• TABLE OF CONTENTS
HIDE
 Title Page
 Dedication
 Acknowledgement
 Table of Contents
 List of Tables
 List of Figures
 Abstract
 Introduction
 Theoretical background and...
 Experimental
 Methods
 Results and discussion
 Conclusions
 Appendix A: Keqives program
 Appendix B: Raw conductance...
 References
 Biographical sketch














Group Title: conductimetric study of some electrolytes in ethylene carbonate-water mixtures at 25 and 40 0C
Title: A conductimetric study of some electrolytes in ethylene carbonate-water mixtures at 25 and 40 0C
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Permanent Link: http://ufdc.ufl.edu/UF00097519/00001
 Material Information
Title: A conductimetric study of some electrolytes in ethylene carbonate-water mixtures at 25 and 40 0C
Physical Description: x, 113 leaves : ill. ; 28cm.
Language: English
Creator: Boerner, Barry Richard, 1945-
Publication Date: 1975
Copyright Date: 1975
 Subjects
Subject: Ethylene carbonate   ( lcsh )
Conductometric analysis   ( lcsh )
Chemistry thesis Ph. D
Dissertations, Academic -- Chemistry -- UF
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
 Notes
Statement of Responsibility: by Barry Richard Boerner.
Thesis: Thesis--University of Florida.
Bibliography: Bibliography: leaves 108-112.
Additional Physical Form: Also available on World Wide Web
General Note: Typescript.
General Note: Vita.
 Record Information
Bibliographic ID: UF00097519
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: alephbibnum - 000162399
oclc - 02704812
notis - AAS8747

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Table of Contents
    Title Page
        Page i
        Page i-a
    Dedication
        Page ii
    Acknowledgement
        Page iii
    Table of Contents
        Page iv
        Page v
    List of Tables
        Page vi
    List of Figures
        Page vii
        Page viii
    Abstract
        Page ix
        Page x
    Introduction
        Page 1
        Page 2
    Theoretical background and development
        Page 3
        Page 4
        Page 5
        Page 6
        Page 7
        Page 8
        Page 9
        Page 10
        Page 11
        Page 12
        Page 13
        Page 14
        Page 15
        Page 16
        Page 17
        Page 18
        Page 19
        Page 20
        Page 21
    Experimental
        Page 22
        Page 23
        Page 24
        Page 25
        Page 26
        Page 27
        Page 28
        Page 29
        Page 30
        Page 31
    Methods
        Page 32
        Page 33
        Page 34
        Page 35
        Page 36
        Page 37
        Page 38
        Page 39
        Page 40
        Page 41
        Page 42
    Results and discussion
        Page 43
        Page 44
        Page 45
        Page 46
        Page 47
        Page 48
        Page 49
        Page 50
        Page 51
        Page 52
        Page 53
        Page 54
        Page 55
        Page 56
        Page 57
        Page 58
        Page 59
        Page 60
        Page 61
        Page 62
        Page 63
        Page 64
        Page 65
        Page 66
        Page 67
        Page 68
        Page 69
        Page 70
        Page 71
        Page 72
        Page 73
        Page 74
        Page 75
        Page 76
        Page 77
        Page 78
        Page 79
        Page 80
        Page 81
        Page 82
        Page 83
        Page 84
        Page 85
        Page 86
        Page 87
        Page 88
    Conclusions
        Page 89
        Page 90
        Page 91
        Page 92
    Appendix A: Keqives program
        Page 93
        Page 94
        Page 95
        Page 96
    Appendix B: Raw conductance data
        Page 97
        Page 98
        Page 99
        Page 100
        Page 101
        Page 102
        Page 103
        Page 104
        Page 105
        Page 106
        Page 107
    References
        Page 108
        Page 109
        Page 110
        Page 111
        Page 112
    Biographical sketch
        Page 113
        Page 114
        Page 115
Full Text










A COIJDUCTIMETRIC STUDY OF SOME ELECTROLYTES 11
ETHYLENE CARBONATE-WATER MIXTURES AT 25 AND 40 C












By

BARRY RICHARD BOERJJER


A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA I:N PARTIAL
FULFILLMENT OF THE REQUIRE'-LENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY











UNIVERSITY OF FLORIDA


1975















DEDICATION


This dissertation is dedicated to my wife, Gaylia, and my son,

Benjamin, for their support, encouragement, and patience.














