 C ’1240 4Cu

 

 

' [OH‘
stlum H (

a .

r/L

14741449411

62

TABLE IV

CONDUCTANCE OF CESIUM, SODIUM AND POTASSIUM
HYDROXIDES IN "WET" ETHYLENEDIAMINE

 

 

Specific Conductance

 

 

 

[OH'] (M x 103) [H20] M (mho x 106)
Cesium Hydroxide
0 0 0.69
6.60 0.26 1.97
10.50 0.41 2.50
19.86 0.78 5.72
29.26 1.14 5.64
55.56 1.50 6.69
58.92 1.52 8.58
44.44 1.75 10.90
50.82 1.99 12.55
58.10 2.27 15.55
64.10 2.51 18.28
72.28 2.85 25.24
[OH'] (M.x 105)
Sodium Hydroxide

0 0 0.40

5.9 0.19 0.58
5.58 0.47 0.87
17.50 0.82 1.26
25.70 1.12 1.57
50.25 1.42 1.97
40.56 1.91 5.67
55.26 2.59 5.65
65.99 5.00 6.96
70.86 5.55 7.86
79.05 5.72 9.22
86.19 4.04 10.56
96.12 4.55 12.09
105.72 4.97 15.42
116.55 5.47 15.24
125.75 5.91 16.52
155.66 6.58 17.90
145.41 6.84 19.54
155.00 7.29 21.11

continued

 

TABLE I

 

Potassi‘

 

 

 

65

TABLE IV--continued

 

 

Specific Conductance

 

 

[0H"] (114. x 104) [H20] M (mho x 106)
Potassium Hydroxide
O 0 1.01
1.96 0.21 1.12
2.41 0.56 5.21
5.10 0.47 4.79
4.60 0.59 6.05
5.45 0.75 7.80
6.51 0.92 8.22
7.05 0.98 9.12
7.90 1.07 10.90
9.02 1.56 12.51
9.99 1.40 15.10

 

64

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How coflumuucmucoo mUonupms aMN mucouosocoo cameommm mo DOHm

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(90: x Cum) aoueqonpuoo DI}IDBdS

65

Since -%:- = 10‘12 then k2 = 108-M,-l sec‘1’ and if
[OH'] = 10“ M then k2 [OH'] = 10“ sec"1

However in a typical experiment, [e_] = 10-4 M and from
earlier results k3 = 1.7 x 105 Mfl sec-1 so that k3[e-] =

1.7 x 10 sec—1“ = 17 sec’l, which is much smaller than the

"neglected" term, k2[OH']. Equation 9 therefore takes the

form
- d_Le_l_ T:— 1.3%?)- [e’] [H20] (15)
Since

31%;— [RNHg] Z 10"“2 [RNHg] 2 1.5 x 10‘“ M

and with k3 = 1.7 i.0.2 x 105 Mfl sec-1, the rate of dis-
appearance of the reducing species according to this mechanism

becomes for these concentrations

 

- -ii 5 —4
_ d4: I S. 1.5 x 10 foE47 x 10 x 10 x 6 M_sec‘l'
(16)

or

d_[e_’l$ 1.55x105Msec'l

This is to be compared with the Observed value

éé%:l = 1.2 x 10'2 M sec—1“

Therefore the observed rate of reaction is three orders of
magnitude larger than that predicted on the basis of the
mechanism presumed applicable in metal-ammonia solutions.

Even if the concentration of hydroxide ion were as low as

66

10’5 M, this mechanism predicts a rate which is still two
orders Of magnitude smaller than that Observed. It should be
noted that in concentrated water solutions (1 to 5 M), the
solubility of the metal hydroxides can be expected to be
higher, thus making agreement Of the predicted rate constant
with the Observed rate constant even worse. It is therefore
clear that a mechanism involving formation of RNH3+ as an
intermediate is not Operative in the reaction of alkali metals
with water in ethylenediamine.

It is evident that the reaction Of dilute solutions of
the alkali metals with water in ethylenediamine cannot be
described by simple first or second order kinetics. It is
also evident that the reaction is faster than the same reac-
tion in ammonia and apparently proceeds by a different mechan-
ism. The reason for this difference might result from the
complex nature of the metal-amine solutions. Recall that in
metal-amine solutions, additional species are present which
are not present in metal-ammonia solutions. .This is best
illustrated by the presence of metal dependent Optical absorp-
tion bands (R-bands) in metal-amine solutions which are not
present in metal-ammonia solutions. The presence of -CH2—
groups in ethylenediamine might also be important.

Solutions Of all the alkali metals except sodium in
ethylenediamine possess a metal-independent infrared absorp—
tion band (IR-band) similar to the Optical absorption Ob-

served in metal-ammonia solutions. As already noted, only

C 1
HI»

:;
v“.

67

one Optical band, at 660 nm, is Observed in solutions Of
sodium in ethylenediamine. Potassium, rubidium and concen-
trated cesium solutions have an intermediate Optical absorp-
tion (R-band), the magnitude Of which decreases relative tO
that of IR-band as the solution is diluted or decomposed
(56). This, COUpled with the fact that the band position is
metal dependent, suggests that the species responsible for
this absorption is a metal-containing species which can dis-
sociate upon dilution. It appears likely that the species
reSponSible for this band has the stoichiometry M- or M2.

For reasons already discussed (Section II, part B),
the infrared absorption Observed in metal-amine solutions has
been assigned to the solvated electron and its "ammonia—like"
aggregates.

Since interconversion of the Optical bands in ethylene-
diamine appears to be fast, and since the magnitude Of the
R-band decreases relative to that of the IR-band when the
solution is diluted, it is reasonable to assume that an equi-
librium exists between the R—species and the IR-species.

If such an equilibrium exists, it is not surprising that this
equilibrium can complicate the kinetics of the reaction with
water.

Conductance and magnetic data (44) indicate the presence
of several Species in metal-amine solutions even when only
an IR-band is present. These Species probably result from

ion-pair interactions which are eXpected to be more

68

pronounced in ethylenediamine than in ammonia because of the
lower dielectric constant Of ethylenediamine. By analogy
with the metal-ammonia case, the expected stoichiometries of
these Species would be e-, M, M— and M2. Assuming equilibrium
among these species,the eXpected rates of disappearance would
beM2>M">M>e".

The evidence which has become available since the earlier
treatments of the kinetics of the reaction with water is
overwhelmingly in favor of the assumption that the Species
present in alkali metal-amine solutions are in equilibrium
with one another. Using this evidence as a starting point,
the consequences of the assumption that an equilibrium exists
and is maintained during reaction with water will be explored.
The details of the following derivation are given in Appendix
A. The major Species assumed to be present can be repre-
sented by the stoichiometries e-, M—, M2 and M (see Section
II).

If the Species responsible for the IR-band Observed in
metal-amine solutions is the solvated electron and its
"ammonia—like" aggregates, then for the case of cesium in
ethylenediamine, four equilibria are necessary for the
kinetic treatment of the reaction with water. The four neces-

sary equilibria are:

M_ —Kl—)~ M + e- (17)
‘__
M 452* M+ + e’ (18)
V.—
+ _
M + OH i3; MOH (19)
‘—

M- + M+ —K‘*-¥ M2 (20)
.‘___

69

where all species are understood to be solvated.

Since it is not known which, if any, of the above
Species reacts preferentially with water, the most general
case will be assumed in which any Of the species listed above
(i.e., e-, M-, M2, M) can react with water to form inter-
mediates which ultimately lead tO hydrogen as a product.
Since the overall reaction of cesium solutions with water
appears to be first order in water over a wide range of water
concentrations (90a), the slow step in the reaction is prob-
ably the bimolecular reaction of the Species listed above

with water.

k
M . H O - +
M + H20 3135’” [Intermediates] Eggzeeé-Hg + OH +-M (21)
ke- H O
_ . _
e + H20 W [Intermediates] ——2_+fast é- H2 + OH (22)
kM H O + -
M2 + H20 mil->- [Intermediates] Egg-s-Ha + 2 M + 2 OH (25)
- , kM" H o + -
M + H20 W [Intermediates] WHZ + M + 2 OH (24)

The total concentration Of reducing species
[MT] = [M] + [e'] + 2842] + ZIM'J (25)

and the rate of hydrogen production is given by

d H _ d
$21 --4—d‘tfil (26)

The time rate Of change Of total metal concentration is

70

M _ k k- _
- 4%= {kM-[M l + k [M2] +321 [M] +—e§(£—l ][H201 (27)
2

M
or
__ gm = U - I I n '-
dt 2kM_ [M ] + 2kM2[M2] + kM [M] + ke_[e ] (28)
where

kX = kX [H20]

Since the time decay of the total absorbance is measured
eXperimentally,the above equations need to be rewritten in
terms of the absorbances rather than the concentrations.

The expression for the total absorbance is
A=A +A +A_+A =A +A (29)

where
AD = AM— + AM2 (50)

is the absorbance due to diamagnetic Species, and

AP = Ae‘ + AM (51)

is the absorbance due to paramagnetic species. The concen-
trations of the individual Species in Reactions 17 through

20 can be written as

2- 4 a
_ K 2 + - -

[M] — (‘12:) [M ] [M ] 7: (52a)

[M2] = K4IM+1 m") 7: (52b)
4} ’2

.Ie‘] = (-L=;?-IEMK]) [M‘] (526)

in which 7+ is the mean molar activity coefficient.

