Electrolytic conductance in dipolar aprotic and mixed solvent systems

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Electrolytic conductance in dipolar aprotic and mixed solvent systems
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xv, 184 leaves : ill. ; 28 cm.
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Klein, Stuart David, 1954-
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Subjects / Keywords:
Conductometric analysis   ( lcsh )
Electrolytes -- Conductivity   ( lcsh )
Electrolyte solutions   ( lcsh )
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bibliography   ( marcgt )
theses   ( marcgt )
non-fiction   ( marcgt )

Notes

Thesis:
Thesis (Ph. D.)--University of Florida, 1980.
Bibliography:
Includes bibliographical references (leaves 176-182).
Statement of Responsibility:
by Stuart David Klein.
General Note:
Typescript.
General Note:
Vita.

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University of Florida
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Full Text

















ELECTROLYTIC CONDUCTANCE IN DIPOLAR
APROTIC AND MIXED SOLVENT SYSTEMS







BY

STUART DAVID KLEIN


A DISSERTATION PEESE:iTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA IN PARTIAL
FULFILLMENT OF THE REQUREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY



UNIVERSITY OF FLORIDA


1980













This dissertation is dedicated to my parents, who

made it all possible.













ACKNOWLEDGMENTS


I would like to express my deepest appreciation and

gratitude to my advisor, Dr. Roger G. Bates. No matter

what the question, no matter what the problem, he was always

there to help; without his great aid and understanding, this

research project would not have been possible.

I would also like to express my appreciation to two

distinguished visiting scientists, who gave unstintingly of

their time and energy in solving a number of problems that

arose during the course of this study: Dr. Roberto

Fernandez-Prini and Dr. Lal Mukherjee. Thanks are also due

the members of my committee, who somehow always had time to

answer a question or discuss a matter of deep philosophic

significance. Thanks as well to Dr. John Dorsey, who

performed a number of important LC analyses, and to Dr. Roy
13
King, for running the C NMR spectra.

I would also like to acknowledge the aid that I received

from the staff of the departmental electronics shop: They

kept me in business despite a large amount of balky equip-

ment. Thanks as well to the department glassblower, Mr. Rudy

Strohschein, who stood ready to repair the results of

fumble-fingered haste.


iii







Finally, special thanks to all the members of our

research group, past and present, who have aided and assisted

me during the course of this study beyond measure. And,

my thanks to my friends and associates in the department,

who have made my stay here so enjoyable. Thanks as well

to Mrs. Jeanne B. Karably, who typed the final draft of this

dissertation, and Mr. Larry Ruiz, for drafting the figures

appearing herein.

This work was supported in part by the National

Science Foundation under Grant CHE76 24556.
















TABLE OF CONTENTS


ACKNOWLEDGMENTS

LIST OF TABLES

LIST OF FIGURES

KEY TO SYMBOLS

ABSTRACT


Page

. iii

. vii

. .viii

. xi

. .xiii


Chapter

I INTRODUCTION . .

II THEORY . .

General Background .

Measurement of Conductance

Conductivity Equations .

III EXPERIMENTAL . .

Materials . .

Solvents ...

Reagents .

Equipment . .

IV DATA ACQUISITION AND TREATMENT

Experimental Technique .

Preliminary Data Treatment

Data Processing .


1




3



. 12

. 21

. 21

. 21

.. 22

. 32

. 46

. 46


. 52

. 55








V RESULTS . . 61

VI DISCUSSION . . .66

Solvent Properties .. . 66

General .. . 66

Sulfolane System ... 68

NM2Py System . 77

Conductance Curves . 87

Ion Size Parameter . .105

General . .105

Bjerrum's Distance .. ... ..106

Choice of Conductance Equation ..109

2-Methoxyethanol-Water System .. ..112

General . . .112

Shedlovsky-Kay Extrapolation .114

Sulfolane-Water Solvent System .117

General . . .117

Pure Sulfolane . .126

NM2Py-Water Solvent System ... 134

VII CONCLUSIONS . . .. 144

APPENDIX A CONDUCTANCE DATA.. ....... .. .150

APPENDIX B COMPUTER PROGRAMS . .. .165

REFERENCES . . .176

BIOGRAPHICAL SKETCH .. .183














LIST OF TABLES


Table Page

I Calculated conductance parameters for HC1
in sulfolane-water solvents at 25, 30, and
400C . . 62

II Calculated conductance parameters for HC1
in NM2Py-water solvents at 250C 64

III Calculated conductance parameters for
electrolytes in 80 W% 2-methoxyethanol-water 64

IV Calculated conductance parameters for
Tris-HCl in water . 65

V Physical properties of sulfolane-water
solvents . . 68

VI Physical properties of M 2Py-water solvents
at 25oC . . 78

VII Comparison of conductance parameters generated
by full Pitts (PITTSEQN) and expanded
equations (EXPEQNS) programs 110

VIII Calculated conductance parameters for the
80 W MetOH-H20 solvent system, utilizing the
variation in a value method .. 112


vii













LIST OF FIGURES


Figure Page

1. Wheatstone's Bridge . 7

2. Jones--Joseph Conductivity Bridge 7

3. Circuit equivalent to conductance cell 9

4. Infrared spectrogram of sulfolane and
sulfolane-HCl . . .27

5. 13C NMR spectrogram of sulfolane 29

6a. Chromatogram of pure sulfolane . 31

6b. Chromatogram of sulfolane-HC . 31

7. Janz-McIntyre Conductance Bridge 34

8. Conductance cell . .37

9. Filler cap and weight buret ..40

10. Cross sectional representation of the constant
temperature bath and its associated components. 45

lla. A plot of the density of the sulfolane-water
solvents vs. the mole fraction of the sulfolane
contained therein at various temperatures.. .. 71

11b. A plot of the excess density of the sulfolane
-water solvents vs. the mole fraction of the
sulfolane contained therein at various
temperatures .. . 71

12a. A plot of the dielectric constant of the
sulfolane-water solvents vs. the mole fraction
of sulfolane contained therein at various
temperatures ..... .. . 74


viii










12b. A plot of the excess dielectric constant
of the sulfolane-water solvents vs. the mole
fraction of sulfolane contained therein at
various temperatures .. 74

13a. A plot of the viscosity of the sulfolane
-water solvents vs. the mole fraction of the
sulfolane contained therein at various
temperatures. .. . 76

13b. A plot of the excess viscosity of the sulfolane
-water solvents vs. the mole fraction of the
sulfolane contained therein at various
temperatures .. . 76

14. Structures of sulfolane and NM2Py .. 78

15a. A plot of the density of the NM2Py-water
solvents vs. the mole fraction of NM2Py
contained therein at 250C . 80

15b. A plot of the excess density of the NM2Py
-water solvents vs. the mole fraction of
NM2Py contained therein at 25C .. 80

16a. A plot of the viscosity of the NM2Py-water
solvents vs. the mole fraction of NM2Py
contained therein at 250C .. 83

16b. A plot of the excess viscosity of the NM2Py
-water solvents vs. the mole fraction of
NM2Py contained therein at 25C .. ... 83

17a. A plot of the dielectric constant of the
NM2Py-water solvents vs. the mole fraction of
NM2Py contained therein at 25C 85

17b. A plot of the excess dielectric constant of
the NM2Py-water solvents vs. the mole fraction
of NM2Py contained therein at 250C .. .85

18. An example of Type I conductimetric behavior.
A plot of the equivalent conductance vs. the
square root of the concentration for KC1 in
water at 250C . .. 89

19. An example of Type II conductimetric behavior.
A plot of the equivalent conductance vs. the
square root of the concentration for HC1 in
25 M% sulfolane-water at 300C .... .. .92


Figure


Page







20. An example of Type III conductimetric behavior.
A plot of the equivalent conductance vs. the
square root of the concentration for HC1 in
50 M% sulfolane-water at 300C 94

21. An example of conductimetric behavior
intermediate to Types III and IV. A plot of
equivalent conductance vs. the square root of
concentration for HC1 in 75 M% sulfolane-water
at 300C . . 96

22. An example of Type IV conductimetric behavior.
A plot of the equivalent conductance vs. the
square root of the concentration for HC1 in
85 M% sulfolane-water at 400C . 99

23. An example of Type V conductimetric behavior.
A plot of the equivalent conductance vs. the
square root of the concentration for HC1 in
100 M% sulfolane at 400C ....... 101

24. An example of Type V conductimetric behavior.
A plot of the equivalent conductance vs. the
square root of the concentration for HC1 in
100 M% sulfolane at 300C ..104

25. A plot of the limiting equivalent conductance
of HC1 vs. the mole fraction of sulfolane
in the solvent at various temperatures .. 119

26. The proton jump mechanism ..120

27. A plot of the pKd (= log Ka) of HC1 vs. the
mole fraction of sulfolane in the solvent
at various temperatures . 123

28. A plot of -log (equivalent conductance) vs.
-log (concentration) for HC1 in sulfolane
at 300C and 400C, after the method of Sellers
et al.110 . . 129

29. A plot of the limiting equivalent conductance
of HC1 vs. the mole fraction of NM2Py in the
solvent at 250C ..... .... 137

30. A plot of the pKd (= log Ka) of HCI vs. the
mole fraction of NM2Py in the solvent at
250C . . ... 140













KEY TO SYMBOLS



a Distance of closest approach of ions
A Coefficient of Kohlrausch conductance relation
A Pitts conductance term
A Debye-Hickel parameter
2 2
b z e /ackT
B Debye-Hiickel parameter
B Pitts conductance term
c Concentration in mol L- (M)
C Velocity of light
C Capacitance
e Protonic charge
E Expanded conductance equation parameter
f, Mean ionic activity coefficient on mole fraction scale
F Force acting on ion
G Pitts conductance term
H Pitts conductance term
I Ionic strength
J1 Expanded conductance equation parameter
J2 Expanded conductance equation parameter
k Boltzmann's constant
K Association constant
a
Kd Dissociation constant
M Molecular weight
n Number of points
N Avogadro's number
q Bjerrum's distance (z2 e 2/2kT)
R Resistance (absolute Q)
S Coefficient of Debye-HUckel-Onsager limiting law
S1 Pitts conductance term

t Transport number
T Absolute temperature
T1 Pitts conductance term
v Ionic velocity
X Mole fraction
y Ka
y, Mean ionic activity coefficient on molar scale
z Charge on ion







a Degree of dissociation
a Relaxation coefficient of D-H-O limiting law
0 Electrophoretic coefficient of D-H-O limiting law
E Dielectric constant
n Viscosity (Poise)
6 Cell constant
K Specific conductance
K (8rNe2I/1OOOEkT)
X Ionic conductance
X Limiting ionic conductance
A Equivalent (or molar) conductance
A0 Limiting equivalent conductance
A. Ionic equivalent conductance
1
v Frequency
p Density
a Standard deviation
a Radial frequency (27v)


xii













Abstract of Dissertation Presented to the
Graduate Council of the University of Florida
in Partial Fulfillment of the Requirements
for the Degree of Doctor of Philosophy