ACKNOWLEDG ELE-NTS


I would like to express appreciation to my advisor, Professor

Roger G. Bates, for his support and advice throughout this project. I

am also grateful to Professor H. A. Laitinen for easing the burden of

completing this dissertation.

Special thanks are also due all my friends and associates in

the department who have made the time I have spent here enjoyable,

educational (both technically and philosophically), and entertaining.

Without their help and support, this work would not have been completed.

This work was supported in part by the National Science Foundation

under grant MPS73-05019.













TABLE OF CONTENTS


Page


ACKNOWLEDGE'MENTS


LIST OF TABLES

LIST OF FIGURES

ABSTRACT . .


Chapter


I. INTRODUCTION . . . .


II. THEORETICAL BACKGROUND AND DEVEI


General Theory . . . .

Basic Measurement Techniques .

Conductivity Concepts . .

Variation of Conductance with


Pitts' Equation . . . .

III. EXPERIMENTAL . . . . .


Materials . . . . .


Instrument Description ..

IV. METHODS . . . . . .


Method of Experiment .. ..

Preliminary Data Handling .


KEQIVES Program Description

V. RESULTS AND DISCUSSION .. ..


LOPilEtT . .


. . . . .


. . . o .

. . . .

Concentration



. . .o

. . . .



. .



. . . . .o


Relevant Properties of Ethylene Carbonate


vii


ix


1

3


3

8

12


13

17


22

22


24


32

32

35

40


43


[








Mixed Solvent Properties . . . .


Plots of A vs. c . . . . . .


Fit to Pitts' Equation Assuming K = 0
a

Fit to Pitts' Equation Assuming K / 0
a

Bjerrum Theory of Ion Association . .


Treatment of the Acetic Acid Data . .


VI. CONCLUSIONS . . . . . . . .


APPENDIX A KEQIVES PROGRAM . . . . .


APPENDIX B RAW CONDUCTANCE DATA . . . .


LIST OF REFERENCES . . . . . . . .


BIOGRAPHICAL SKETCH . . . . . . . .


. . . . . 46


. . . . . 55


. . . . . 64


. . . . . 65


. . . . . 78


. . . . . 83


. . . . . 89


. . . . . 93


. . . . . 97


. . . . 108


. . . . 113













LIST OF TABLES


Table Page

1. Comparison of the accepted values of limiting equivalent
conductance and association constant to the values
determined by the KEQI'ES program for acetic acid
in water at 25 OC . . . . ... . . . . 42

2. Summary of calculated conductance parameters for NaC1,
NaAc, HCI in 20 mole percent ethylene carbonate at
25 and 40 oC assuming K = 0 ...... . . . .65
a
3. Summary of calculated conductance parameters for NaC1,
NaAc, and HCI at 25 and 40 C assuming K / 0 .... 66
a
4. Comparison of calculated and experimental K values . . 82