71

Substitution of Equations 52a, 52b and 52c into Equations 28

and 29 leads to:

 

AD = (em- + 6M2K4[M+]’y_2_tl [M-] = r[M—] (55)
and
EMIM+173 _
AP = [Ee— + K2 - [e ] = q[e‘] (54)

In Equations 55 and 54, r and q are constants at fixed values

oflM+land ionic strength and

EX = E); z (55)

where:

e; = molar extinction coefficient of
Species x

E = path length.

Using these results, the net rate of disappearance of

total metal is then given by

- dlM ] = (ké_ + kfi_[M+]7:/K2)A + 20:151- + kM2K4[M+]7:)AD
dt q P r

(5 6)

Solving these equations for the time decay Of the total ab-

sorbance leads to

*

a u + A A . ' + A
_ 21:1, p: 2r,(ke:.tk MIM lvi/kg)xgimn+§?.)+4q(km_+kmax4 [M 17:) (13.13433)

 

A

+
r 33 (1+[M 17: ) + 4q(1 + K4[M+]7: )
D Kg (37)

72

as one form of the solution. Unfortunately, neither the
equilibrium constants nor the rate constants are known in
ethylenediamine.

In order to put Equation 57 into a more usable form,
some further simplifications are necessary. If the assign-
ment of the infrared absorption band in metal—amine solutions
to the solvated electron and its "ammonia-like" aggregates
is valid, then the results Of the extensive treatments Of
metal—ammonia solutions can be used to simplify the kinetic
treatment under discussion here.

Recall that the species M and M2, which are thought to
exist in metal-ammonia solutions, are probably ion-paired
Species of the form (M+- e-)and (M+- M-). The species of
stoichiometry M- is thought to be an ion pair composed Of a

pair of weakly interacting electrons in the coulomb field of

a metal cation (e_ - M+ e-). If these same species are
responsible for the IR-band in metal ethylenediamine solu-
tions, then several assumptions can be made regarding the

rates of reaction of these various species with water.

First, the ion pair association constants for Reactions

18 and 20 should be approximately equal. Therefore, K4 ; 1/K2.
Second, since the species of stoichiometry M is probably a
loose ion pair between an alkali metal cation and a solvated
electron (M+ - e-), its rate of reaction with water should be

nearly the same as that Of the solvated electron. By the

same argument, one might expect that the rates of reaction of

75

M2, (M+- M ) and M- with water will also be approximately
the same. Finally, since the Optical absorption band in
metal-ammonia solutions appears tO obey Beer's Law (17) and
is consistent with the assumption of weak interactions, the
extinction coefficients of the various Species are related

by their stoichiometries according to

€ €
_ = = —‘b—d—-— = la '
Ee EM 2 2 (58)

Using these three assumptions, Equations 52, 55, 54 and 57

can be combined tO give

 

 

. k'-
-dAP—k-AP+I;l AD
dt
1+2§M
AP
and A2
-dAD= 2ke_AD+k_ X2
(it p
1+2.A_D
AP

subject to the condition given by Equation 29.

Since the previous mechanisms were shown to be invalid, the
kinetics data of Dewald and Feldman were re—analyzed by using
this mechanism. The results of this re-analysis are listed
along with the data Obtained in this work and will be SO noted.

Of major concern to progress in the study of the reac-
tion Of the alkali metals with water has been the improvement
in "kinetic control." The major progress in this area has
been the improvements made in solvent purification technique.

In previous studies and in the early studies in this work, when

metal solutions were mixed with "pure ethylenediamine at the

74

beginning of a run, a slow decay Of the absorbance always

was Observed. This decay was always Slower than that Ob-
served during reaction with the lowest water concentration.
In later runs (particularly studies with sodium and rubidium),
no observable decay was observed when the metal solutions
were mixed with the solvent at the beginning of a run.

It will be apparent from the discussion and the data listed
in the following sections that the data obtained from these
runs showed better internal consistency than in those cases
where a Slow decay Of the absorbance was Observed when the
metal solution was mixed with solvent. Also in the runs where
no decay was observed when the metal solution was mixed with
solvent, the metal absorbance was always fairly reproducible.
In runs where the metal solution decomposed when mixed with
solvent, the initial absorbance showed a great variation from
push to push during the course Of the run. A comparison Of
these two cases is shown in Figure 16 where the metal absorb-
ances are plotted as a function of push number. InSpection
of this Figure shows that in those cases (rubidium and sodium)
where mixing of the metal solution with "pure" solvent at the
beginning of the run produced no detectable decay, consistency
Of the values of the initial absorbance, over the course of
the run, was observed. However, in the case where a decay

Of the absorbance occurred when the metal solution was mixed
with water, the values Of initial absorbance during the

course Of the run were not constant, indicating that some

75

 

 

 

 

A--Rb
2.0- El-—Na
®--CS
1.8—.
A
1.6A A AA A A
A AAA A A
g A A A A
m 1.45
.0
H
812
.Q ° "
7 Emma Game a EEG
7'3 1.0— BEE ‘3 ‘3 EH35) E
'13 E] BENZ]
~r-l
£3
H 0.8—
[3
0.6—
(D
0.4— 00 @o
C) C) (3
0.2—-
CXDC> (D
C) C)
lllilniilliilLII;JilllJllllll
10 15 20 25 50

Push Number

Figure 16. Plot Of initial absorbance gs, push number for
the reaction Of cesium, sodium and rubidium
with water, in ethylenediamine.

76

decomposition of the solution had occurred prior to mixing
with water.

The most difficult metal solution to work with, from
the point Of view of stability, has been cesium. Unfortunately,
this was the first metal solution used in the study of the
reaction of the metal solutions with water. The reason for
using cesium initially (i.e., the fact that it showed only
the IR-band) at the time outweighed the disadvantages result-
ing from the difficulty in preparing a stable solution.
However, recently, solutions of cesium in ethylenediamine
have been prepared which Show the same stability as the rubid—
ium and sodium solutions described above (104). With these
thoughts in mind, the results Obtained in this work and the
Significance of the proposed mechanism for the reaction Of
the alkali metals with water in ethylenediamine can now be

discussed.

B. Alkali Metals Plus Water

1. Cesium

The cesium solutions used in this work possessed only
one Optical band which had a maximum in the infrared at 1280
nm. Since the sensitivity limit Of the detectors is only
about 1110 nm, the band maximum was never actually observed
in these studies. The band shape of the IR-band Observed in
the cesium solutions is Shown in Figure 15. The kinetic

data for cesium were initially analyzed by numerical solution

77

of Equation 59 and the values Of the four parameters ké_,
kfi_, Ap and AD which gave the best fit to the data were
calculated. Figure 17 Shows a comparison of the Observed
decay of the total absorbance with that given by the best fit
of Equation 59 to this set of data. This fit is typical for
those cases where the decay was not complicated by the cata—
lyzed decomposition at long times. A typical fit in the
latter case is Shown in Figure 18. The tail of the decay
curve Shown in this Figure is lower than first—order in the
absorbance and it can be seen that it does not fit well with
the curve calculated using Equation 59.

In Spite Of the apparently good fit to the decay of the
absorbance, the values of the parameters, which gave the best
fit, Showed a greater than expected variation for pushes
within a given run. In all cases, where the four parameter
equation (Equation 59) was used to fit the data, the value
Of ké— calculated to give the best fit had a very large un-
certainty and was for all practical purposes statistically
undefined. Inspection of Table V Shows this and also Shows
that in some cases the best fit to the experimental data was
accomplished by assigning a negative value to ké-° These
facts suggest that an equally good fit to the data can be ob-
tained using only the three parameters kfi-, Ap and AD.

The cesium data were analyzed using a differential equa-
tion which involved only the three adjustable parameters kfi_,

Ap and AD. The derivation of this equation is algebraically

equivalent to the derivation of the four parameter equation,

78

 

 

 

 

0.4 -
0 Exp.
-Calc'd.
0.5
00
000000
\‘2’0
1 1 l I

 

L. l
0.01 0.02 0.05 0.04 0.05 0.06 0.07

t(Sec)

Figure 17. Comparison of Observed decay of the absorbance
with that given by the best fit of Equation 59
for the reaction of cesium with water in
ethylenediamine.

79

 

[H20] = 0.025 M.
O EXp.

-Calc'd.

Abs.

0.1 _

 

_.
.—
(-
—
)-

 

 

 

t(sec.)

Figure 18. .Fit of Equation 59 to Observed decay at
absorbance for reaction of cesium with
water when a long tail is Observed.

80

TABLE V

VALUES OF kM‘ AND ké- CALCULATED FROM THE BEST FIT

OF EQUATION 59 TO THE DATA OBTAINED FOR THE

REACTION OF CESIUM WITH WATER IN ETHYLENEDIAMINE

 

 

[H20](!)