ELECTROLYTIC CONDUCTANCE IN DIPOLAR
APROTIC AND MIXED SOLVENT SYSTEMS

By

Stuart David Klein

December, 1980

Chairman: Roger G. Bates
Major Department: Chemistry

There has been much interest in the study of the

properties of electrolytes in dipolar aprotic solvents. Two

such solvents were chosen for this study: sulfolane, and

1-methyl-2-pyrrolidinone (NM2Py). The electrolyte chosen for

this study was hydrogen chloride (HC1), a stong electrolyte

in water. The conductimetric behavior of HC1 was studied

in sulfolane and sulfolane-water solvents at 25, 30, and

400C, and in NPI 2Py and NM2Py-water solvents at 250C. A

study was made of the conductimetric behavior of sodium

chloride (NaC1), sodium acetate (NaAc), tris(hydroxy-

methyl aminomethane hydrochloride (Tris.HCl), acetic acid

(HAc), and HC1 in the mixed solvent containing 80 weight-%

2-methoxyethanol and 20 weight-% water (80 VW7 MetOH-H20).


xiii







Conductances were measured with fill cells of the Kraus

type, in conjunction with a transformer bridge based on the

design of Janz and McIntyre. Measurements were made at

2.5, 5.0, and 10.0 kHz and extrapolated to obtain the true

ohmic resistance by the method of Hoover. The conductance

data were analyzed with the full Pitts equation, setting the

ion size parameter equal to the Bjerrum critical distance.

Analyses were also made with log-log plots and the

Shedlovsky-Kay extrapolation. A comparison of the full and

expanded conductance equations was also made.

The study of the sulfolane solvent systems showed

increasing ion association and decreasing limiting equi-

valent conductance with increasing sulfolane content. In

pure sulfolane, HC1 was found to exist primarily in an

associated form, with evidence of homoconjugation with

chloride. There was evidence of a change in the dis-

sociation process for HC1 in pure sulfolane with increasing

temperature.

The study of HC1 in the NM2Py solvent systems showed

a sharp decrease in limiting equivalent conductance with

increasing NM2Py content, coupled with a gradual increase

in ion association. As opposed to sulfolane, NM2Py gave

evidence of being able to solvate the proton. For both

sulfolane and NM2Py, the electrostatic models of ion

association were generally unable to predict the amount of

association that was found.


xiv







Both of the dipolar aprotic solvents studied gave

evidence of disrupting the water structure, with sulfolane

causing a decrease in the over-all structuring of the

solvent. The NM2Py was found to cause an increase in the

structuring of the solvent, with evidence of the formation

of an associated species of the form NM2Py.2H20.

In the study of the 80 W% MetOH-H20, all electrolytes

studied, except HAc, were found to be slightly associated.

The conductance of Tris.HCl in water was studied, and a

comparison between the two systems was made. Acetic acid

was found to exist in a primarily associated form, with the

dissociation constant comparable to that found in other

such alcohol-water solvents.


xv













CHAPTER I

INTRODUCTION



The last two decades have seen a growing interest in

that class of solvents characterized as being both dipolar

and aprotic. Some of these solvents, such as acetonitrile,
1-6
have been extensively studied;- others have been less well

characterized. One such is sulfolane (tetrahydrothiophene-

1-1-dioxide, tetramethylene sulfone). One reason for this

lack of research may be that sulfolane is a solid at room

temperature, requiring measurements at temperatures of

300C or above. Yet despite this drawback, sulfolane remains
7-8
an excellent solvent. Possessing a moderately high
9
dielectric constant, sulfolane would be expected to reduce

the ion-ion interactions found in solvents with smaller

dielectric constants. With its high dipole moment0 it

would be expected to increase ion-dipole interactions. For

both these reasons, sulfolane is expected to have a moderate
11-12
solvating power. Sulfolane has been characterized as

having extremely weak acid-base properties, facilitating the

study of strong acids and bases.

Another of the lesser dipolar aprotic solvents is

l-methyl-2-pyrrolidinone. For the same reasons cited for

sulfolane it is expected to have moderate solvating power;

-1-





-2-


8
it is, however, more basic than sulfolane, and has been

shown to enter into extensive hydrogen bonding with water,13
14
something which is not true of sulfolane. It would be of

interest then to compare the behavior of electrolytes in

these two dipolar aprotic solvents.

A far more common class of solvents is that considered

to be protic, the most common of these being water. One of

the lesser studied of this class of solvents is the mixed

solvent consisting of 80 weight percent 2-methoxyethanol

(methyl cellosolve) and 20 weight percent water. First

studied by Simon15 in the middle fifties, a number of

studies have since been published regarding this solvent,618

but questions about the behavior of electrolytes within it
17
remain.
19
Conductance studies have been shown to be an excellent

tool for characterizing the behavior of electrolyte solu-
20
tions, due in part to the great accuracy attainable. It

is the major tool employed in these studies.













CHAPTER II

THEORY



General Background

The resistance of a uniform cross section of a

homogeneous substance, with length 1 and area A is given

by the equation:

1
R A (1)

where K is a constant called the specific conductance

and is characteristic of the material under study. If a

conductivity cell had a uniform cross sectional area and

electrode separation,then by measuring the resistance of a

solution we could obtain the specific conductance. Since

cell geometry varies with manufacture, however, it becomes

necessary to introduce a parameter called the cell constant.

This will have units of length divided by area and can be

determined by measuring the resistance of a solution whose

specific conductance is known. The relationship between

specific conductance and cell constant is:

K = (2)

Since the conduction of electricity by an electrolyte

solution depends on ions as the charge carriers, the

specific conductance will vary with the concentration of ions.








By dividing the specific conductance by the concentration

we obtain a conductance per mole, useful for making compar-

isons between solutions of differing concentrations. This

is the molar conductance, also known as the equivalent

conductance. It is defined by the equation:

A 000K 1000 (3
A (3)
c Rc

where c is the molar concentration. The resistance is

usually corrected for the conductance due to the solvent:

1 1 1
1 (4)
RR R
m solv

where R is the measured resistance and Rsolv is the
m solv
solvent resistance. In this study the terms equivalent

conductance and molar conductance are used interchangeably,

since for a 1:1 electrolyte, such as is studied here,

equivalents per liter and moles per liter are identical.

It was in 1883 that Arrhenius, by studying the varying

conducting power of solutions came to the conclusion that

electrolytes could supply varying amounts of ions depending

on the electrolyte concentration. He concluded that as the

concentration tended toward zero (infinite dilution), the

degree of dissociation, a, tended toward unity. Noting that

at a fixed temperature A increased as concentration

decreased, he ascribed this to increasing dissociation. Thus

at infinite dilution, A would reach a maximum value, A,

which would correspond to the conductance for a totally

dissociated electrolyte, and the degree of dissociation





-5-


at any given concentration could be expressed as a ratio

of the molar conductance at the concentration to the molar

conductance at infinite dilution:


A
a (5)


From this, Ostwald later derived the famous dilution

law:

2 2
K ac Ac (6)
d (1 a) A(A A) ()


This was in accord with the Arrhenius proposition that

at low concentrations the molar conductance should vary in
21
a linear manner with the concentration.

However, Kohlrausch, a contemporary of Arrhenius,

had made some precise measurements of the conductance of

solutions at low concentrations, and he came to the conclu-
1 2
sion that A varied with c2 and followed the relation:2

0 1
A = A Ac' (7)

There were sets of data which conformed to one theory;

there were data sets which conformed to the other. This

seeming paradox held sway for many years.





-6-


Measurement of Conductance

Before proceeding further, a few words are in order

on how the conductance of a solution is measured. Such

measurements are extremely sensitive and require very care-

ful technique in order to insure accurate results. As
23
Shedlovsky has pointed out, the resistance measured for

a solution will change approximately 2% per oC; to have a

precision of 0.01% thus requires that the temperature be

regulated to 0.0050C or better. This is but one of several

factors that need to be considered in conductance measure-

ments.

When determining conductance one is actually measuring

the resistance of a solution. As with most precision

resistance measurements, some variant of Wheatstone's bridge

is usually used. A schematic diagram of such a bridge

appears in Figure 1. The circuit is such that, when the

detector registers a null (i.e., there is no current flowing

in the circuit) the following balance condition is met:

R R
c = S (8)
1 2

R1 and R2 are precision resistors whose values are known

(and preferably equal); thus at null, the cell resistance

is equal to the resistance set on the standard.

Such a bridge was designed primarily for direct current

measurements. However, if a direct current is applied to

an electrolyte solution there will be migration of ions to

the electrodes; this electrolysis will produce a change in
























Figure 1

Wheatstone' s Bridge


Figure 2

Jones-- Joseph Conductivity Bridge








the solution concentration and a concomitant change in

the resistance.

Initially, it was Kohlrausch who proposed to solve this

problem by the use of alternating current for resistance

measurements. This, however, introduces a problem of its own.

Given the parallel plate configuration of most conductance

cells, there will arise a capacitance due to the flow of

alternating current through the cell. This means that the

bridge must not only balance resistances, it must now balance

capacitances as well. As a result, modern bridges are

designed to balance impedance.

A great deal of the early work on bridge design and
20 24
conductance measurement was done by Shedlovsky,20 Parker,2

Jones and his students25,26,27,28,29 and others. Much of

this early work has been summarized elsewhere30 and will not

be covered in any great depth here. A typical bridge circuit
25
designed to measure the impedance of a conductance cell is

presented in Figure 2. In more recent times, Ives and his

coworkers have demonstrated31 the usefulness of the trans-

former bridge circuits found in commercial impedance

comparators. This study utilized just such a bridge,
32
designed by Janz and McIntyre. It will be described in

more detail in a later chapter.