5. Comparison of calculated and experimental K values
using the Bjerrum distance as the ion size parameter 82

6. Summary of calculated conductance parameters for HAc
at 25 and 40 OC . . . . . ... . . . 88














LIST OF FIGURES


Figure Page

1. Circuit diagram of a Wheatstone bridge . . .. . . 8

2. ScherL:-.tic diagram of Ives model of a conductance cell. . 10

3. Schematic of the proton jump mechanism . .. . . 13

4. Block diagram of tie conductance bridge . .. . .25

5. Circuit diagram of the two different connections in a
four-lead measurement . . . . .. . . . 26

6. Drawing of the card connecting system . . . .. 27

7. Drawirc of a cell of the Kraus design . . . . .. 27

8. Drawing of a sectional view of the constant temperature
bat.: and associated components . . . . . .. 31

9. Comparison of a conditioned and an unconditioned run for
HCI in 50 mole percent ethylene carbonate at 25 OC . 33

10. Drawing of a special filling cap . . . . . .. 34

11. Plot of the inverse of the calculated specific conductance
v.. the measured resistance . . . . .... . .38

12. Ethylene carbonate molecule, showing bond angles and
distances . . . . . . . . . . . 43

13. The unrit cell of crystalline ethylene carbonate . .. 44

14. Plot of density and excess density vs. the mole percent
ethf.lenc carbonate . . . . . . . ... 48

15. Plot of dielectric constant and excess dielectric constant
vs. the mole percent ethylene carbonate . . .. 51

16. Plot of viscosity and excess viscosity vs. the mole
percent ethylene carbonate . . . . . . .. 53

17. ExampL. of type I behavior. Equivalent conductance vs.
the sCuare root of concentration for HCI in 20 mole
percent' t ethylene carbona- e at 25 C . . . . .. 57






18. Example of behavior intermediate between type I and type II.
Equivalent conductance vs. the square root of concentration
for NaCl in 20 mole percent ethylene carbonate at 25 "C 58

19. Example of type II behavior. Facsimile . . . . ... .59

20. Example of type III behavior. Equivalent conductance vs.
the square root of concentration for HCI in 60 mole
percent ethylene carbonate at 25 OC . . . . ... .60

21. Example of type IV behavior. Equivalent conductance vs.
the square root of concentration for HC1 in 60 mole
percent ethylene carbonate at 40 C . . . . ... .62

22. Example. of type V behavior. Equivalent conductance vs.
the square root of concentration for HC1 in 100 mole
percent ethylene carbonate at 40 OC . . . . 63

23. Plot of limiting equivalent conductance vs. mole percent
ethylene carbonate for HC1 at 25 and 40 OC . . ... 70

24. Plot of limiting equivalent conductance vs. mole percent
ethylene carbonate for NaCl at 25 and 40 C ...... 71

25. Plot of limiting equivalent conductance vs. mole percent
ethylene carbonate for NaAc at 25 and 40 OC . . .. 72

26. Plot of Walden product vs. mole percent ethylene carbonate
for HC1, NaCl, and NaAc at 25 and 40 OC . . . .. 74

27. Plot of Walden product vs. the quantity 100 over the
dielectric constant, 100/E, for HC1, NaC1 and NaAc
at 25 and 40 C . . . . . . . . . 75

28. Plot of association constant vs. mole percent ethylene
carbonate for HC1, NaC1, and NaAc at 25 "C . ... . . 76

29. Plot of the log of the association constant, pK vs.
the quantity 100 over the dielectric constant, 100/E,
for HC1, NaCI, and NaAc at 25 and 40 *C . . . .. 77

30. Plot of the negative log of the equivalent conductance vs.
the negative log of concentration for HAc in 20 mole
percent ethylene carbonate at 25 OC. . . . . .. 85

31. Plot of negative log of the equivalent conductance vs.
the negative log of concentration for HC1 in 100 mole
percent ethylene carbonate at 40 OC . . . . . 86


viii








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



A CONDUCTIMETRIC STUDY OF SOME ELECTROLYTES IN
ETHYLENE CARBONATE-WATER MIXTURES AT 25 AND 40 C

By

Barry Richard Boerner

December, 1975

Chairman: Roger G. Bates
Major Department: Chemistry

There has been much interest recently in the study of the solvent

properties of n-imethylacetamide and n-methylpropionamide and related

compounds. Probably the major reason for this interest is because of

their high dielectric constants. However, these amide derivatives all

form hydrogen-bonded chains, and it would be interesting to study a

system of high dielectric constant incapable of forming hydrogen bonds.

Ethylene carbonate, with a dielectric constant of 90.36 at 40 oC, is

aprotic and was chosen for such a study. Ethylene carbonate is a solid

at room temperature, melting at 36.4 OC, and a mixed solvent system of

ethylene carbonate-water was used to avoid this difficulty. This also

allowed the study of intermediate compositions.

The electrolytes studied in this solvent system were NaC1, NaAc,

HCL, and HAc. Kraus cells were used, in conjunction with a bridge based

on the design of Janz and McIntyre, to determine equivalent conductances.

Analysis of the results was accomplished by the use of Pitt's conductance

equation or log-log plots.