A(nm)

6

 

e k e“ M‘ kM-
0.0244 1100 12.95 14.061 6.985 4.100
0.0244 1100 5.225 6.910 6.957 4.955
0.0244 950 0.254 0.844 7.799 --
0.0244 750 5.197 9.847 7.184 4.871
0.0728 1100 5.542 7.165 2.170 --
0.541 1100 41.55 150.840 2.572 1.212
0.541 950 50.65 106.486 28.57 16.890
0.928 1100 -4.565 -- 5.240 --
0.928 1100 -4.864 -— 6.580 --
1.7755 1100 ~5.291 -- 5.89 --
1.7755 1100 5.42 8.744 0.825 0.461
1.7755 1100 1.656 -- 1.25 --
6.11 1100 -52.85 -- 26.44 --
6.11 1100 55.89 -- 18.68 --
6.11 1100 -250.51 -— 19.81 --

 

81

with the exception that no direct reaction is assumed to take
place between e- or M and water so that ké_ = kg = 0.
The resulting differential equations have the form:
I I 2
_ dAP _ kM- AD/Z dA kM" AD /AP

D -
dt 1 + 21>.D/AP dt 1 + 2 I‘D/AP

 

 

(40)

‘0

The results Obtained by using these equations to fit the data
are given in Table VI. A comparison of the values of kM-
calculated from Equation 40 above and those from Equation 59
Show that they have about the same values. The consistency
of the calculated values Of kM' within a given run is,
however, not improved. As might be expected, the uncertain-
ties on the individual values of kM" have decreased somewhat.
Figure 19 Shows that in Spite Of this improvement it is im-
possible to tell whether kM‘ has any dependence on the water
concentration.

The possible factors involving the non-reproducibility
of the values of kM- will be discussed later, since the same
factors affecting the kinetics of the reaction of cesium with
water also will affect the reaction of the other metals with

water.

2. Sodium
The sodium solution used in this work was more stable
than any other metal solution used. When a sample of the

sodium solution was mixed with ethylenediamine at the beginning

82

TABLE VI

VALUES OF kM- CALCULATED FROM THE BEST FIT OF EQUATION 40
TO THE DATA OBTAINED FOR THE REACTION OF CESIUM

WITH WATER IN ETHYLENEDIAMINE

 

 

 

 

 

continued

[H20](M) i(nm) kM_ km-
[Cs] = 1.5 x 10‘4 Mia)
0.0244 1100 8.907 0.915
0.0244 1100 6.195 0.750
0.0244 950 8.626 0.112
0.0244 750 12.251 0.557
0.541 1100 2.55 0.016
6.11 1100 26.455 4.05
6.11 950 18.655 1.062
6.11 750 20.596 2.85
6.11 750 19.082 2.21
[CS] = 4 x 10-4 M“)
0.025 1100 20.076 4.98
0.025 1100 19.171 0.577
0.025 1100 16.991 0.558
0.025 1100 16.181 0.454
0.025 950 16.772 1.656
5.60 950 55.544 2.20
5.60 750 49.587 5.91
lggl == 5 x 10" M,(a) '
0.075 ' 1100 10.022 0.651
0.075 1100 2.554 0.518
0.928 1100 15.007 8.155
0.928 1100 59.090» 9.061
1.7755 1100 8.425 1.69
1.7755 1100 8.725 2.02
1.7755 1100 .9.558 1.52
1.7755 1100 2.476 0.21
1.7755 1100 4.250 6.58

85

TABLE VI--continued

 

 

 

 

, 0
[H20] (1)1) A (DIR) kM- kM-
[Cs]=5;54x 10" M.
0.84 1052 11.651 2.911
0.84 1052 5.966 0.544
0.84 1052 8.715 2.281
1.016 1052 9.161 2.740
1.016 1052 29.745 7.648
1.016 1052 15.811 5.617
1.667 1052 5.755 0.677
1.667 1052 15.614 5.215
1.667 1052 50.704 11.758
1.667 1052 9.220 2.871

 

(a) Reanalyzed data Of LHF (90).

84

 

 

 

 

 

 

 

 

so -
4o—
50- .- -- l
km-
(2
I:
.. '
20~ §
(3
1o-
9
0.025 0116?. 1.0 2:0 ”sic é...

0.05 0.75 [H20](M)

Figure 19. Plot of _, calculated from Equation 40, versus
water concentration for the reaction Of cesium
with water in ethylenediamine.

85

Of this run, no detectable decay Of the 660 nm band occurred.
In general, other metal solutions always showed a slow decay
of the absorbance when mixed with ethylenediamine. Also,
considerable difficulty was encountered in dissolving the
sodium. This difficulty was not encountered in the prepara-
tion Of any of the other metals.

A typical decay of the 660 nm band during the reaction
of sodium with water is Shown in Figure 20. Figure 21 shows
a plot of log thersus log [H20]. -](is the pseudo-first-order

rate constant and is defined by:
‘h
)(= k[H20] (41)

Least squares treatment of the data shown in Figure 21 yields
a slope of 1.86 1.0.1. The line drawn in Figure 21 has a
lepe of two. Only reactions which had half lives of 5 seconds
or less were used in constructing this plot. The reasons for
this will be discussed later. InSpection of Figure 22 re-
veals that no change in the shape of the 660 nm band occurs
during the reaction with water and that there is no apparent
band shift during the reaction.

The values of the Specific rate constants for the reac-
tion of sodium with water are listed in Table VII. InSpection
of this Table shows that there is good agreement among the
rate constants for this run. Comparison of these rate con-
stants with those Obtained by Feldman also Shows good agree-
ment. The reasons for the apparently good agreement here will

be discussed later.

86

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87

 

100

II’TT

1

CHI]

10.

TIIIIT

I

TTIII]

1
CI]

 

 

l l Llllll

 

[H20] M

Figure 21. Plot of log )(yg, log (water concentration) for
the reaction Of sodium with water in ethylene—
diamine. The line drawn has a Slppe of tWO.

88

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COwuucsm m mm EDwOOm m0 pawn Es 0mm may no cofiuwmom Usm macaw Osmm .NN musmwm

as:

 

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.HMHOE hO-N MO COHHMHUCQUCOU HORN}, HMHUHGHIIm

.HmHOz em.m MO SOHDMHDOOOCOU HODMB HafiuficHlnd

 

 

 

 

89

TABLE VII

VALUES OF THE RATE CONSTANT FOR THE REACTION OF SODIUM

WITH WATER IN ETHYLENEDIAMINE

 

 

 

[H20] [M) )x (rim) ){(sec'1) X(M-asec-l)
5.94 660 12.15 0.544
5.94 660 10.64 0.502
5.94 660 12.51 0.549
5.94 660 15.55 0.578
5.94 660 15.27 0.576
5.94 660 15.14 0.572
4.45 660 6.7 0.558
4.45 660 7.47 0.577
5.96 660 4.29 0.275
5.96 660 4.55 0.277
5.96 660 5.72 0.257
2.97 660 5.04 0.544
2.97 660 4.06 0.460
2.97 660 2.55 0.289
2.97 660 5.45 0.589
2.97 660 5.42 0.588
2.97 660 5.29 0.575
1.96 660 0.44 0.114
1.96 660 0.40 0.104
1.96 660 0.42 0.109

 

90

Recall that sodium solutions possess only an absorption
band at 650-700 nm and show little or no infrared absorption.
Since this indicates a low concentration of solvated electrons
and "ammonia-like" aggregates, reaction of the V—species with
water gig intermediate formation of the IR—species is not
favored. The following calculation shows that the reaction
involving prior formation of the IR-Species is too slow to
account for the observed rate.

A possible mechanism for the reaction of the V—species

with water is

K H20

V—AIR

 

k= 20 M‘lseC'l;’ Products (42)

in which "V" represents Na- and/or Nag and "IR" represents
the solvated electron and its "ammonia-like" aggregates.
Absorption Spectra of sodium-ethylenediamine solutions show
only the V-band and indicate that K <10"2 (89 ). This is
confirmed by the reaction of cesium solutions with sodium
bromide in ethylenediamine in which the IR-band completely
disappears and the V-band appears unless there is an excess
of cesium present.

These results would require that the reaction with water
through prior formation of the IR-Species has a second order
rate constant of less than 0.2 Mfl sec'lg Even at water
concentrations as high as 6 g, the contribution of this

mechanism to the observed pseudo-first-order rate constant

(12 fiflsec'l) could not exceed 10%. It may, however, become

91

important at lower water concentrations. Therefore, the reac-
tion of sodium with water probably involves the V-Species
directly, and this direct reaction leads to the observed
second order dependence on water.

At water concentrations below 1 g, the reaction is very
slow and in some cases is zero-order in the absorbance.

This behavior probably occurs because the catalyzed decompo-
sition reaction becomes important at these low water concen-
trations. It is for this reason that only data with half-
lives of 5 seconds or less were used in constructing

the log )<' versus log [H20] plot which is shown in Figure
21.

The mechanism for the reaction of sodium with water is
still unknown. Any prOposed mechanism must account for the
observed second order dependence on water. The species
responsible for the V-band is probably the same species
responsible for the R-band in other metal-amine solutions and
for reasons already mentioned is probably a two electron
species which is not a simple ion pair.