When measuring resistance with such a bridge, a

dependence of resistance on the frequency of the alternating

current used is unavoidable. For precise measurements to

have any meaning, there must be some way to eliminate this








frequency dependence and obtain the true ohmic resistance.

A large amount of the frequency dependence has been found

to be caused by extraneous factors and can be removed by

proper cell design24,33 and the use of a proper thermo-

stating medium. 2

Platinization of the electrodes helps to reduce the

remaining frequency dependence greatly,34 and is of great

aid when measuring the conductance of concentrated solutions;

in dilute solutions, the large surface area of the platinum

black favors adsorption of the electrolyte under study.23

Consequently, in this study, shiny platinum electrodes were

used.

A conductance cell may be schematically represented as

shown in Figure 3:

R2

R1



C2


Figure 3
Circuit equivalent to conductance cell.

31
This circuit was proposed by Ives and his coworkers and

endorsed by Robinson and Stokes, who added the Warburg
34
impedance, -W-. In this circuit, R1 is the true ohmic

resistance of the cell, which is what we wish to determine.

This is independent of frequency over the limited range of

measurement (between 1 and 10 kHz). In series with R1




-10-


is the capacitance C1, due to the double layer. This is

also expected to be independent of frequency in the range

of frequencies used in this study. It is this capacitance

which in fact is responsible for transporting through the

double layer the current passing through RI; it has been

shown that a cell has a definite resistance with only a few

millivolts of potential applied, too small a potential to

cause electrolysis at the electrodes. There is, however, a

small amount of electrolysis which takes place, probably due

to discharge of solvent ions, and this is represented by

"faradaic leakage" in parallel to the double layer. It is

represented by resistance R2 and the Warburg impedance, both

of which are expected to vary with w-". Capacitance C2

is the capacitance due to the leads and connections, and in
34
cells such as were used in this study it is negligible.3
31
Ives has assumed a negligible Warburg impedance and

determined the frequency dependence of the measured

resistance to be of the form:

R
R = R1 + 2 (9)
1 + aw

where:

R 2 2
R1R22 C1
a R + R

and:


w = 2ir, v being the frequency.





-11-


35
Hoover has compared a number of models for bridge

balance conditions and has come to the conclusion the model

proposed by Ives is of sufficient accuracy to use for the

extrapolation to remove the frequency dependence and obtain

the true ohmic resistance. A more detailed discussion of

this frequency extrapolation method appears in a later

chapter.

Over the years there have been a large number of cell

designs for the measurement of electrolytic conductance. For
36
the purposes of this study a cell of the Kraus design was

used. This type of cell helps to eliminate several sources

of error, including some sources of frequency dependence

in the measured resistance alluded to above. A discussion

of this style of cell appears in the experimental section

along with a photograph of the cell actually used.





-12-


Conductivity Equations

As mentioned previously, in the early days of

conductance studies there was something of a paradox. The

Ostwald dilution law, based on the Arrhenius theory of dis-

sociation, indicated a linear dependence of equivalent

conductance on concentration and therewere data to back it

up. Yet Kohlrausch showed a dependence, not on c but on

c2, and had data to confirm the variation. Kohlrausch had

also proposed his law of independent migration, which,

succinctly stated, says that the limiting conductance (the

conductance at infinite dilution) is equal to the sums of

the limiting conductances for the individual ions:

A = X + X_ (10)

there being no interaction between moving ions at infinite

dilution. Since it is unlikely that both ions will contri-

bute identically to the total conductance, the fraction

carried by one ion may be expressed by the transport number

0 0
tot


o +o
t (11)
+ A

The expression for the negative ion is identical, and thus

from Equation 10 one finds:

t + t= 1 (12)
+

The paradoxical problem continued to plague conduc-

tivity through the first several decades of this century.

In 1923, Debye and HUckel37 proposed their theoretical





-13-


treatment of interionic interactions, and this was further
33
applied to conductance studies in 1927 by Onsager. This

combined Debye-HUckel-Onsager theory was the first major

attempt to theoretically account for the variation of

conductance with concentration.

In an electrolyte solution placed under the influence

of an external electric field there are two major interionic

interactions: the electrophoretic effect and the relaxation
34 39
effect. These have been extensively discussed elsewhere3439

and thus will be dealt with in a more succinct manner here.

The electrophoretic effect arises from viscous drag.

An ion moving through a solution will tend to drag along

solvent molecules with it, both through frictional forces and

through having solvent molecules associated with the ion

(solvating the ion). Neighboring ions will thus experience

a net solvent flow, in the direction of their movement if

they are the same charge type as the central ion, and

against their motion if of opposite sign to the central ion.

Quite clearly, this effect will decrease as the concen-

tration of ions decreases, and will reach zero at infinite

dilution.
34)
It has been shown that the electrophoretic

increment to the velocity of the ion is given by the

equation:

n n-lk1 n-1
z(z k z k+)
z ( + :+)
v = A (13)
n=l a(z z+)





-14-


where n arises from Boltzmann distribution functions, k

is the force acting on the ion, and An is given by:


A _)n e n-ln (Ka) (14)
n n!67n -kT n

The function n (Ka) is given by:



4 (ca) = (Ka) 2( e Ka)nSn(Ka)
(15)
n-2 -nKr
S (Ka) = a-nr dr
n an-1 r

K in this case is not the specific conductance, but the

Debye-HUckel reciprocal radius of the ionic atmosphere, and

a is the distance of closest approach of the ions; K is

given by:

8 Ne2
K = (lOc0kT 2 (16)

with the remainder of the symbols having their usual

meanings.

The relaxation effect arises as follows. The ion

being studied is at the center of an atmosphere of spherical

distribution. If the central ion moves, the atmosphere

will move with it, but a little more slowly, As a result,

the ion feels a net restoring force in the direction

opposite to its motion, until the atmosphere has once again

assumed the spherical symmetry. If the field acting on the

ion is designated by X, then the relaxation field may be

denoted as AX. Initially, Debye and Hfckel examined the

relaxation field, but it was elaborated by Onsager. For





-15-


the 1:1 electrolytes we are concerned with in this study,

the expression derived by Onsager is:

22
AX z e q 7)
X 3EkT 1 + /q

where q is a function of charge z and ionic conductance

at infinite dilution A'. For a 1:1 electrolyte its value

is i. The velocity of the ion, corrected for the relaxation

effect becomes:

2
v. = v (1 + 12 q r (18)
vi 3EkT 1 + /q

The effective force acting on a moving ion must be
40
equal and opposite to the force of the external field4 and

may be expressed as:

-z.eX = F.i + F + F. (19)

vis
where F. is the viscous drag of the solvent on the moving

ion, F' is due to the electrophoretic effect, and F. is due

to the relaxation effect. It might be noted that at

infinite dilution F" and F. decrease to zero, and it is thus
J J
F which determines the limiting conductance, X..
ji j
Combining all of the above factors, Onsager derived

what has come to be known as the Debye-Hickel-Onsager

limiting law:

22 o 2
o 22 zAqK F
A = A o z e qK F (2z)K (20)
3ckT 1 + /q 67rnN

For a 1:1 electrolyte, this reduces to:

S= Sc (21)
A = A0 Sc (21)





-16-


where:

S = aA + 6

3
a = 82.0460 x 104 (22)
(eT) .

and:

3
S= 82.487 z1
n(ET)2

As can be seen, the final equation has the same form that

was empirically determined by Kohlrausch, the same depen-

dence on c2. But now, the constant S has a theoretical

basis.

Since the equation was first proposed by Onsager, there

have been numerous treatments devised. Most of them

concentrate on elaborating the terms for the relaxation

field, while the electrophoretic effect has also been
20;
modified. Shedlovsky2 proposed a form of the limiting law

suitable for extrapolation to determine Ao. Robinson and
41
Stokes41 did much the same but included a parameter to
42
reflect finite ion size. Shedlovsky and Kay devised4 an

extrapolation for very weak (i.e., highly associated)

electrolytes, based on an earlier treatment by Fuoss and

Shedlovsky.43

Today, there are two main equation systems for

analyzing conductance data. One is the result of many
44 45-47
successive treatments by Fuoss and his coworkers.445-47

The other is based on a theoretical treatment by Pitts. 50





-17-


Both theories are quite complex, with the main equations

containing several exponential integrals. Both have

been expanded51'52 to the same form:

1 15
A = A Sc2 + Ec log c + J1c J2cl5 (23)

In both terms, the constants S (the Onsager limiting law

slope) and E are identical. The terms J1 and J2 differ

depending on the theory used; it is these terms which contain

the so-called ion-size parameter. This will be discussed

in depth in the discussion chapter.
40
The equations, in the expanded format, are as follows:

22 2 2
ba 16.7099 x 104 z
ekT ET

K = 50.2916 z/
(ET)2

E = El A E2

2 6
E (Kab) = 2.94257 x 1012 z
1 24c (T)3

KabS z
E = b = 4.33244 x 107 z
2 T 2
16c2 n(ET)


J1 = 2E1A (ln( ) + A1) + 2E2 (A2 InC(a))
C C


J2 = a (4E^1 o3 + 2E24 5
C2

The delta functions are complex, and may be obtained in

Reference 40. Their values depend on the theory being used.

They are for the Pitts equation and the latest of the Fuoss





-18-


44
equations, that of Fuoss and Hsia, both of which have
52
been expanded by Fernandez-Prini and Prue. '

In recent years, there has been a great deal of

discussion as to which of the theories and its associated

equations best fits the experimental data available. What

is truly remarkable is that this has been going on for

better than a decade and a half and there is still no

conclusive proof that one theory is better than the other.

That being the case, the theory used for data analysis is

really serendipitous, depending on individual whim.

As will be mentioned in a following chapter, the

expanded equations given above are approximations only and

tend to break down at high concentrations (i.e., where Ka

becomes relatively large). For this reason, the data of

this study were analyzed with the full Pitts equation

described below.