The study showed decreasing limiting equivalent conductances and

increasing ion: association with increasing concentrations of ethylene

IX






carbonate (and hence increasing dielectric constant). There was also

evidence for dimer and trimer formation for the two acids, as well as

complex association species. Trends of association constants were, in

general, opposite to that expected from Bjerrum's simple electrostatic

model.

Ethylene carbonate is a dipolar aprotic solvent of high dielectric

constant with minimal self-association. Water structure is broken down

by addition of the ethylene carbonate, resulting in reduced solvating

power for the mixed solvent. This poor solvating power is probably due

primarily to poor anion solvation. Nevertheless, the solvent mixture is

well suited for both practical and theoretical studies.












CHAPTER I

INTRODUCTION


Ethylene carbonate, with a dielectric constant of 90.36 at 40 OC,

is one of the few solvents possessing a dielectric constant greater than

water which is.not an amide derivative or extremely exotic, as, for

example, hydrogen cyanide. Ethylene carbonate is aprotic and hence

incapable of forming hydrogen bonds with itself. However, the presence

of the carbonyl oxygen permits hydrogen bonding if appropriate hydrogens

are available. There has been much interest in using both ethylene

carbonate23 and propylene carbonate4 as nonaqueous battery solvents.

Pistoia et al. suggest that ethylene carbonate is superior to propylene

carbonate with respect to viscosity and specific conductance.

Despite theoretical and applied interest in ethylene carbonate

as an electrolytic solvent, very little research has been published to

date. This is probably because of the high melting point (36.6 OC) and

the poor solubility of many common salts (the alkali metal halides, for

example ) in ethylene carbonate. The use of an ethylene carbonate-water

mixed solvent system removes both of these difficulties, and as an added

bonus allows studies to be done in mixtures approaching isodielectric

properties. Because of its high dielectric constant and dipole moment,

the solvating power of ethylene carbonate is expected to be high. This

is based on two properties of solutions. First, the electrostatic forces

of attraction between oppositely charged ions are inversely proportional

to the dielectric constant. This would imply less ion interaction in









solvents of higher dielectric constant. Second, higher dipole moments

would imply stronger ion-dipole interaction between the solvent and

the solute. Hence, ion-ion interactions are expected to be small and

ion-solvent interactions are expected to be large, resulting in negligible

ion association. The use of ethylene carbonate-water mixtures provides

an excellent opportunity to test theoretical relations bLeween ion

association and dielectric constant.

Conductivity is a useful technique for the study of electrolytes

6,7
in solvent systems because of its high accuracy and general value

in assessing lonic solution properties. It was the najor tool used in

this work.














CHAPTER II

THEORETICAL BACKGROUND AND DEVELOPMENT


General Theory

The modes of conduction of electricity can be divided into two

main types: that characteristic of metals, involving the transfer of

electrons; and the conduction of electrolyte solutions. In the latter,

the transfer is of free ions. While both modes of conduction are

basically similar in that charge transfer is involved in each, there are

significant differences in their modes of transfer. This is evidenced,

for example, by changes in conduction with temperature. Metallic

conduction is inversely proportional to temperature, while solution

conduction is directly proportional. Although this work was concerned

for the most part with electrical conduction in solutions and its

implications to solution theory, metallic conduction played a major role

in the collection of the data on solution conductance.

At this point, it may be helpful to discuss some basic concepts

concerning the forces between charges and relate them to aspects of

solution behavior.*



*For a more detailed description, see, for example, G. Kortum, Treatise
on Electrochemistry second edition, Elsevier Publishing Co.,
Amsterdam,1965.








Coulomb's law states that the force, F, acting on two point ions

of charges zle and zz2e separated by a distance r in a vacuum is propor-

tional to:

2
F =lz (1)
r

Here e is the unit of elementary charge of the proton.

However, solution studies are not done in a vacuum. The parameter

which allows the determination of the change in field strength resulting

when the vacuum is replaced by a fluid is called the dielectric constant.