.One mechanism which could account for the available data
and also lends itself to future testing is the following:

Na" + H20 —Kl—\ Na- - H+ + 0H" (45)

ast
followed by

Na- - H+ + H20 —k—‘-> Na+ + 0H“ + H2 (44)

so that

92

gap-trial = k1[Na' 0 H+] [H20] (4:5)

Assuming that equilibrium is maintained in the first step

gives:

- _ _.LL__-_L.[_2_l
[Na - H+] — K I‘ESH_]HO (46)

which when substituted into equation 45 yields

 

d[H2] _ k K [Na'][H 01?
dt ‘ l lfofl-j *2 (47)

The validity of Equation 47 can be tested by observing the
effect of added hydroxide on the rate of reaction of sodium
with water. If this mechanism is correct, then the reaction
should be slower in the presence of added hydroxide. It is
also possible that the first step involves equilibrium
formation of the hydrated ion, Na’ - H20, followed by the
rate-controlling reaction with H20 to produce H2. In this
case the reaction rate would not decrease when hydroxide
ion is added to the solution. The effect of hydroxide ion
on the rate of reaction of sodium with water is currently
being tested (104). However no conclusive results have yet

been obtained.

5. Rubidium and Potassium

 

In all the runs using potassium solutions, the kinetics
were complicated by the presence of two Optical absorption

bands in addition to the infrared absorption. One of these

95

bands was located at 850 nm and the other at 650 nm. In
light of Tuttle's results (54) concerning the nature of the
650 nm band, the 650 nm band observed in these solutions was
probably due to sodium contamination. Figure 25 shows a
typical spectrum of a potassium solution used in these studies.
Figure 24 shows that the decay of the absorbance during the
reaction with water is not first-order in the absorbance.
The kinetic data were analyzed by the methods discussed in
the introduction to this Section. The results of these
analyses are shown in Table VIII.

The rubidium solutions used to study the reaction with
water showed two optical absorptions. One was located at
890 nm (R-band) and the other in the infrared (IR—band).
A typical optical Spectrum of the rubidium solutions used in
this work is shown in Figure 25. It is clear from Figure 26
that both optical bands disappear during the reaction with
water but that the R-band disappears faster than the IR-band.
Inspection of Figure 14 shows that the decay of the absorb-
ance during the reaction with water does not obey simple
first or second order kinetics. It should be noted that the
rubidium solutions used in this work showed stability similar
to that of the sodium solutions used.

The kinetics of the reaction of rubidium and potassium
with water are complicated by the fact that in addition to
the presence of the IR-band, the intermediate Optical absorp—

tion (R-band) is also present. In view of previous arguments

94

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coHufiUpm ca camnl> m we wocmmmnm man mcfl30£m .mcwamfln
Imsmamnum CH Eswmmmuom How Um>nmm£0 Esuuummm Hmoflmha

185 K
OOOfi 00m 00m 00» com
_

.MN musmflm

 

— ___ .m. . q

 

 

eoueqxosqv

 

 

Absorbance

95

 

 

 

 

1.0 4‘4
r
7
O
C)
T O
O
‘O
0O
C)
C)
0 <3 (D
C) 0
0.1— 00
_ C) C> o
I
4 4 1 1‘ 1 I l l
0.01 0.02 0.05 0.04 0.05 0.06 0.07 0.08
t(sec)
Figure 24. Plot of log (Abs.) versus time for the

reaction of potassium with water in ethylene-
diamine.

96

TABLE VIII

VALUES OF kM‘ CALCULATED FOR THE REACTION OF POTASSIUM WITH
WATER IN ETHYLENEDIAMINE CALCULATED USING EQUATION 59

 

 

 

0
[H20] (5) %(nm) kM_ km-
[K] = 1.15 x 10-4 Mia)
0.0258 1110 12.897 6.492
0.0258 1110 7.554 2.105
0.0258 950 9.555 2.011
0.0258 850 10.102 2.551
0.0258 700 8.904 4.889
0.0258 700 9.771 4.501
0.5895 1110 16.650 6.466
0.5895 1110 11.685 2.514
0.5895 1110 25.470
0.5895 800 57.897 14.454
0.5895 800 55.556 10.555
0.5895 800 26.986 6.491
0.5895 700 7.005 5.085
4.057 1100 42.591 8.561
4.057 950 59.904 5.49
4.057 950 27.481 2.544
4.057 950 18.595 2.179
4.057 850 58.922 16.589
4.057 700 59.822 4.954
[K] = 5.05 x 10-4 gfb)
4.45 1052 16.251 4.861
4.45 1052 10.046 2.897
4.45 1052 7.655 1.876
4.45 850 24.615 6.486
4.45 850 8.922 2.510
4.45 850 9.167 5.544
0.578 850 14.615 4.614
0.578 850 8.221 2.580
0.578 850 6.557 5.166
0.578 1052 45.612 8.497
0.578 1052 10.561 2.865

continued

TABLE VIII--continued

97

 

 

 

[H20] (1_~4_) 1 (nm) 4M- 6k M_

[x] = 2.2 x 10-4 g_b
0.157 850 10.161 2.516
0.157 850 24.501 5.861
0.157 1052 8.957 2.466
5.05 1052 10.755 5.015
5.05 1052 26.457 7.484
5.05 850 50.817 5.586
5.05 850 8.641 6.971
2.16 850 21.697 4.612
2.16 850 57.411 9.866
2.16 850 42.156 8.194
2.16 850 18.117 5.791

 

aReanalyzed data of LHF (90).

bData of this work.

98

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AECV K

.mm 083m

 

 

OOOH 00m 00m ooh
a — a

1“ J _

 

 

(snrun KIEJQIQIE) aoueqxosqv

99

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on can mpchImH Ucm Im on» nuon mo mmomv one. .HmumS prz
sowuommu may mafiusw Esnuuwmm Eswpansu may mo amumv Hmowmma

Aummvu

 

 

 

 

 

 

 

.mm musmflm

(sutun Axexqthe) eoueqxosqv

100

(c.f. Section II and the Introduction to this Section), the

R-species is probably in equilibrium with the IR-species, as:

R 495—4- IR (48)
T.—

and this further complicates the kinetics of the reaction with
water. Since in all cases, the studies of the reaction of
potassium solutions with water were further complicated by
the presence of a V—band, presumably due to sodium contamina-
tion, the following discussion will be focussed primarily on
the reaction of rubidium solutions with water. However, it
should be remembered that anything which is said about rubidium
solutions should, in principle, also apply to those of
potassium.

The derivation of the eXpression for the rate of decay
of the total absorbance during the reaction of rubidium with
water is algebraically equivalent to the eXpression derived
for the reaction of cesium with water (see Appendix A). The
general form of the rate expression is also similar to that
derived for the cesium case, but the additional equilibrium
between the R- and IR-Species makes the final expression more
complex for the reaction 0f rubidium (and potassium) with

water. The expression has the form:

 

 

+ 2 ., A.’ +é-A'
_ 223. = kfi' 1+K4[M 17¢.+ kR/kfi'KS p A D (49)
+ 1 +
1 + K4IM17: + 21./K5 23“?
D

where the definitions of the terms are given in Appendix A.

101

This eXpression is derived assuming no direct reaction between
e- or M and water. The reasons for this assumption have
already been discussed (c.f. Introduction to this Section).
Equation 49 can be simplified somewhat. It will be shown
later that if the process is similar to that involving sodium,
then the direct reaction of the R-species with water cannot
compete with the dissociative reaction through the IR—Species.

This implies that
I I
kR << KM-
Since in the case of rubidium, K5 g 1, the term kfi/kfi_K5 is

small and can be neglected so that:

 

- 251.: ’_ 1 + K4[M+]Y: A + i'AD
dt km + 1 - A (50)
1+K4[M]y:+R-; 1+§§E

InSpection of Equation 50 shows that it is difficult, at best,
to sort out a Specific rate constant for the reaction with

+
water without knowledge of the values of K4, K5, and [M_].

Numerical solution of Equation 50 gives only the value of A:

 

given by
+ 2
x: 1.5,- 1 + KM“ 174 (51)
+ 1
1 + K4 [M 17: + if;

The values listed in Tables VIII and IX for potassium and
rubidium are values of "Kappa" for the reactidn of these

metals with water.

102

TABLE IX

VALUES OF kM' CALCULATED FROM THE BEST FIT OF EQUATION 59
TO THE DATA OBTAINED FOR THE REACTION OF RUBIDIUM
WITH WATER IN ETHYLENEDIAMINE

 

 

 

 

 

[H20] 0;) 7((nm) 1.“. 61M-
a
[Rb] = 1.5 x 10-3 L4
0.025 750 21.504 7.658
0.025 750 21.445 7.107
0.5895 1100 5.542 2.516
0.5895 1100 12.169 5.914
0.5895 750 11.499 4.067
5.60 1100 18.772 4.715
5.60 950 18.467 4.258
5.60 750 26.495 6.858
[Rb] = 5 x 10-4 Mjb
0.124 900 22.056 5.514
0.124 900 26.571 7.252
0.124 900 24.170 4.906
0.229 900 16.494 4.701
0.229 900 15.886 4.755
0.229 900 17.129 5.574
0.229 900 19.899 4.696
0.229 900 12.569 4.589
1.05 900 19.585 4.446
1.05 900 18.689 4.205
1.05 900 15.555 4.401
0.124 1052 21.685 6.574
0.124 1052 22.901 5.259
0.124 1052 20.051 5.554
0.229 1052 17.552 5.194
1.05 1052 18.882 4.815
1.05 1052 15.515 5.952
1.05 1052 26.881 5.672
2.04* 900 27.995 7.587
2.04* 900 24.668 5.822
3.74* 900 14.821 4,594
5.74* 900 21.445 4.574
5.74* 900 18.511 5,257

 

a—-Reana1 zed data of LHF.
b--Data o

*--Fixed wavelength.

this work.