The Pitts conductivity equation takes the general

form:

A = A A (( A + BcS1) + G/c ( + 1
(1 + y)(/2 + y) + y)
(24)
A/c__ H / T9
(1 + y)2 y) (1 + y)

where:

A = H(v- 1)

B = 3H2

SkTHN109
G = C2 is the velocity of light
IrnC2





-19-


2 2
H = z K
3 kT /c


S 9 10 + y(3/2 + 1) + 2y2
1 8(1 + y)2( + y)2


+ M e(2 + )y E.
16 ( + y)2( + y)

+ e(1 + 8)y
16 (1 + y)(/+ y)G y)) Ei


T 33 (3/e(" + 1)y
1 4(/2 + y) +8 7 + y

1 U
Ei(x) =f eu
X


Y
e
4(1 + y) Ei(Y)


((6 + 2)y)



((o + 1)y)


((f + l)y)- 2eYEi(y))


8 irNz e c
y = Ka, where K = (8LNz kT J




All other symbols have their usual meaning. Values for the

physical constants are taken from Reference 53.

This equation applied to dissociated electrolytes. To

make it applicable to associated electrolytes, concen-

trations (c) were replaced by ionic concentrations (ac),

where a is the degree of dissociation. Similarly, the

calculated equivalent conductance calculated by the program,

Ai, which is the conductance for a completely dissociated

electrolyte, was multiplied by the degree of dissociation

to get the equivalent conductance, according to equation 25:


A
a"=
SA.
1


(25)





-20-


The association constant, Ka, can be derived from the mass-

balance equation utilizing the degree of dissociation:

K = a (26)
a 2 2
a cy+

In equation 26, y is the mean activity coefficient on the

molar scale. For low ionic strength media such as were

studied, the activity coefficient can be calculated with

the Debye-Hickel law:

2Az2 v
2 1 + Baci
f2 10 Ba (27)

where A and B are the usual Debye-Hickel parameters:

1.8246 x 106
(ET) 1.5
(28)
S50.29 x 108
B T-- -5
(ET)2

This yields the activity coefficient on the mole fraction

scale. To obtain the coefficient on the molar scale

requires a conversion factor:


y2 ( -3 2 f+2 (29)
p + 10 c2M M
solvent solute

where:

M = molecular weight

p = density of solvent

The computer program, called "PITTSEQN," designed to

perform the calculations associated with the Pitts theory

is described in more detail in a following chapter.














CHAPTER III

EXPERIMENTAL



Materials

Solvents

Sulfolane was obtained from Eastman, a division of

the Eastman Kodak Company. The material obtained was of

a practical grade and was purified by a double distillation

at reduced pressure.52'54 The first distillation was at

2 torr pressure, stripping the boiling material with

nitrogen. The second distillation was at 0.5 torr, from

solid potassium hydroxide. The middle 75% was collected in

each case, and in the final distillation it came off at

104C. The product had a specific conductance of

4.09 x 108 S cm1.

1-Methyl-2-pyrrolidinone was obtained from Eastman,

and was reagent grade. It was purified by double distil-

lation at reduced pressure, both distillations being

conducted at 0.5 torr pressure. The second distillation was

from solid sodium hydroxide. The middle 75% was collected

in each case, and the final product had a specific
-7 --1
conductance of 3.64 x 10- S cm-

2-Methoxyethanol was obtained from Eastman, and was

reagent grade. It was purified by a single distillation at


-21-





-22-


atmospheric pressure. The middle 75% was collected.

When the 80 weight-% solvent was prepared, it was found
-7 -1
to have a specific conductance of 1.11 x 10 S cm

Conductivity water was prepared by the distillation of

water which had previously been treated by reverse osmosis

followed by passage through a deionizing system. The

specific conductance of this water was found to be in the

range on 7-9 x 10 S cm quite reasonable since no

effort was made to protect it from CO2 in the atmosphere.



Reagents

Potassium chloride (for determination of the cell

constants) was Mallinckrodt Analytical Reagent Grade,

purified by double recrystallization from conductivity

water. Tris base (tris(hydroxymethyl)aminomethane) was

obtained from Sigma Chemical Company and was their Trizma

Reagent Grade. It was purified by double recrystallization

from 70% methanol-water. Sodium acetate and sodium chloride

were Mallinckrodt Analytical Reagent Grade materials; they

were recrystallized from water. After recrystallization,

all salts were dried in vacuo at 750C overnight and were

stored in a desiccator which was charged with indicating

Drierite.

The glacial acetic acid used was Mallinckrodt Analytical

Reagent Grade and was purified by several fractional

freezing. The final fraction was stored in a desiccator

charged with indicating Drierite.




-23-


Solutions of hydrogen chloride were prepared by the

double distillation, at atmospheric pressure, of analytical

reagent grade hydrochloric acid, to obtain the constant

boiling acid-water azeotrope. The final concentration of

this azeotrope was determined by gravimetric determination

of chloride with silver nitrate; its composition was found
-3
to be 5.27335 x 10-3 mol HC1 per gram of solution.

Hydrogen chloride gas was prepared in two manners.

In the early portions of the study, it was prepared by

dropping redistilled hydrochloric acid onto reagent grade

phosphorus pentoxide. The resulting hydrogen chloride gas

was forced, by a stream of dry nitrogen, through a tower

of indicating silica gel, and into a flask containing the

solvent. In the latter portions of the study, the gas was

prepared by dropping reagent grade sulfuric acid onto

analytical reagent grade sodium chloride. The resulting

gas was passed into the solvent via the method described

above.

The concentrations of the acid solutions thus prepared

were determined as follows. A solution of analytical

reagent grade sodium hydroxide in water was prepared and was

titrated pH-metrically against NBS primary standard

potassium acid phthalate. This sodium hydroxide solution

was then used in the pH titration of the acid solution.

Approximately 0.5 g of acid solution was weighed into

a beaker containing about 100 ml of conductivity water.

After mixing, this was titrated with the sodium hydroxide





-24-


solution, using a microburet. In the titrations,

consistently sharp endpoints were noted.

The concentration of the solution of hydrogen chloride
-4
in sulfolane thus determined was 1.1155 x 10-4 mol HC1
-1
g soln- For the solution of hydrogen chloride in 1-
-4
methyl-2-pyrrolidinone, it was found to be 5.8359 x 10
-1
mol HC1 g soln 1. Upon adding hydrogen chloride gas to

sulfolane a color change was noticed. This intensified

with time, until a deep golden hue was attained. This

observation raised questions about the purity of the

sulfolane, and tests were carried out to determine its

purity.

At first, infrared spectroscopy was used. Figure 4

is the resulting spectrogram. Superimposed on it is a
55
reference spectrogram. Both the sulfolane solvent and the

sulfolane containing HC1 gave identical spectrograms, with

no evidence of a major impurity.
13
A second test was 1C nuclear magnetic resonance

spectroscopy. Figure 5 is the spectrogram obtained, with

the reference spectrogram superimposed.55 Again, there was

no noticeable trace of other material.

Finally, liquid chromatography was utilized in an

attempt to determine any trace impurities. Figure 6a shows

the chromatogram of the purified sulfolane; Figure 6b shows

the chromatogram of sulfolane containing hydrogen chloride.

Neither shows any impurity in sufficient quantity to affect




-25-


the results of this study. It was concluded that despite

the formation of the color, the sulfolane utilized for this

study was pure.

Acid solutions in mixed dipolar aprotic-water solvents

were prepared by one of two methods. For those solvents

with a large mole fraction of the nonaqueous component,

the reagent was prepared by dilution of the stock solution

of acid in the pure solvent. Water was added to bring the

solution to the proper solvent composition, and the

resulting solution was diluted to produce the working stock

solution.

For those solvents relatively rich in water, the

acid stock solution was prepared by adding the nonaqueous

component to redistilled hydrochloric acid to achieve the

proper solvent mix. This was then diluted to produce the

working stock solution.

All stock solutions for the conductance measurements

were prepared on a strictly weight basis.


































a)
r-i















S C


cS
r-I






0






0
')





-)





c0
i-l
(U r-
o
k
bJ3
*I l
f^






(d
+-
0H
0)





-27-











I

-C o




-- --- i -- ------
' \ S ...... [ I > ~ i l ..... 1 l llllll-














-
_- __' _____ ii -- : l i i I





. ..... Ig I T- -______











o il .-.. -- -- r : -- _-- _- i 7- -
1 .
_- I .. -





-. I- : I











































CH
(i
r--l
0
4-1





LO
rzl
tH



Cd



c(U o




,- -4
Pi kP







Z

U
CO
T-(




-29-


,,~~, .4, -.!^ ,-** ?^

9"" 3 "I'
;i C Jj "* 'J :
.: ^ '< ^ il'




= -. _
-- 1











ioo.



: I


:' 'l[l l l l .....I .... r :'-,





S I







IJ 0 : *V^'.5;^ J '.
9 I






33
Qfl fO: 9 .' o
i s5 ^ I !


a.! ao-- 'S -
3~~~ ~~~ & ''
-*s ~ ~ 1I I. .S
3!__________i L g :- g l- 1




















Figure 6a


Chromatogram of pure sulfolane
Reverse phase column




















Figure 6b

Chromatogram of sulfolane-HC1
Reverse phase column






-31-


....ft











Injection.. .20 L : :
-1 -
Flow Rate ....1 mL min -- -
Scale......... 0.04 AUFS__
Dilution ..... 25:1 H20:sulf. .-- :
Eluant........50/50 CH CN/HO. -
32 2 -



..........~--,- Z.. ~~..r_ ,:__ -~ f- .. :f ... .. .. i .. .. ...... .. .


----- I ----


A "-I-


_-- 4- 7~--


-- F---- -- -


7 ---- -
r.7 ,7-


- I-


'1


Injection.....20 pL
-1
Flow Rate..... 1 mL min
Scale.........0.01 AUFS
Dilution......20:1 H20:sulf.
Eluant ........ .50/50 CH3CN/II20


cir C,


--


7


'^-----f


------- Cr:
--- --- i


__ i I





-32-


Equipment

The major instrument used in this study was a conduc-

tance bridge, in general of a design suggested by Janz and
32
McIntyre.32 A schematic diagram of the bridge appears in

Figure 7. At the heart of the bridge is a General Radio

Type 1654-9002 impedance comparator. Originally designed

to measure impedance at 0.1, 1.0, 10.0 and 100.0 kHz,

the instrument was modified by General Radio to measure at

1.0, 2.5, 5.0, and 10.0 kHz. The instrument utilizes a

transformer bridge measurement circuit, with the trans-

former bridge of toroidal design. The secondary winding of

this transformer is center-tapped, and consists of two

identical wires, twisted together and wound on the torus.