The dielectric constant, generally symbolized by E, is a measurable

property of the fluid and enters the expression of Coulomb's law in the

denominator:


F O zze (2)
Er2

If an electric field of strength E is applied to an electrolyte

solution, each ion present will experience a force proportional to its

charge z. and to the applied field:
1

F = z.eE (3)
1

The ions will move under the influence of this force and attain a

velocity v. proportional to the field and inversely related to the ion

size, r., and the viscosity of the solvent, n:
F
v. = (4)
1 6iTrir.


In the special case of unity field strength, the final velocity,

called the absolute mobility of that ion, is symbolized by u Combining

equations (3) and (4) gives:

z. |e
Zi le
u. = (5)
1 6nmrr.








The mobility is characteristic of the ion and also depends on external

conditions such as concentration, solvent properties, and the temperature.

A cubic centimeter of an electrolyte solution contains tN cautions

and N anions of z+ and z_ charges respectively. The net number of unit

charges crossing a unit plane (cm2) per second is the current, symbolized

by I, and is given by:

I = eE(N z u++ N z u ) (6)

Combining this relationship with Ohm's law allows the calculation of the

resistance of a unit cube of solution. This parameter is symbolized by

0, and called the specific resistance. The inclusion of the distance

between electrodes, Z, and their area, A, allows the determination of

the resistance of the volume of solution between any pair of electrodes,

R .
1
R -. (7)
m e(N z u++ N z u ) A A


The inverse of p is K, the specific conductance. The specific conduc-

tance is dependent on concentration, and it is advantageous to remove

this dependence by dividing K by the concentration c. A factor of 1000

is introduced because the initial unit size was one cubic centimeter,

and concentration is based on the liter (1000cc). Hence A, the equiva-

lent conductance, is given by:
A 1000 (8)
c

Now the equivalent conductance can be related to a measurable resistance

and concentration by:

A 1 1000 (9)
ARc
m

By definition, an electrolyte placed in a solvent forms a conduct-

ing medium. For conduction to occur, the presence of charged, r.cbile









particles, called ions, is necessary. In general, there are two basic

types of electrolytes. In one type, the ions are present before the

addition of solvent, as, for example, inorganic salts. The other type

forms ions by interaction with the solvent, as do the organic acids.

However, both types are solvated by various interactions, as described

below.

The most straightforward force possible between a molecule and an

ion is simply due to the electrostatic forces that exist between charges.

The charge associated with a neutral solvent molecule is the result of

its dipole moment. These electrostatic ion-molecule interactions are

particularly important in the solvation of ions. Of course, interactions

involving dipolar and quadrapolar geometries are more complex than the

case of simple point charges.

In the absence of a permanent dipole moment, the field of the ion

can induce a dipole in the solvent molecule. The forces thus generated

are called induction forces and are independent of temperature. Induc-

tion forces are strongly dependent on the polarizability of the neutral

molecule.

Dispersion forces are the most general in nature and are respon-

sible for the cohesion of molecules without charge or permanent dipole

moments. Dispersion forces are the result of instantaneous dipole

formations caused by random fluctuations in the electron cloud distribu-

tion of the molecules. These forces are additive for the interaction

of several molecules and can result in a significant attractive force.

In addition to these non-specific coulombic forces, which generally

result in non-stoichoimetric associations, different types of specific

interactions are also possible. These specific interactions lead to

definite co.cositions.








A goc-i example of a specific interaction is hydrogen bonding.

Generally associated with the presence of hydrogen bonding are several

unique properties, including a high boiling point, low intermolecular

separations, and unusual solvent structure. There is some evidence that

the hydrogen b-.nd is somewhat electrostatic in nature, since stronger

bonds are on-7 formed in conjunction with the highly electronegative

atoms fluorine, chlorine, oxygen, and nitrogen. A complete explanation

of all the r.zoporties of hydrogen bonds has not yet been formulated.

Anot:-er specific force results from charge transfer processes

between ne.ti-al molecules. Here an electron is transferred from one

molecule to ariother. Some degree of electron sharing is evident, indicat-

ing a similarity to chemical bonding. The resulting species generally

possesses a high dipole mo7:.cnt. A good example of such a species is

BF3'0(CHI3)2. The BF3 contains a incomplete external electron shell,

while the ether O(CH3)2 has free pairs of electrons, which serve to

complete the shell in boron trifluoride.