103

As mentioned above, the calculation of the specific rate
constant, k -, can only be carried out by determination of
the values of K4, K5 and [M+]. At present these values are
not known. In Spite of these complexities, several important
observations are worth noting.

First, the values of the calculated parameter K,
in the analysis of the rubidium show better consistency
from push to push than the data for cesium or potassium.
However, the magnitudes of the uncertainties in the values
of the parameters for a given push are about the same for all
metals.

Secondly, as has been mentioned, both the R- and IR-bands
decay together during the reaction with water. However, the
individual decay rates are probably determined by the stoi-
chiometric requirements of the equilibria among the species.
The Spectrum of the R—band alone during reaction can be ob-
tained in two different ways. If the shape of the spectrum
observed in cesium-ethylenediamine solutions (IR-band only)
is normalized at 1100 nm and then subtracted from the spectral
decay observed during the reaction of rubidium with water,
the decay of the R-band with time is obtained. This is
illustrated in Figure 27. That this shape corresponds to
that of the R-band can be seen by the comparisons made in
Figure 28. Here a Spectrum of the R-band was obtained using
CAT. The Spectrum near the end of a push (after about 80%

reaction) was subtracted from the spectrum at the beginning

104

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mm3 cowuomnunsm 0n» mnommm .mwfivsum oflumcflx mgu ca Um>ummno EDHuommm
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q
s

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m

4m.o

L 0.9

 

 

 

 

105

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Hmym3 ayy3 SOyyUmmu may no 0am may Hmma Esyyummm mo GOyyUmquDm

 

fig Uwcflmyflo umay Syw3 NN musmflm EOHH Tawnm UGNQIM 03y M0 Gomfihmmfiou. .mN wuflmfim
155 2
oooa 00m oom ooh
. _ a 4 _ _ _ _ . m
no my
no
6 0

 

 

mu 068(.qu)/(.qu)

 

 

106

of the push. The resulting R-band shape is compared to that
which was obtained by subtraction of the cesium Spectrum in

Figure 28. It can be seen that the band shapes are the same.

C. Band Interconversion Reactions

1. Cesiumglus N+

Several studies were made of the reaction of cesium
with sodium ions in ethylenediamine. The cesium solutions
used in these studies possessed only an infrared absorption.

Although the reaction
Cs solution (IR) + Na+ -—+'"V-Species"(660 nm) + Cs+ (52)

appears to be too fast to be studied quantitatively (té_<'.10'3
sec.) using the stOpped-flow technique, a few qualitative
observations are worth noting.

In those cases where the concentration of Na+ was in ex-
cess, the cesium infrared band decayed completely during, or
Shortly after, mixing, leaving only the 6.60 nm band.

A typical Spectrum after mixing is shown in Figure 29. Also
shown in this Figure is the Spectrum observed in solutions
of sodium in ethylenediamine. It is evident from Figure 29
that the shapes and positions of these two absorption bands
are the same, indicating that the Species responsible for
the V-band in sodium solutions is the same as that formed

by Reaction 52. Also, it can be seen from this Figure that

107

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cam mUyEoya Egypom mo COnyHom m @awxyfi Hmymm Um>ummao Esuyummm .mm musmym

AEGV K

 

.SOnyHow mayEMyUmcmamaymnfisyUom M MD Esuyommwllm

.mcHEMypmcmawaym :y Egymmo tam mpyeoya
anyhow mayxys Hmymm Um>ummao Enuyummmllm

 

 

 

m.o

o.d

aoueqxosqv

108

there is no detectable infrared band remaining after reaction

of cesium solutions with an excess of sodium ions.

2. Rubidium E163 K+
The fact that no 660 nm absorption (V-band) was observed

after the reaction:

Rb solution (IR, 890 nm) + K+ -9'K solution (IR,850 nm)

+ Rb+ (55)

tends to confirm Tuttle's observation that the V-band some-
times observed in potassium, rubidium and cesium solutions
is due to sodium contamination.

Since the R-bands of potassium (850 nm) and rubidium
(890 nm) are so close together, no decay of the rubidium
R-band with concomitant formation of the potassium.R-band was
observed. However, Figure 50 gives a comparison of the Optical
spectrum before and after mixing. It can be seen that the
spectrum after mixing shows a Slight asymmetry and an apparent
shift of the band maximum toward the visible. This indicates
the presence of an additional absorption band at Shorter
wavelengths. Since in all cases, the concentration of rubid-
ium was in excess, this result is the expected one if
Reaction 55 proceeds as written.

An important question needs to be considered at this
point. If the V-Species observed in sodium solutions is in-
deed of the same type as the R-Species observed in rubidium

and potassium solutions, how can we ignore direct reaction

109

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Um>ummao ymay m m>uso Ocm,mayxye mnommn Om>ymmao Esuyommm may
my a m>usu .mCyEMHOmamywaym Cy mOyEOHQ EDymmwyom Oam EDHOstH

 

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AECVK
oops 00m oom co.
# _ 4 q q u q _
4||VI m

 

 

 

mu OSOT(°sqv)/('sqv)

110

of the R-Species with water as has been prOposed for the
case of sodium?

Since, with sodium solutions there is no detectable
IR-band, the V-species must react with water directly, as

previously described. In sodium solutions then, the process

may be described by,

k1 l H20

products

(54)

However, with rubidium and potassium solutions which show

both R- and IR-bands, the following scheme is possible:

R -l-<-5—-’~ IR (55)

R; H2O k2 H2O
products products
with
K5 = [IR]/[R] ”=’ 1
Assuming that the R-band could react directly with water at

a rate comparable to the V-band in sodium solutions, and

that the IR-band reacts at a rate comparable to the IR—band

in cesium solutions, then:

15:31 = k. [R] [H.012 + kaKs [R1 [H20] (56)

or

111

9:18:41 = R[H20] {k1[H20] + k2K5} (57)

Of course this equation should also be valid for sodium solu—

tions. However, in this case, the optical spectrum shows that
N

K5'< 0.02. Therefore, for the case of sodium, at a water

concentration of 1.5 I!

N —‘|

0.41 M *sec-l

k1
Taking kg:20..yl_"lsec‘l for cesium, then for sodium

kng = 0 .04:
and

K5 = O .002

so that there is very little competition of the direct reac-
tion with the dissociative mechanism in the reaction of
sodium with water since the equilibrium heavily favors the
V-species.

In the case of rubidium and potassium however, there
are about equal amounts of R and IR-bands (see Figures 24 and

26), so that K5'3 1. Taking kg 3'20 Mflsec'l, then
szs = 20

in the case of rubidium (and potassium). If k; has the same
value as for sodium (i.e., k1 = 0.41 flflseC‘1 at [H20] =

1.5 Q) then

k1 = 0.41 g 0.10 k2K5

112

So that in the reaction of rubidium with water, the direct
reaction of the R-Species cannot compete with the dissoci-
ative mechanism. This is true of all water concentrations
up to 4 M, [Thus it can be seen that although the V- and R—
species might indeed be the same, the reaction of these
Species with water can proceed by different mechanisms,
depending upon the metal used.

An understanding of the mechanism by which molecular
hydrogen is produced in the reaction of the alkali metals
with water in ethylenediamine is necessary for a detailed
understanding of the nature of these reactions. The results
of pulse radiolytic studies in water (71,72) have shown
that the reaction

kH + on;

H + OH- egq + H20 (58)

is relatively fast (k(H + OH“): 1.8 x 107 gfl sec‘l).
However, the addition of hydroxide ion has no apparent effect
on the rate of reduction of water by cesium in ethylene-
diamine (90). This suggests that although hydrogen atoms may
be formed in these systems by the direct reaction of the
reducing species with water, they are probably short lived in

ethylenediamine and that molecular hydrogen is produced by a

reaction other than

H + H ———+- H2 (59)

In light of these facts, a plausible alternative mechanism

113

for molecular hydrogen formation is necessary. One possible
mechanism involves the production of hydrogen atoms by the
direct reaction of the reducing species with water with sub—
sequent abstraction of a hydrogen atom from the solvent.
Since the overall reaction produces one-half mole of hydrogen
for every mole of metal consumed, the solvent radicals formed
by hydrogen atom abstraction probably react further with

the reducing Species to form other products. It has been
suggested (90) that the d-hydrogen atoms of the solvent are

abstracted to form molecular hydrogen according to
(e-) + H20-———+-H + OH- (60)

followed by
H + HgN-CHg-CHg-NHZ —-———>- H2 + HgN-CH-CHg-NHg (61)
and

(e-) + HgN-CH-CHg-NHg ————->'H2N-CH2-CHg-NH- (62)

The validity of this mechanism and any other involving
a—hydrogen atom abstraction was tested using as the solvent,
ethylenediamine which was labelled at the a position with
tritium. A cesium solution was prepared using the labelled
ethylenediamine and was mixed with a water solution of known
concentration. The hydrogen formed was collected and burned

to water by the reaction

100°C
Ago + H2 ——————+- H20 + Ag. (65)

114

If the mechanism of molecular hydrogen production indeed
proceeds through abstraction of an d-hydrogen from the sol-
vent, then the water collected as a result of Reaction 65
should contain tritium and therefore show activity. The
results of three such experiments showed that not more than
2% of the hydrogen formed in the reduction of water by metal
solution could originate from the a-positions of the solvent.