The two halves of this secondary act as the ratio arms of
6
the bridge and are equal to within one part in 10 The

other two arms of the bridge consist of the unknown

impedance (the conductivity cell) and the standards.

The standards used in this instrument are a General

Radio Type 1433-F decade resistor and a General Radio Type

1412-BL decade capacitor connected in parallel to the decade

resistor. The resistor has seven decades of resistance,

with steps of 10 kQ down to steps of 0.01 0. The capacitor

has five decades of capacitance, ranging from steps of 0.1

pF down to steps of 1 pF. Using both of these standards, it

was possible to measure both the resistance of the test cell,

for conductivity, and the capacitance, for dielectric

constant measurements. For typical readings, the precision

of the standards is 0.01%.







































a)
bfl
a3

10








0
a) u




4 -
ad










In
bn C.)


0
bC u
*i-f
F^ (U
k-








a:
1-1





-34-


;-4
s
P3 k
4-,

Cd

U3





-35-


The null-point of the bridge was monitored with a

Keithley model 191 digital voltmeter. This permitted far

more accurate zeroing of the meter (0.001 volt) than

visual observation of the meter needle.

To eliminate the problem of irreproducible contact

resistances between the bridge circuit and the test cell,

and to obviate the necessity of making corrections for lead

resistances, the instrument was adapted to utilize a

four-lead measurement system. This is the same system
56a,b
utilized with four-lead platinum resistance thermometers56b

and requires two measurements with alternate sets of leads.

The mean of the two measurements effectively averages out

resistances inherent to the leads and the connections.

To further cut down on problems associated with

connection of the cell to the bridge, printed circuit boards

and edge connectors were used. Standard equipment with 15

contacts was used, allowing three contacts per lead, with

one contact between live connections as a spacer. The

multiplicity of contacts per lead insured good and

reproducible contact.

The conductance cells used in this study were of the
36
type designed by Daggett, Bair, and Kraus, and were

obtained from Beckman Instruments. The constants determined
-1
for the cells were 1.05393 and 0.120695 cm The cell

appears in Figure 8. The leads are held well separated to

help reduce the Parker effect.24'27 This effect is caused

by the electrical leads passing through the electrolyte

































Figure 8

Conductance cell





-38-


solution, and gives rise to a capacitative effect causing

a frequency dependence in the measured resistance.

Another source of error in conductance measurements

related to the measuring cell is the Soret effect. This
33
has been discussed in depth by Stokes.33 Briefly, this

effect is due to a slow thermal diffusion of the electrolyte

within the electrode compartment. The design of the flask-

type dilution cell used in this study, coupled with constant

stirring, minimizes this effect.

The electrodes of the cell were shiny platinum, with

a circular cross section. They were spot welded to

platinum wire, which in turn was welded to tungsten wire to

achieve a seal with the glass. Heavy gauge copper wire was

welded to the tungsten to form the cell leads, and the

copper wire was doubled at the top of the cell to produce

the four-lead measurement system.

With two cells in the temperature bath simultaneously,

held in close proximity to one another, any shaking could

result in mutual damage. For this reason, a special filler
57
cap was designed to facilitate additions to the cell

without shaking. The filler cap and its companion weight

buret appear in Figure 9. By adjusting the position of the

3-way stopcock, additions could be made, and then solution

forced up the fill-tube into the upper chamber. This

permitted the washing down of any splashes made during the

addition and facilitated solution mixing. Both the weight

buret and the filler cap were manufactured by the









































'X RY4

I
ixi"* QM

































Figure 9

Filler cap and weight buret







































* .* ....





-41-


departmental glassblower and utilize standard ground-glass

joint connections.

The constant-temperature bath utilized in this study

was constructed by the departmental machine shop out of

stainless steel, with all seams welded. It was insulated

with styrofoam and was supported by an aluminum box frame

mounted on a welded angle-iron cart. The bath was filled

with BP food-grade white oil, which further helped to
25
minimize the Parker effect mentioned previously. The oil

was circulated by two American Instrument Company 1.3 A

circulating pumps, to assure temperature uniformity

throughout the bath.

Temperature control was achieved with a Yellow

Springs Instrument Company model 72 proportional temperature

controller. The usual three-quarter turn potentiometer

used for regulation of fractions-of-a-degree was replaced

with a ten-turn potentiometer to provide far more precise

control of the temperature setting. The controller was

used with a YSI thermistor probe and was used to drive two

heaters. One was a standard 500-watt Vycor sheathed

immersion heater. The other was constructed of nichrome

heating wire wound around a plexiglas frame; it was placed

to take full advantage of the flow from the two circulating

pumps.

Immersed in the bath were a number of coils of copper

tubing. Through these coils was circulated water from an

external bath. This bath was cooled by a Blue-M




-42-


Constant-Flow model PCC-24A-2 cooling unit, which has

thermostatic control. This external water bath was kept

approximately 3C cooler than the temperature of the main

bath; as a result, the heaters in the main bath were never

completely shut off. This allowed constant regulation of

the temperature of the bath rather than the cycling usually

associated with proportional temperature controllers. The

water from the external bath was circulated by an American

Instrument Company 1.3 A circulating pump, and the

regulation of temperature in the main bath by the apparatus

described above was 0.002C.

Temperatures were monitored with a Hewlett-Packard

model 2801A digital quartz thermometer and quartz probe.

This digital thermometer was calibrated across the entire

temperature range of interest, and the appropriate correction

factors were determined. It was calibrated against a Leeds

and Northrup platinum resistance thermometer, model #8160.

The resistance of the resistance thermometer was measured

with a Leeds and Northrup type G-2 MUller bridge, model 8069,

which allowed measurement of thermometer resistance to

0.0001 Q. A response printout from Leeds and Northrup

permitted the determination of temperature measured directly

from the resistance reading.

To further cut down on heat loss from the bath, and

to prevent debris from entering the oil, a plexiglas lid

for the bath was constructed by the departmental machine

shop. This lid had a hinged door over the cell area to

allow access to the cells therein.





-43-


The cells were stirred constantly by a Poly Science

Corporation model RZR-10 stirrer motor, which permitted

variable stirrer speed. The motor was connected via a

driveshaft and two Sears Craftsman right-angle drives to

a Pic chain-and-sprocket drive. This drive turned two

large teflon stirbars positioned under the two cells. The

temperature bath and its associated components are diagrammed

in Figure 10.

Dielectric constants were determined using a Balsbaugh

Laboratories model 100-T3 dielectric constant cell. This

cell had a three-terminal arrangement and was constructed

of cylindrical nickel-steel electrodes. A special wiring

harness was constructed to allow connection to the four-lead

measuring system of the conductance bridge. The cell was

thermostated in the constant temperature bath, and after

thermal equilibrium was reached no appreciable drift in

capacitance was noted.

Viscosities were determined with a Canon-Fenske type

viscometer, calibrated with conductivity water at the

various temperatures studied.

Densities were determined with three pycnometers of

the Gay-Lussac type, obtained from the Fisher Scientific

Company. The pycnometers were calibrated with conductivity

water at the temperatures studied, and the three readings

were averaged together to obtain the mean density.

























4P-,U



CO
r0

C z
oaO
o

0c
00






4-),
U)
0 d



4) -H
C



c d
4-)






C0



*H+ a)
r)-,
0


(U rt







UIcd

U)a)
C 3



o f
Uw
0
Q )
U -


0
0
0

)0
cd

-H


0 0





0 a)
0 0



O 0
0
U 0

a) *

0
0 0


4-,
a)


4-,



a)
0)
J






4- 0
Cd 0
4-,

rt













U)
r k

cd 0






r-4 p



a) c
0 0
0
PO

M O


*C a
O! C
O Ol +
O O. K


C: a0

0S
i4-
a a
0
t4 0)
4-
M C
0C n




-- 0
il E



0 *H


c4-4
C
>




C) G
O a



-4
o 00


a) a 4-,
6 i4


Hl- >





H O-


0



0

0

a)




4-)
4-,
0
a)



0

.H









Cd 0
a) 4-
-P
E
0
c,


1 1

a 'H

3 a)

0
O S

*H





W E


*

a)
4,



M


C
Ori
r0
OH

O1
0 i9
O 3
0

a)

-i


-H C
*H 0
0
u E

0

a E
a 3
u

-H




W
0 a)
0 C
-H 0
4) H




>1 CO
0 0



0 4-
-H U
EU)

O a
SH$l
C O

&- -
K) K


<' M U Q 0 -i '-Z o 0 P C






-45-


4 --------1


- S
* I



* :
1



S..
I S.


-oi I--


0000000


c 0000000


So11


s














CHAPTER IV

DATA ACQUISITION AND TREATMENT



Experimental Technique

A standard procedure for conductance measurements was

adopted and adhered to for this study. An amount of

solvent (usually about 350 g) was weighed into the

conductance cell, which was then placed into the constant

temperature bath. After thermal equilibrium was reached

(in about an hour), the resistance of the solvent was

measured. Since solvent resistances generally range from
5 6
10 to 10 Q, and since the decade resistance standard had

a maximum resistance of 99,999.99 0, it was found necessary

to employ a resistive shunt. This shunt, in parallel to

the conductance cell, was a precision resistor whose

resistance was evaluated on the bridge as 10,006.8 Q.

Response was found to be flat across the frequency range

of the measurements. This allowed measurement of the very

high resistances according to the equation:

RR
R sm (30)
a R R(
s m

where R is the solution resistance, R is the measured
a m
resistance, and R is the shunt resistance.
S


-46-





-47-


Once the solvent resistance was determined, the cell,

with contents continuously stirred, was allowed to remain

undisturbed and the resistance was monitored as a function

of time. If the solvent were to leach any impurity out of

the glass of the cell, the resistance would decrease with

time. This was not noted for any of the solvent systems in

this study.

A concentrated solution of the electrolyte under study

was prepared in the solvent of interest. Weighed amounts

of this stock solution would be added incrementally to the

cell via the filler cap. After each addition, the fill

tube would be rinsed with the solution in the cell by

forcing the solution up into the fill tube with the rubber

bulb. After equilibrium was reached, as indicated by

stability of the measured resistance with time, the solution

resistance was recorded and another addition of stock

solution was made. Usually, 12 such solutions were

measured, and after the last measurement the density of the

final solution was measured.

Resistances were measured with a test voltage of 0.3 V

at three frequencies: 2.5, 5.0, and 10.0 kHz. These

resistances were then extrapolated vs. a function of

frequency to eliminate the frequency dependence, as described

in a following section.

Solution equilibrium, for the 2-methoxyethanol/water

solvent system, was found to be attained in about 15

minutes. For the sulfolane/water system, equilibrium took





-48-


up to one hour, probably due to the very slow solvation of

the cation by the solvent. For the l-methyl-2-pyrrolidinone/

water system, equilibrium was achieved in about 15 minutes.

Quickest of all was the system of Tris-HCl in water, with

equilibrium in less than 5 minutes.

Making the conductance measurements in the manner

described above gave rise to a set of concentration (in moles

of solute per gram of solution) vs. resistance points.

Treatment of these data is described in a following section.

Dielectric constant measurements were greatly

facilitated by the use of a three-terminal dielectric

constant cell. The bridge was balanced (shunt in place)

with the cell disconnected. With the cell connected, the

capacitance of the empty cell (i.e., with air as the

dielectric medium) was measured. The cell holder was then

filled with the solvent of interest and placed into the

constant temperature bath. The cell was inserted, and the

solution was allowed to come to thermal equilibrium. The

capacitance was then measured, and the dielectric constant
58
was very simply calculated with the equation:58

C
= S (31)
a

where C is the solvent capacitance and C is the
s a
capacitance of the empty cell.

Cell constants were determined utilizing the method
59
described by Lind, Zwolenik, and Fuoss.9 Utilizing data

available for the conductance of aqueous potassium chloride,





-49-


they derived an equation to give the equivalent conduc-

tance, A, for a given concentration of KC1:

A = 149.93 84.65/C + 58.74c log c + 198.4c (32)

where c is the molar concentration of KC1. They found

this equation to give excellent results when compared to the
26
Jones and Bradshaw26 conductance standard, probably the

most widely accepted standard for conductance measurements.

The method was utilized by making a conductance run

using water as the solvent and adding increments of a

concentrated KC1 stock solution. Once the concentrations

were converted to molarity and the resistances extrapolated

to remove frequency dependence,the cell constants were

calculated.

As was shown in a previous chapter, the resistance of

a solution is directly relatable to the specific

conductance:

K = R (33)
S

The solution resistance is the measured resistance, after

extrapolation, corrected for the resistance of the solvents:

1 1 1
S( 34)
R -R R
s m solv

The specific conductance may also be related to the

equivalent conductance:

SAc
K -000 (35)
1000





-50-


Combining equations 33 and 35 we obtain an expression

relating cell constant, solution resistance and equivalent

conductance:

10006
A = R (36)
R c
s
-I
where c is the concentration in mol L

By plotting A, calculated with equation 32, vs. the
-1
quantity (R c) a line is obtained whose slope is 10006.

In this study, two separate calibration runs were

made, with a total of 10 measurements for each of the two

conductance cells. The cell constants were determined by

linear regression analysis to be 1.05393 cm1 and 0.120695
-l
cm In both-cases, the correlation coefficient for the

regression was greater than 0.99999, indicating extremely

good reproducibility between runs.

Recently, an alternate equation for the determination

of the equivalent conductance of potassium chloride solutions

has been proposed by Justice. His equation has the form:

A = 149.87 94.87/c + 58.63c log c + 224.1c 254.5c1.5 (37)

It can be seen that this equation has a similar form to

the equation of Fuoss et al. but is extended to include

the c term. By doing so, the applicability of the

equation is extended up to approximately 0.04 M KC1, as

opposed to 0.012 M KC1 for the Fuoss equation.
44
A more recent paper by Fuoss and Hsia44 contains a

modification of the original equation which incorporates

the 1.5 term:
the c term:





-51-


A = 149.936 94.88V/ + 25.48c In c + 221.Oc 299c1.5 (38)

As can be seen, the constants differ slightly from the

equation proposed by Justice. It is stated that the new

Fuoss equation will provide agreement with the Jones and

Bradshaw 0.1 demal KC1 standard, thus extending the concen-

tration range over which the cell can be calibrated.

Since this study, however, was done at concentrations

on the order of 0.01 M maximum, the original Fuoss equation

was used for the determination of the cell constants. At

such low concentrations, the difference between the A

values generated by that equation and the values generated

by the two later equations is less than one-half of one

percent.




-52-


Preliminary Data Treatment

As has been mentioned previously, concentrations were

determined by weight, and solution additions were by

weight. This resulted in experimental concentrations in

units of mol g soln1. Since equivalent conductance

is in terms of molarity, it was necessary to convert to

molar concentrations. This was done through use of the

density of the solution.

Both the solvent density and the density of the final

most concentrated conductance solution were determined. The

densities of the more dilute solutions were assumed to lie

on a straight line connecting the two experimental points.
-1
The concentration in mol g soln and the molar concentration

may be related by the equation:

c(M) = 1000m(pslm + Psoln) (39)

-l
where m is the concentration in mol g soln Ps1 is the

slope of the line connecting the two experimental densities,

and psolv is the solvent density. The quantity Pslm + Psolv

is in fact the density of the solution whose concentration

is m.

Resistances were measured at 2.5, 5.0, and 10.0 kHz

and were then extrapolated to infinite frequency by use of

the method endorsed by Hoover for shiny platinum electrodes

such as were used in this study.35 The extrapolation is

based on an equation of the form:

R
R =R + (40)
measured ohmic 2 (40)
1 + aw




-53-


where:

F 1
a =
2 2
S3 F2

and:

2 2
F a3 R R1
12 3 2 R 1Ri
S 1 2.2 22R R1


with w = 2wv. At infinite frequency, the term on the right-

hand side of equation 40 drops out, leaving the true ohmic

resistance. The measured resistance is plotted vs.

(1 + aw )- ; the intercept is the ohmic resistance.

Usually, the measured resistance was found to decrease

with increasing frequency, which is considered normal.

However, when dealing with very high resistances, such as

those associated with pure solvents, a reversal of this

trend was noted; the resistance increased with frequency.
61
This phenomenon has been described by Mysels et al. and

is attributed to a leakage to ground. Their recommendation

is that the resistance be extrapolated to zero frequency vs.
2
a However, their recommendations are for frequencies

of measurement less than 0.5 kHz, far lower than those

employed in this study.

Where the resistances were found to be sufficiently

high to cause anomalous frequency dependence (pure solvents,

HC1 in sulfolane, acetic acid in 2-methoxyethanol/water)

the resistance values at 10 kHz were used for further

calculation of conductance parameters.





-54-


The preliminary data treatment to this point was

performed with a single computer program, called "FREQEXTR,"

written in the Level II Basic language to utilize a Radio

Shack TRS-80 microcomputer, operating under the NewDos+

disk operating system, with 32 KBytes of random access

memory (RAM). A copy of the program appears in the Appendix.

After inputting the various parameters (density slope,

solvent density, cell constant) the resistances and the

corresponding frequencies were input, along with the

experimental concentration. The computer supplied:

1) The resistance at infinite frequency;
-1
2) The concentration in mol L ; and

3) The equivalent conductance, calculated via equation 36.

Solvent corrections were always applied.

Treatment of the experimental data with this program

yielded a set of molar concentration vs. equivalent

conductance data points which were then processed as des-

cribed below.





-55-


Data Processing

The conductance vs. concentration data were processed

with a computer program designed to utilize the full Pitts

equation described previously. The program was initially

written in the Fortran IV language to utilize the

facilities of the Northeast Regional Data Center on the

campus of the University of Florida.62 With the acquisition

of the microcomputer system described previously, the

program was translated into the Basic language; at the same

time, the program was streamlined and rendered more

efficient. The Fortran IV subroutine "EXPI" for the

evaluation of exponential integrals was translated in full.

All calculations were carried out in double precision.

The program is designed to utilize an iterative

procedure devised by Ives,6364 using the following

expression for the dissociation constant, Kd:

2 2
ci Y+
K = c (41)
u

where the subscripts i and u refer to ionic and nondis-

sociated quantities, respectively. Since the degree of

dissociation, a, may be expressed as:

A ci
a (42)


both c. and c may be expressed in terms of total concen-
tration of electrolyte and the degree of dissociation:
tration of electrolyte and the degree of dissociation:





-56-


c. = ac
1
(43)
cu = (1 a)c

Combining the preceding four equations, one arrives at

an expression for Kd in terms of A:

2 2
A cy+
Kd = Ai(A A) (44)


In general, A., the ionic equivalent molar conductance,
1
may be expressed as a function of A the limiting

equivalent conductance:

A. = A + A (45)
1 r

where A is an expression for altering A to obtain A.;

Ar will vary with the theory being applied.

Kd may now be expressed as:

2 2
A cy
K = (46)
Adi(A + Ar) A


or:

2
o A cy 2
A Ar = A (47)
r A.K
i d

If we now set up two variables, X and Y, such that:

Y = A A
r
2 2 (48)
X A.


we may reduce the equation to the form:

Y = A X (49)
Kd





-57-


With both X and Y known, this reduces to a simple linear

least-squares procedure for obtaining A0 (the intercept),

and Kd (-slope)-. Since X and Y depend on A, Ives

proposed an iterative procedure whereby an estimate for

A is provided. A set of X and Y values is compiled using

this estimate, a least-squares calculation is done, and a

new value for Ao is obtained. This is then used to generate

new values for X and Y, and so forth, until no change in A

is noted. This usually takes less than five iterative

steps.

In his original treatment, Ives used the Onsager

limiting law to obtain Ai; an exact solution for this

quantity can thus be obtained. When using the Pitts theory

of conductance, however, this is not the case. From

Equation 45:

A. = A + A (45)
1 r

In the Pitts equation, A is a transcendental function of
r
A. and a direct solution is not possible. Hence, the

program was designed to iterate to obtain the Ar value.

The program is designed to take the estimate of A0

as the first approximation of A.. It then calculates the
1
various parameters needed (a, ci, Pitts terms, etc.) and

using these calculates the Pitts Ar term. Using this, it

calculates A. and compares it to the original estimate. If
1
the difference is greater than 0.001, it takes the new A.
1
value and goes through the iteration process again. This

is continued until convergence occurs.





-58-


The iterative process described above takes place for

each data point; once it is concluded, the X and Y values

are generated, and the program proceeds to the next point.