The exact mechanism of molecular hydrogen formation is
not yet clear. However, it is evident at this point that
the abstraction of d-hydrogen atoms of the solvent plays only

a minor role in the mechanism.

D. Summary

The reactions of the alkali metals with water in ethylene-
diamine are faster and proceed by a different mechanism than
the same reactions in liquid ammonia. In the case of sodium,
the principal absorbing species (V-Species) apparently reacts
directly with water by a process which is second order in
water. In the case of rubidium, potassium and cesium, the
preferred reaction seems to be through dissociation of the
R-species to the IR-species. The rate-determining reaction
apparently involves "ammonia-like" diamagnetic Species rather
than isolated solvated electrons.

The stability of the metal solutions used is critical
to reliable rate studies in these systems. Only when the

metal solutions used Showed no decomposition when mixed with

115

pure solvent were the Observed reaction rates with other
solutes reproducible. Finally, the mechanism described for
the reaction of the alkali metals with water in ethylene-
diamine is not only consistent with the observed rates but
is also consistent with the current models for metal-amine
solutions. However, further eXperimentation is necessary

to fully validate this mechanism.

E. Suggestions for Future Work

The study of the effect of added alkali metal cation and
also added hydroxide on the rate of reaction of metal solu-
tions with water should be investigated. These studies are
particularly important in determining the extent of the valid-
ity of the mechanism described in this work. Also of impor-
tance for further work is the investigation of the equilibria
which apparently exist in metal-amine solutions. Hopefully
these studies would permit measurement of equilibrium con-
stants which then would allow a more exact kinetic treatment
of the reaction of the metal solutions with water. Both of
these studies involve a great deal of effort, but are neces-
sary if the exact mechanism of the reaction of metal solutions
with water is to be understood.

0f secondary importance in further studies are the
elucidation of the origin of molecular hydrogen in the re-

action with water and also the factors contributing to the

116

formation of pyrazine in metal solutions in ethylenedi-

amine.
Hopefully, the present study can be extended to the

investigation of the kinetics of other reactions of the

solvated electron.

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11.
12.
15.

14.

15.

16.

17.

18.

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J. Phys. Chem., 19, 5558 (1966).

50. R. R. Dewald and J. L. Dye, J. Phys. Chem., 22, 128 (1964).

51. M. Ottolenghi, K. Bar—Eli, H. Linshitz, and T. R. Tuttle,
Jr., J. Chem. Phys.,‘12, 5729 (1964).

52. M. Ottolenghi and H. Linshitz, p. 149 in Ref. 14.

55. J. L. Dye, L. R. Dalton, and E. M. Hansen, Abstracts,
149th National Meeting of the American Chemical Society
(April 1965), p. 455.

54. Ian Hurley, T. R. Tuttle, Jr. and Sidney Golden,
J. Chem. Phys., 12, 2818 (1968).

55. Marc G. DeBacker, personal communication.

56. J. L. Dye and R. R. Dewald, J. Phys. Chem., 22, 155
(1968).

 

57. A. Debierne, Ann. Physigue (Paris), 2, 97 (1914).

58. D. E. Lea, "Actions of Radiation on Living Cells,"
The Macmillan Co., New York, p. 47 (1947).

59. G. Stein, Disc. Fara. Soc., 1_2, 227 (1952) .

120

60. R. L. Platzman, "Physical and Chemical ASpects of Basic
Mechanisms in Radiobiology," U. S. Nat. Research Council,
Pub. No. 505, pp. 22-50 (1955).

61. A. 0. Allen, "The Radiation Chemistry of Water and Aqueous
Solutions," Van Nostrand, Princeton, 1961.

62. N. F. Barr and A. 0. Allen, J. Phys. Chem., 2;, 928 (1959).

65. E. Hayon and J. J. Weiss, J. Chem. Soc., 5091 (1960).

 

64. J. H. Baxendale and G. Hughes, Z. Phys. Chem. (Frankfurt),
14, 506 (1958).

65. G. Czapski and H. A. Schwartz, J. Phys. Chem., _2, 471
(1962).

 

66. F. s. Dainton, E. Collinson, D. R. Smith, 6. Tazuké.
Proc. Chem. Soc., 140 (1962).

67. E. J. Hart and J. Boag, J. Am. Chem. Soc., 21, 4090 (1962).
68. J. Boag and E. J. Hart, Nature (London), 197, 45 (1965).

69. M. Anbar and P. Neta, Int. J. Appl. Radiat. Isotoges,
l§J 495 (1967).

70. E. J. Hart, S. Gordon and E. M. Fielden, J. Phys. Chem.,
19, 150 (1966).

71. M. S. Matheson and J. Rabani, J. Phys. Chem., 22, 1524
(1965).

72. J. Rabani, p. 242 in Ref. 14.
75. M. Anbar, p. 64, in Ref. 14.

74. L. M. Dorfman and I. A. Taub, J. Am. Chem. Soc., 22,
2570 (1965).

75. E. A. Shaede and D. C. Walker, "The Alkali Metals,"
Spec. Pub. NO. 22, The Chemical Society, London (1967).

76. D. C. Walker, Can. J. Chem., 12, 807 (1967).

77. R. W. Ahrens, B. Suryanarayana and J. E. Willard, J. Phys.
Chem., 22, 2947 (1964).

78. D. M. Compton, J. F. Bryant, R. A. Cesena and B. L.
Gehman, in "Pulse Radiolysis," M. Ebert, J. P. Keene,
A. J. Swallow and J. H. Baxendale, Ed., Academic Press,
London and New York, 1965, p. 45.

79.

80.

81.
82.
85.
84.
85.
86.

87.

88.
89.

90.

91.
92.

95.
94.
95.

96.

97.

121

B. Ward, Advances in Chemistry Series, 21, "Radiation
Chemistry," Vol. I, R. F. Gould, Ed., American Chemical
Society, Washington, D. C., 1968, p. 601.

M. C. Sauer, Jr., S. Arai and L. M. Dorfman, J. Chem.
Phys., 12, 708 (1965).

L. M. Dorfman, p. 56 in Ref. 14.

J. P. Keene, Rad. Res., 22, 1 (1964).

 

M. S. Matheson, p. 47 in Ref. 14.
J. H. Baxendale, Rad. Res. Sgpp1,, 1, 159 (1964).
K. H. Schmidt and W. L. Buck, Science, 151, 70 (1966).

R. R. Hentz, Farhataziz, D. J. Milner and M. J. Burton,
J. Chem. Phys., 11, 574 (1967).

J. Rabani, W. A. Mulac and M. S. Matheson, J. Phys. Chem.,
69. 55 (1965) .

J. Jortner, Rad. Res. Sgp2_,, 1, 24 (1964).

R. R. Dewald, Ph. D. Thesis, Michigan State University,
1965.

(a) L. H. Feldman, Ph. D. Thesis, Michigan State Univer—
sity, 1966; (b) L. H. Feldman, R. R. Dewald, and J. L.
Dye, p. 165 in Ref. 14. .

K. Keskey, S. Spleet and J. L. Dye, unpublished results.
M. A. Elfroymson in "Mathematical Methods for Digital
Computers," A. Ralston and Herbert S. Wilf, Eds., John
Wiley and Sons, Inc., 1964.

R. N. Jones, Can. J. Chem., 11, 5051 (1966).

W. E. Wentworth, J. Chem. Ed., 12, 96, 162 (1965).

W. C. Hamilton, "Statistics in Physical Science,"
Ronald Press Co., New York, N. Y., 19 , ch. 4.

Kuo, "Numerical Methods and Computers," Academic Press,
New York, N. Y., 1965.

R. R. Dewald, J. L. Dye, M. Eigen, L. DeMaeyer,
J. Chem. Phy§.,.22, 2588 (1965).

98.
99.

100.

101.

102.

105.

.104.
105.