When all points have been processed, the program performs

the least-squares calculation to obtain the values for

A and Kd. In this study, a slight alteration was made to

have the program calculate the association constant

K (= d), rather than the dissociation constant.
a Kd

This procedure was carried out for five iterations;

values of A and K have usually converged by the fourth.
a
The complex point-by-point iterations repeated five times

explain why the microcomputer execution time for this

program runs in excess of 3.5 hours for a typical set of

conductance data! The performance of the program has been

tested and found to yield results in very good agreement
57
with those considered standard.5

As mentioned in a previous chapter, the full Pitts

equation has been expanded by Fernandez-Prini and Prue to

give an equation of the familiar form:

A = A S/'c + Ec log c + J c J2c1.5 (23)

During his visit to the laboratory, Dr. Fernindez-Prini

graciously helped to prepare a computer program designed to

utilize this form of the conductance equation, for both the

Pitts and Fuoss-Hsia theories. This program was also

adapted for use with associated electrolytes by replacing c

with ac. Since the conductance due to free ions (the ionic




-59-


conductance) at concentration ac is given by the following

relation:

A = A.(ac) Ay+2K ac (50)

derived from equation 26, the final form of the conductance

equation for associated electrolytes, combining equations

23 and 50 becomes:

A = A S/c + Eac log ac + J1ac J2(ac)1.5 KaAy ac (51)

As mentioned earlier, the S and E terms are identical for

both theories; the J1 and J2 terms differ. The program

using this form of equation has several advantages over the

program utilizing the full Pitts equation. It can give us

the results using both theories; using the least-squares

iterative method of Kay65 it operates in single precision

and takes only a few minutes to complete the calculations.

However, it has one major disadvantage.

In the course of the study, it was found that the

program utilizing the expanded equations broke down for the

2-methoxyethanol/water and 1-methyl-2-pyrrolidinone systems.

The similarity here is that both systems have dielectric

constants of about 32, and consequently Bjerrum's distance
0
is about 8.7 A. This means that Ka = 0.45 at a concentration

of 0.01 M, and, as has been pointed out,40,60,66 in this

region the expansions tend to break down. This was

manifested by a divergence in Ao values rather than the

expected convergence.





-60-


For this reason, among others, the full Pitts equation

program, "PITTSEQN" as described, was used to analyze the

data in this study. It might be pointed out that, where the

expanded equation program worked, it was quite useful for

obtaining a close approximation of A to use as the estimate

for A in "PITTSEQN"; this cut down initial iteration time.

Copies of both computer programs, "PITTSEQN" and "EXPEQNS,"

in the TRS-80 Level II Basic language, appear in the Appendix.

In both programs it will be noted that when the

equivalent conductance is input it is multiplied by the

factor 0.999505. This is to convert the conductance in

international ohms, as measured, into the absolute ohms

which are standard.

For those systems studied, where the solvent conduc-

tance was an appreciable fraction of the total conductance

(i.e., where the association constant was exceedingly high),

neither program was able to perform the extrapolation to

infinite dilution. Rather, another program was written to

utilize the Shedlovsky-Kay extrapolation method.42 This

was devised for use with data for very weak acids in mixed

solvent systems (e.g., acetic acid in methanol-water mix-

tures), and depends on obtaining an estimate for A which

cannot be directly obtained from the data. This is done by

using the Kohlrausch law of independent migration, and will

be discussed in depth in the following section. The program

for this extrapolation, "SHEDKAY," may be found in the

Appendix.














CHAPTER V

RESULTS



This study may be divided into three main sections:

first, -an examination of the conductimetric behavior of

HC1 in sulfolane and sulfolane-water solvents of varying

compositions at various temperatures; second, a study of

the conductimetric behavior of HC1 in l-methyl-2-

pyrrolidinone (NM2Py) and NM2Py-water solvents of varying

compositions; and third, and examination of the behavior of

various electrolytes in the solvent consisting of 80 weight-%

2-methoxyethanol and 20 weight-% water in order to determine

the amount of ion pairing present for the electrolytes.

In order to avoid the inclusion of large amounts of

data in this chapter, the actual conductance results have

been placed in Appendix A, which may be found following

Chapter VII of this dissertation.

Table I is a summary of the calculated conductance

parameters for HC1 in sulfolane and sulfolane-water solvents

at 25, 30, and 400C. The solvent composition is expressed

as mole fraction of sulfolane (Xs); A is the limiting

equivalent conductance, Ka is the experimental ion pairing

constant, a is the value used for the distance of closest

approach parameter in the Pitts conductivity theory, and

-61-






-62-


cd cQ D 0


CO 1^M CM m (3i

000000





o
00





I O

0
~) co 0~c






o CDo n i 0 0









o o oo00
o co
vC.


















r1 ":00 0 0
0 CD COOM 0

















O c ** *0
E Cj4 n ti
C to



















0
or



TLO
0










o CM


cd n .Q


H r- oCo r-i
ioooo
D OOrD n










C(D -CD

r-1 O* CO ti t0








LO OH t 0
C 0000
LOC n (D
emr1 ^







SC o n 00












0 LO LO 0 LO 0
r0 0000
S(1 1 t C
NNOO0




HH 0HO





ttitli
00be O




***0*0
0OOOOO


co co) t 0

0 0 0r-

00000


C(
0
H (DQ V C)



C M o







CO CD CC 010














000000
O


H


+




-63-


SA-A is the standard deviation between the experimental
c
and calculated equivalent conductances.

The distance of closest approach parameter, a, was,

in this study, set equal to the Bjerrum critical distance;

this is discussed in the following chapter.

Table II presents the calculated conductance parameters

for HC1 in NM2Py and NM2Py-water solvents. The symbols

have the same meanings as in Table I.

Table III presents the calculated conductance results

for several electrolytes in the 80 W% 2-methoxyethanol-water

(80 W% MetOH-H20) solvent. These electrolytes were chosen

in view of their general importance in acid-base chemistry,

and to tie in with other research under way at this
71
laboratory. Furthermore, for a comparative evaluation of

the results obtained in 80 W% MetOH-H20 with those in pure

water, the behavior of aqueous solutions of Tris-HCl

(tris(hydroxymethyl) aminomethane hydrochloride) was
72
studied.72 The results of this study are summarized in

Table IV.

In this case, various trial values of a were used to

obtain a minimum in the standard deviation between the

experimental and calculated conductances. The value of

a which gave the minimum in _A-A was that selected for
c
use in generating the conductance parameters listed in

Table IV.





-64-


0

<
&


000000












inLO Cil co O

o0 t- MCo 0 <


OMOrO I
0 0 0 I
0 0 0 0 I
0000 I


0


<









co

0
H





1-4
o
^











I0

E
o^


Q0 CO 0
*< Q0 Q LO 0

HOOO *
T(D(OH C- 0
tOCo N 0



0coC 0 cD
,Ito 0 o 0 mC
00 N 0) (O 00 M

00 CO )Ln M CO
r-i N CO O C\
1114


-.

S o o D
0 00 0 O0 00 0
w O co o o, tx-
o co a co co 0

u n cH CO Co >
U LO C0) N
CO""
LnM\Iil


0 LO00 0
HOqOCO


I-'
U


-( U Hr ~ C.
U ckd 6
~2ZEHZ;3


I-
Go
0
H 0 0 0 0 0

o 0 o Co 0co
0 00000
O






00


cO c( n T-
H
O H H Z 1
Si r-i CN 6 J
^ 4


O

fq
0
> u

O 2
o EC
0





-65-


TABLE IV

Calculated conductance parameters for Tris-HCl in water.

T Ao K a AA
a A-A
(C) (S cm2 mol ) (mol-1 L) (cm x 108)

25 106.07 1.01 2.60 0.225

37 133.65 0.99 3.75 0.098














CHAPTER VI

DISCUSSION



Solvent Properties

General

In general, electrolytic conductance will depend, to

a large degree, on the properties of the solvent. If

the solvent is able to solvate strongly the ions present,

this will aid the dissociation process and increase the

conductance of the solution.

There are two basic types of electrolytes.39 In the

first, the ions are already present, as in inorganic salts,

and dissociate when dissolved. In the second type, ions

are formed by reaction between the solvent and the solute;

for example, the reaction which takes place when an organic

acid is dissolved in water:

RCOOH + H20 t RCOO + H30+ (52)

The most obvious force between a neutral solvent

molecule and an ion is the electrostatic force arising from

the interaction of the charge on the ion with the permanent

dipole moment of the molecule. If the solvent molecule has

no permanent dipole moment, one may be induced by the

presence nearby of the charged ion. Of a similar nature are


-66-





-67-


the dispersion, or London forces. These are the forces

responsible for the cohesion of molecules lacking charge

or dipole moments and are due to random formation of dipoles

due to fluctuations in the electron clouds of the molecules.

Aside from these non-specific forces, there are several

types of specific forces aiding the solvation process. A

good example of such is hydrogen bonding. An example is

the dissolution of an acid in water, as depicted in equation

52. It is this hydrogen bonding, and the solvent structure

that it gives rise to, that leads to the proton jump

mechanism which causes abnormally high conductances for

strong acids in water. This will be discussed in a later

section.

Another of the factors whereby the solvent influences

the conductance of an electrolyte therein is the viscosity.

Quite obviously, as the viscosity of the solvent increases,

the drag on moving ions increases, and the conductance will

thus decrease. Yet another factor is the solvent dielectric

constant. From Coulomb's Law, it is seen that, as the

dielectric constant decreases, the electrostatic forces of

attraction increase; thus, the mutual attraction between

oppositely charged ions increases, increasing ion association

and decreasing conductance.

In view of the above, it is interesting to examine the

properties of the solvent systems utilized in this study

and to see if any conclusions can be reached concerning

solvent properties and conductance.





-68-


Sulfolane System

The physical properties of sulfolane and sulfolane-

water solvents are summarized in Table V. They are

primarily experimental values, supplemented where

appropriate by values from the literature.



TABLE V

Physical properties of sulfolane-water solvents.


Temp.
(C)


25





30


Xsulf



0.85
0.75
0.50
0.25
0.00

1.00
0.85
0.75
0.50
0.25
0.00


40 1.00
0.85
0.75
0.50
0.25
0.00

a---Reference
b---Reference


K
-1
(S cm- )
( x 10-7)

0.735
2.658
4.5
6.3
7.0

1.260
0.298
20.88
2.740
3.610
9.0


0.506
4.388
5.7
8.4
12.00
10.0


Density Viscosity


(g mL-1)


1.2564
1.2492
1.2290
1.1726
0.99707

1.2623
1.2535
1.2464
1.2214
1.1698
0.99567

1.2568
1.2483
1.2353
1.2082
1.1579
0.99224


(cP)


7.490
6.772
4.583
2.738
0.890

10.30
7.236
5.994
3.797
2.287
0.798

7.039
5.240
4.743
3.212
1.928
0.653


Dielectric
Constant


45.23
46.77
52.28
59.70
78.36

43.30
44.69
46.26
51.25
57.57
76.58

41.68
43.34
45.49
49.64
56.83
73.15


The values for sulfolane at 300C are in accord with those

found in the literature. 9,10,74 At 400C, the dielectric

constant is in good agreement. The viscosity is found to




-69-


be somewhat low and the density somewhat high (7.953 cP

and 1.2534 g mL-1 respectively)74 compared to the values

available from the literature. The experimental values

were those used for the calculations.

It can be seen that as the mole fraction of water

increases, the viscosity and density decrease and the

dielectric constant increases. This is what one would

expect. However, the decrease in density with increasing

water content is not as great as would be expected were it

simply a case of mixing the two components. There, the

density would be expected to be the linear combination of

the two component densities:

p = XsP + XwP (53)

where s and w denote sulfolane and water respectively. The

density of the solvent mixture vs. mole fraction of sul-

folane is plotted in Figure lla. The deviation from

ideality, called the "excess density" is plotted in Figure

lib. This excess density is defined by the equation:

Pe = P (X sP + X P) (54)

where pm is the measured density.

It will be noted that the maximum in the plot of

excess density occurs at about 33 mole-% sulfolane, at all

of the temperatures measured. The deviation from ideality

has been taken to indicate association between the two

components of the system.75 Geddes76 has indicated that

the composition of the system at the point of highest





















Figure 1la


A plot of the density of the sulfolane-water solvents vs.
the mole fraction of the sulfolane contained therein at
various temperatures. The plot for the densities at 250C
is not distinguishable from that for 300C with the scale
employed.

















Figure 11b

A plot of the excess density of the sulfolane-water solvents
vs. the mole fraction of the sulfolane contained therein at
various temperatures. See text for definition of excess
density.




-71-


1.20-










1.05-


1.00-


0.12-

0.10-

0.08-

0.06-

0.04-

0.02-

0-


MOLE FRACTION


1.25-


30


SI I
0 0.20 0.40 0.60 0.80 1.00


_ II


SULFOLANE





-72-


deviation from ideality is that of the associated species.

In this case, that would correspond to sulfolane*2H20.

Figure 12a is a plot of the dielectric constant vs.

the mole fraction for the sulfolane-water solvent system.

The excess dielectric constant, defined in an analogous

manner to the excess density, is plotted in Figure 12b.

Here the deviation is negative and again has a maximum

deviation at about 33 mole-% sulfolane. This is in accord
77
with the results of Reynaud, and gives further validity

to the assumption of an associated species with the com-

position sulfolane-2H20.

Figures 13a and 13b are plots of, respectively, the

viscosity and excess viscosity of the sulfolane-water

solvent system. Here the situation is more confused than in

the previous two cases. There is a maximum deviation, but

this shifts with the temperature. Although drawing con-

clusions from this plot is less certain than with the plots

of excess density and excess dielectric constant, one thing

stands out. The addition of just a small amount of water

causes, at 300C, a drastic decrease in the viscosity of the

mixture, indicating a decrease in the structure of the

solvent. This is true to a lesser extent at 400C. It has

been shown that sulfolane is an excellent "structure-

breaker" with regard to water;78 apparently the same can be

said for water with regard to sulfolane. It has been shown

as well that the heat of mixing for sulfolane and water is

endothermic; this would correspond to heat being extracted





















Figure 12a


A plot of the dielectric constant of the sulfolane-water
solvents vs. the mole fraction of sulfolane contained
therein at various temperatures. The 250C plot terminates
at X = 0.85 since sulfolane (X = 1.0) is a solid at this
temperature.

















Figure 12b

A plot of the excess dielectric constant of the sulfolane-
water solvents vs. the mole fraction of sulfolane contained
therein at various temperatures. See text for definition
of excess dielectric constant.




-74-


250


MOLE FRACTION


80-


70-



60-



50-



40-






0-


-4-

-6-


-10-

-12-


I 0. I 0I I I
0 0.20 0.40 0.60 0.80 1.00


SULFOLANE





















Figure 13a


A plot of the viscosity of the sulfolane-water solvents
vs. the mole fraction of the sulfolane contained therein
at various temperatures. The 25C plot terminates at X
= 0.85 since sulfolane (X = 1.0) is a solid at this
temperature.

















Figure 13b

A plot of the excess viscosity of the sulfolane-water
solvents vs. the mole fraction of the sulfolane contained
therein at various temperatures. See text for definition
of excess viscosity.





-76-


300


25'


400


MOLE FRACTION


109-
9-


0.0-

-0.4-

-0.8-

-1.2-

-1.6-

-2.0-


I 0I I I 0 1
0 0.20 0.40 0.60 0.80 1.00


_ __


SULFOLANE





-77-


from the solution to break the hydrogen-bonded water

structure. As will be shown in the next section, this is

significant. It indicates that while there is interaction

between the sulfolane and water, it is a structure-breaking

process. For other dipolar-aprotic solvents, such as NM2Py

which is discussed next, just the reverse is true.

Pure sulfolane is a somewhat inconvenient solvent to

work with. Since it melts at 28.50C,9 most work has been

done at 300C, the first even temperature at which sulfolane

is a liquid. However, the drastic decrease in viscosity

with temperature (drastic when compared to sulfolane-water

solvents) seems to indicate that, at 300C, the sulfolane

still retains a great deal of the structure that it had as

a solid. This will be explored further when the conductance

results are discussed.



NM2Py System

l-Methyl-2-pyrrolidinone (also N-methyl-2-pyrrolidinone,

abbreviated as NM2Py herein) is a dipolar aprotic solvent

similar in many respects to sulfolane. Both solvents have

five member heterocyclic ring structures; both have double-

bonded oxygens. The structures appear in Figure 14.

The physical properties of NM2Py and NM2Py-water

solvents are summarized in Table VI. For the most part,

these are experimental values, supplemented with literature

values where appropriate.













s
0 '0


Sulfolane


Structures





Physical properties

XTp K
i2 IPy
-1
(S cm- )
( x 107

1.00 3.637
0.75 7.759
0.50 13.86
0.33 28.39
0.25 12.12
0.00 7.0

a---Reference 73


Figure 14

of sulfolane and NM2Py.



TABLE VI

of :'l Py-water solvents at 250C.
; 2t


Density
-1
(g mL 1)


1.0277
1.0348
1.0432
1.0477
1.0451
0.99707


Viscosity

(cP)


1.648
2.269
3.711
5.000
4.843
0.890


Dielectric
Constant



32.06
37.12
45.01
52.25
57.00
78.36 a


The experimental values for the physical properties of

pure NM2Py are in excellent agreement with those reported

in the literature.77,79

It can be seen that, as the mole fraction of water

present in the solvent increases, both the density and the

viscosity increase and eventually pass through a maximum at

33 mole-% NM2Py. Figure 15a is a plot of the density vs.

the mole fraction of NMPy for this solvent system, while
Z'


-78-


NM2Py




















Figure 15a


A plot of the density of the NM2Py-water solvents vs. the
mole fraction of NM2Py contained therein at 250C.




















Figure 15b

A plot of the excess density of the NM2Py-water solvents
vs. the mole fraction of NM2Py contained therein at 250C.




-80-


1.05r


1.04-


1.031-


1.022


1.01 -


1.00 -


0.06 -


0.04 -


0.021 -


_1I _I I I


0 0.2


0.4


0.6


0.8


1.0


MOLE FRACTION


z
i,

t.
U)


u
x
wU


NM2Py





-81-


Figure 15b is a plot of the excess density, as previously

defined. Figures 16a and 16b are, respectively, plots of the

viscosity and excess viscosity for these systems. Both

excess functions pass through a sharp maximum at 33 M%

NM2Py, indicating a structure for the associated species of

NM2Py2H20, analogous to that found for the sulfolane

systems. As can be seen in Figures 17a and 17b (plots of,

respectively, the dielectric constant and the excess

dielectric constant), this excess function also reaches a

maximum value at 33 M1. This finding is in accord with the

density and viscosity results, and with the results of
13
Assarson and Eirich,3 who demonstrated through heat of

mixing and phase diagram studies the formation of the

aforementioned species NM2Py 2H20. Therefore, it is

believed that these results for the dielectric constants

must supersede those reported by Reynaud,7 who showed a

maximum for the excess dielectric constant at XNM py = 0.2,


corresponding to the species NM2Py-4H20.

Although the species formed.apparently have the same

stoichiometry, the associative processes for NM2Py-H20

and sulfolane-H20 must be quite different. As was

mentioned in the previous section, it is believed that the

association of sulfolane with water is a structure-breaking

process. When mixing NM2Py and water, it was quite evident
78
that the solution became warm. It has been reported7 that

the heat of solution of NM2Py in water is highly exothermic,




















Figure 16a


A plot of the viscosity of the NM2Py-water solvents vs.
the mole fraction of NM2Py contained therein at 250C.




















Figure 16b

A plot of the excess viscosity of the NM2Py-water solvents
vs. the mole fraction of NM2Py contained therein at 250C.




-83-


0 2-
U)
3








- 4-


0
u 2-

U)
n I
0 4


o





U)
w
c. o!--------- L

0
W
w 0l
0 0.2 0.4 0.6 0.8


MOLE FRACTION NM2Py


1.0





















Figure 17a


A plot of the dielectric constant of the NM2Py-water
solvents vs. the mole fraction of NM2Py contained therein
at 250C.




















Figure 17b

A plot of the excess dielectric constant of the NM2Py-water
solvents vs. the mole fraction of NMTPy contained therein
at 250C.





-85-


0 0.2 0.4 0.6 0.8


MOLE FRACTION


80i


60


40


30


-12


1.0


NM2Py