122

R. Catterall, personal communication, 1968.

J. S. Waugh, Ed., "Advances in Magnetic Resonance,"
Vol. 1, Academic Press, New York, N. Y., 1965.

J. L. Dye, Weyl Colloqium II, Cornell University,
June 1969, Ithaca, New York.

R. R. Dewald and J. H. Roberts, J. Phys. Chem., 12,
4224 (1968).

 

S. Matalon, S. Golden and M. Ottolenghi, J. Phys. Chem.,
15. 5098 (1969) .

R. R. Dewald and J. H. Roberts, J. Phys. Chem., 12,
4224 (1968).

M. DeBacker, personal communication.

I. A. Taub, D. A. Harter, M. C. Sauer, Jr., and L. M.
Dorfman, J. Chem. Phys., 11, 979 (1964).

APPENDICES

APPENDIX A

A DETAILED DERIVATION OF THE RATE EQUATION FOR THE
MECHANISM DESCRIBED IN SECTION IV

Any assumptions made in this derivation will be so noted.
The derivation will be divided into two parts, one for the
rate eXpression for the case of the reaction of cesium with
water and the other for the reaction of rubidium or potassium
with water. Although the two cases differ in principle, it
will be seen that the general form of the rate expression in

each case is the same.

Case I: Cesium and water. The necessary equilibria are:

K

M -—l“ M + e (1A)
F
M JAR Ml + 6 (2A)
6
M + 0H _._3_x MOH (5A)
9
M +M —A_\ M2 (4A)
F

In the above equations, all Species are understood to be sol-
vated. For reasons discussed in Section IV, the slow step
in the reaction is assumed to be the bimolecular reaction

Of the reducing species with water, which may be represented

125

- ---——_—»——.£'-

 

124

by the following reaction.

M- + H20 §;%%+- [Intermediates] E§§Ee>H2 + M+ + OH- (5A)
kM . H O + —

M2 + H20 £1336» [Intermediates] EE§E9’H2 + 2M + 20H (6A)
kM . H O + -

M + H20 W [Intermediates] f—afié H2 + M + OH (7A)
k _

e- + H20 giggé-[Intermediates] Egggé-i-Hg + OH- (8A)

The concentration of total metal is
[MT] = [e’] + [M] + 2m”) + 2 [M2] (9A)

and the rate of hydrogen formation is

k

k .. _
9.4551 = - .1. iafltil = {kM_[M‘1+kMZ[M2J+2—”1(MJ+ -§——(e ]}(8201 (10A)

The concentrations of e-, M2 and M are obtained from inspec-

tion of the equilibria listed above, and are given by

5
[e‘l = (1%?) (14') (11A)
[M2] = K.[M*1 Mn: (12A)
and .
M - ( 51-)é' + 1. ' 2. 2 (15A)
(1- K2 [M1 [M1 vi

Since the total absorbance, A is measured as a function

TI

of time, it is defined as

AT = AM + Ae— + AM_ + AM2 (14A)

and for convenience let

A + Ae- = A (15A)

and

Ame + AM" = AD (16A)

Where AP is the absorbance due to the paramagnetic species

M and e- and AD is the absorbance due to the diamagnetic

Species M2 and M'. Equation 14A now becomes
A = A + A (17A)

Expressing the total absorbance in terms of the extinc-

tion coefficients and concentrations of the species gives
= " + + — +
AT Ee-[e ] €M[M] em-[M J €M2[M2] (18A)

and substituting the expression for [M] and [M2] into Equation

18A yields,

AT = tee- + eMIM+17:/K2 )[e'] + (eM-+eM2K.[M+ij__ )[M‘] (19A)

Identification of terms in Equation 19A with those in Equation

17A above shows that

qle‘] (20A)

AP ( 6e. + €M[M+]v_i_/K2 He']

and

A6 = (eM- + eM2K4[M+Jv: } [M'] = r [14'] (21A)

where q and r are constants at fixed values of [M+] and

ionic strength and have obvious definitions. The time

126

derivatives of A and A are

P D
dA _
P = d|e |

'5?- q dt (22A)
and

dAD _ d [M']

dt r dt (25A)
subject to the condition that

LAT = 93-F— + in (2..)

dt dt dt

the

Note that in taking the time derivatives of AP and AD,
time derivatives of q and r are assumed to be zero. Inspec-
tion of the definitions of q and r show that the quantity
Qé%:l. is taken to be zero. Substitution of the values of
[e‘] and [M’] from Equations 20A and 21A into Equation 11A
gives a relationship between AP and AD, which after simplifi—

cation is

A2 (25A)

AD = K1K2q2 P

+
r[M 17:_ :}
The derivation from this point on is concerned with
deriving an eXplicit expression for the decay of the total

absorbance with time.

The rate of disappearance of total metal is

d[M1] = d[e‘] d[M] d[M’] 6mg]
dt dt + dt + 2 dt + 2 dt (26A)

Substitution of the eXpressions for gé%21-and Qé§l .

127

obtained from differentiation of Equations 11A, 12A and 15A,
into Equation 26A gives

dd»: = [1+[M+]7_-21/K2} 413.111 + 2 (1+K4[M+17:) d_%l%l (27A)

Upon substitution of the eXpressions for §é%:l and Qé%:l

from Equations 22A and 25A, Equation 27A becomes

 

 

d[MI] =E+IM+171fl<2 + 4[M+]'Y§-_(1+K4[M+17§)AP} 9113. (28A)
dt ( q K1K2q2 dt

Now, the rate of disappearance of total metal may also

be written
.. w = k- [2‘] + k' [M] + 2k' [M'] + 2k' [M ] (10A)
t e‘ M - M2 2
where for convenience
k}; = kX [H20]

Substitution of the expressions for [M] and [M2] (Equations

11A, 12A, 15A) into Equation 10A yields

— 93%11 = {ké— + kfilMJ'Jvi/Kal [e‘] + Zik'-+ 135,qu. (Hui) [M’]

(29A)
which upon substitution of the expressions for [e-] and

[M-] (Equations 20A and 21A ) becomes

 

d[Mg:] = _ { (ké- + kfi[M+]7_.2t/K2) AP + 2(kfi-+kaZK. [14+])? AD}
dt —
q r

(50A)

is obtained by equating 28A

[591

The expression for

9L}?

t

and 50A and solving for . The result, after

 

128

simplification, is

 

 

 

 

 

(k'-+ '[M+]y2/k ) (k'_ + k' K [M+] 2)
dA e kM i' 2 A + 2 M M2 4 yi’ A
_ __E.= q 1p r D
at 1 + Whit/Kg Mn: (1 + K4IM+Jvi) (51A)
q K1K2q

The time derivative of Equation 25A is

+ 2
2 AP r[M ]7$: dAP

legq2 dt

 

dt

dt—' A (52A)

Substitution of the eXpression for.%%§ from Equation 51A

into Equation 52A gives the expression for , which after

dt

simplification is

+ 2 . . + 2 2 + 2 . .
dAD 2r[M in_ (ke_+kM[M in. 2)AP + 4[M inflk _+kM2K4

 

 

 

 

 

' dt — K1K2q3 + 2
KiKaq2 2
+ 2/ + 2 + 2
1 + [M ]7+ K2 4[M JVicl- + K4 [M lyi) A
_. + 2* P
q K1K2q
(55A)
Recalling that
dA dA dAD
__E. = ._42 .___
dt dt + dt (24A)
dA
and using the expression for dt—' and HEB. derived above,

one form of the expression for the rate of decay of the
total absorbance is, after simplification,

A A
-.E§1.= {2r(ké_+kfi[m+]7:/kg)xfi + 4q(kfi_+kfi2K4[M+]7§)}(AD+ 220

dt

 

A
r X11 (1+[M+]y:/K2) + 4q(1+K4[M+]7__2t)

D (54A)

129

Equations 51A and 55A can be further simplified by using
the three assumptions discussed in Section IV. These assump-
tions are:

(i) The rate of reaction of e with water is assumed to
be approximately equal to that of M_with water.
Similarly the rate of reaction of M with water is
assumed to be approximately equal to that of M2 with
water. The results of these assumptions are

ke‘ RM

and

m

kM kMg

(ii) The ion pair association constants K2 and K4 are
assumed to be approximately equal, so that

K2 “=’ 1/K4
(iii) The extinction coefficients of the various species

are assumed to be related by the stoichiometries
of the species, thus

The simplification gives

:‘in = 2ké_ AD + 1:151- AD2/AP . dAP .. kg- AP + kb'r AD/Z
dt

1 + 2 AD/AP dt 1 + 2 AD/AP
(55A)
These coupled differential equations were used to fit

the cesium data subject to Equation 17A by a non-linear

least squares procedure.

150

Case II: As discussed in Section IV, when Equation 55A
was used to attempt fitting the cesium data, it was apparent
that a better fit of the data could be obtained using only
the three parameters kfi_, A: and Ag. This corresponds to
the case where there is no direct reaction of e- or M with
water (i.e., ké_ = hi = O). The derivation of the rate
equation for this case is the same as that for Case I but

with ké- = kfi = O. The resulting differential equations now

have the form

932 '_ AS/AP . dAP _ kn'r AID/2
dt

1 + 2 AD/AP dt 1 + 2 AD/AP

 

(56A)
Case III: gubidium (or potassium) with water. This
is the case of the reaction of metal solutions which possess
an intermediate R-band in addition to the IR-band. This fact
necessitates the inclusion of one additional equilibrium.

This equilibrium has the form

R 154- IR (57A)
.1—

Since experimental evidence points to the fact that the
R Species is a two electron Species (see Sections I and IV),
it is assumed to be in direct equilibrium with the two elec—

tron "aggregate" Species of the IR-band. That is

R 355—3- M- (or M2) (58A)
V.—

30 that

r = __LIM' (59A)

The following discussion will assume that the R species
is in direct equilibrium with M— although the derivation is
the same if the R Species is in equilibrium with M2.

The eXpression for the total absorbance now becomes

= A
AT P + AD + AR (40A)

where Ap and AD have the same meanings as before and AR is

the absorbance due to the R Species. For convenience let

AD + AR = A5 (41A)
So that

A = A + A' (42A)
also

r ' [M' 1 (45A)

where r' has the definition

6 G
R + 2 R
r r + —- EM 6M2K4[M 17' K5 (44A)

The eXpression for the rate of disappearance of total

metal is
_ W = I — I I I - I
dt 2 kM_[M ] + 2 kM2[M2] + 2kR[R] + ke_[e ] + kM[M]
(45A)
and also
dmm] = 2d[M-] + 2d[Mg] + 2d[R] + d[e_] + d[M] (46A)
dt dt dt dt dt dt

152

From this point on, the derivation is algebraically
equivalent to that for Case I. The final exPression for the
rate of decay of the total.absorbance is similar in form
to that for Case I. It is

+ 2 I I I
dAT={ EB+ku {1 +K‘IM W-'t+kR/k1~a"K5 AP+§AD
M-

_ , + 2
dt e AD 1+K4[M in+1/K5 ,. AP
1 + ——
2A6

 

(47A)
For the case that ké- = kfi = O, the above equation has

the form

_ 522 = {13'1— [1 + “If”: + kit/1‘13““ } AP + 2‘ A6 (48A)

dt + 2 A
1 + K4IM Hi + 1/K5 1 + ——P

21%

APPENDIX B

DESCRIPTION OF COMPUTER PROGRAM FOR ANALYZING DATA

The computer program used to analyze data in this re-
search was designed primarily to handle kinetic data punched
on IBM cards using a Varian C-1024 Time Averaging Computer
(CAT). However, the program was written with enough flexi-
bility to accept manually punched kinetic data of the
appropriate format.

The principle advantage of this program is its ability
to test a number of possible mechanisms. The user has the
option of comparing any kinetic mechanism to any set of
kinetic data. The best least squares fit of the data of the
mechanism can be obtained provided that the necessary infor-
mation about the mechanism has been supplied to the program.

A block diagram of the general sequence of operation of
the Program Kenanal is given in Figure 51. A description of
the necessary subroutines and the function of each is given

at the end of this Appendix.

155

154

 

Reads eXperimental data from CAT and
organizational data SUpplied by user.

 

 

 

 

 

 

Optional: Corrects absorbance data by
least squares fit of the absorbance of
the calibrated neutral density filters.

 

 

 

 

 

Spike rejection: Fits polynomial to
individual spectra and rejects signals
which are more than four standard deviq
ations from the line.

 

 

 

 

 

 

Optional: Smooths experimental data
to Speed convergence of fitting func-
tions. This is done using two passes
of a symmetric, five point smoothing

formula.

Fits experimental data to mechanism(s)
supplied by user and prints results of
each step of least squares procedure.

L

Output: Prints SXperimental data, re-
sults calculatedgfrom best fit of
eXperimental data to mechanism, sum of
squares of residuals and linearized
estimates of standard error

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Optional: Line printer graph of data
in form desired by user (i.e., Abs. vs.
time, log (Abs.) vs. time, etc.).

Figure 51. Operational block diagram of program KENANAL.

 

 

 

 

 

155

The following is a functional description of the sub-

routines used with Program KENANAL.

KENANAL

This is the main program from which all of the sub-
routines are called. The principal function of the main pro-
gram is the reading and organization of the data necessary

for the subroutines.

ABSCOR
This is a subroutine for calibration of the neutral
density filter data. A polynomial fit of the neutral density

filter is performed. This polynomial has the form:

74%;: 2 ) = f (Abs .)

obs.
where (Abs’)obs. is the absorbance read from CAT and Abs. is
the calibrated absorbance of the neutral density filter.
This polynomial is then used later in the program to correct

the eXperimental absorbances. (The use of this absorbance

correction is Optional.)

MEKANISM

This subroutine contains the information about the
mechanism or mechanisms to be used in analyzing the kinetic
data. At present, the program can be eXpanded to analyze
Up to twenty-five different mechanisms for a given set of

experimental data. A control card supplied by the user

156

selects the mechanisms to be used. Also contained in
MEKANISM are the initial values of the parameters used in
fitting a particular mechanism to a set of data. Mechanisms

may be added by the user as needed.

MULTREG

This is a subroutine which performs linear multiple
regression analysis (92). It can only be used when the
equation is linear in the adjustable parameters. This sub-

routine was programmed by John Bartelt.

CURVEFIT

This is a non-linear least squares subroutine which will
fit an equation to a set of experimental data. This routine
was written by Vince Nicely, using the ideas found in papers
by Jones (95) and wentworth (94). This subroutine also calcu-
lates the relevant statistics for estimating the goodness of
the fit of given equation to a set of experimental data.
The basis for the statistics used in this subroutine can be
found in Hamilton (95). To use this subroutine, the user

must also supply subroutines FN and SIMUL5.

SIMUL5
This is a subroutine which inverts matrices using the

Gauss elimination method. It was written by Duane Knirk.

FN

This subroutine contains the functional form of the

equations to be used by CURVEFIT for least squares analysis.

157

RUNGE

This subroutine performs Runge-Kutta integrations and
is necessary only when the rate equations cannot be inte-
grated analytically. This subroutine is essentially that

described by Kuo (96).

APPENDIX C

OBSERVATION OF PYRAZINE ANION IN DECOMPOSED
RUBIDIUM~ETHYLENEDIAMINE SOLUTIONS

One interesting but annoying eXperiment was inadver-
tently performed during the course of this work. In several
attempts to prepare solutions of rubidium in ethylenediamine,
a competitive reaction was noted. As the solvent was thawed
and allowed to come into contact with the rubidium metal, a
purple color was observed instead of the usual blue color.

In one of the three observations of this phenomenon, the
purple color disappeared or was obscured by the formation of
the blue solution. However, when this blue solution was
mixed with ethylenediamine in the stopped-flow system, using
the rapid scanning monochromator, a fast decay of the 8901un
band resulted and a purple solution formed. This purple
solution had an optical absorption in the visible at 520 nm.
The absorbance at the maximum grew from 0.2 to 0.85 over a
period of twenty-five minutes.

In two other attempted solution preparations using
rubidium metal, only a transient blue color was observed in
the solution, which was not stabilized by further dissolution

of the metal. The resulting solution had a deep purple color.

158

159

A small amount of this purple solution was poured, in vacuo,
into an ESR tube and the X-band EPR Spectrum of the solution
was examined using a Varian V4500 EPR Spectrometer. The
solution was found to be paramagnetic. Its EPR Spectrum is
shown in Figure 52. This Spectrum yields splitting values
of 2.6 and 6.9 gauss. An Optical Spectrum was taken on a
Cary 14 spectrOphotometer and one peak was observed at 525
nmJ

It was suggested that the EPR Spectrum resembled that
of an aromatic negative ion such as anthracene or naphthalene
negative ion (98), but the splitting values were not in
agreement. A search of the literature, revealed that the

spectrum agreed well with that observed for pyrazine negative

[:23 ’

The two splitting values given in the literature for the

ion,

negative ion are 2.66 and 7.1 gauss (99). No data on the
Optical Spectrum of the pyrazine negative ion were avail-
able in the literature.

The vapor above the purple solution was found to consist
of two major components. This was determined by vapor phase
chromatography, using an Aerograph Model A-90-P gas chromato-
graph. A five foot column, packed with 15%‘Tetraethylene-

pentamine and 5%‘THEED (Tetra-hydroxy-ethyl ethylenediamine)

140

.mcofluoaom mcflewflpmcmawsumIESflOwnsu
Ommomaoomo ca Omauom Sodom mcflumumm msu mo Esuuommm mmm .Nm wusmflm

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

141

was used for this determination. The two components were
identified as ammonia and ethylenediamine. It is likely
that the reaction by which the pyrazine is formed has ammonia
as one of its products.

The exact mechanism for the formation of pyrazine is
not clear although it probably results from ring condensation
of 2 Species having the carbon skeleton of ethylenediamine.
The first step in the overall process probably involves the

formation of an<X-free radical of the solvent,
NH2 - CH2 - CH - NH2

The actual ring condensation, mentioned above, also would
produce ammonia. After the pyrazine is formed, it then at—
N .—
- r /
taches an electron as e801 + EN] —->- E D to
N/’ ‘\N

form the ammonia which was identified as a product. The
mechanism of this reaction bears further investigation since
it seems to be important to the chemistry of metal-amine

solutions.

CHIGQN STATE UNIV. LIBRRR

I | 2III IIIIIIIIIIII III IleIlIIL 0M.