Fro:. the above discussion it is evident that there are many

possible interactions between molecules and ions. The relative strengths

of these various interactions are responsible for the differences between

solvents with respect to their ion-solvent interactions. Specific

interacticin. .ire strong enough in some instances to overcome the more

general assoc-iations. For example, the fact that electrostatic forces

of attractioni are inversely proportional to the dielectric constant

implies that ionization should be more probable with increasing

dielectric constant. This conclusion, generally referred to as the

Nernst -- Tho'.son rule, has been disproved repeatedly, and is









inadequate to handle the complex interplay of interactions recognized

in modern solution chemistry. This study has attempted to shed light

on the solvent properties of a specific solvent system, ethylene

carbonate-water.


Basic Measurement Techniques

The measurement of the electrical conductance of solutions is a

very sensitive technique, requiring strict attention to details in order

to obtain precise results. For example, the temperature coefficient of

the conductance of many aqueous solutions is approximately 2 percent per

OC. Thus temperature control good to t 0.005 OC is required to obtain

data with a precision of i 0.01 percent. Other conditions of measurement

are equally important and are discussed below.

The measurement of solution conductance is a precise resistance

determination, and this is most conveniently done using a Wheatstone

bridge, diagrammed schematically in Figure 1.


Figure 1. Circuit diagram of a Wheatstone bridge.








Basically, the standard resistance, Rs, is adjusted until the meter

indicates a null (that is, no flow of current). At the null, the

potential across the meter is equal to zero, and the relationship

between the resistive components of the bridge curcuit is:

R R
m s (10)
R R
3 4

However, under direct-current conditions, the ions migrate to the

electrodes in response to the applied field. The effects of electrolysis

would obviously change the bulk concentration and consequently the

resistance. Kohlrausch eliminated the problem of direct current polari-

zation by the use of alternating current where no net flow of ions takes

place. However, the use of alternating current in conjunction with the

standard cell configuration of parallel plates requires the

capacitances of the circuit to be balanced as well. The major change

that the use of alternating current introduces is the balancing of

impedance rather than resistances.

Early work by Grinnell Jones et al.0-17 and Shedlovsky8 forms

the basis for most aspects of precision bridges today. More recent work

by Feates, Ives, and Pryorl9 demonstrates the usefulness of the trans-

former bridges found in many commercial impedance comparators for

conductance measurements. The instrument used in this study is based

on a design of Janz and McIntyre20 and is discussed in more detail in

the experimental section.

A frequency dependence of the measured resistance remains with

even the most refined bridges of today. Hence, a reliable method of

removing this frequency dependence is required to obtain accurate and

precise conductance data. Fortunately, a large fraction of these










frequency variations have been removed by cell design and the use of
10
mineral oil of low dielectric constant as the thermostated bath fluid.

There remain additional effects due to complex electrode processes

which require careful study. Platinizing, or coating the electrodes

with platinum black, reduces these effects.6 However, platinization

produces a coating of high surface area and high catalytic activity.

Problems of adsorption and reaction associated with the platinum black

coating have resulted in the choice of shiny platinum for the electrodes.

The generally accepted equivalent circuit of a conductance cell

is that given by Ives,19 with the addition of the so-called WarburQ

impedance21 (symbolized by VAL-). A schematic of the components of this

model is shown in Figure 2.

R


R!


C


2


Figure 2. Schematic diagram of Ives model of a conductance cell.


R is the true ohmic resistance of the cell, the quantity to be

determined. It is independent of frequency in the range over which

the measurements are made (generally between 1 and 20 kHz). Electronic

relaxation times do not become an important factor until radio frequencies

are reached. In series with the ohnic resistance of the solution is the

double layer capacitance, C which is also independent of frequency in

the frequency range of the measurements. The capacitance C is the
2

external cap;citance cf the leads, and generally is negligible in well

designed cells ianersed in oil baths.









While no actual discharge or ion formation occurs at the

electrodes at the potentials used in this study (0.3 volt), some

spontaneous electrolysis does occur. This electrolysis is due to the

depolarizing action of dissolved oxygen or possibly ion discharge, and

represents a Faradaic leakage in parallel with the double layer

capacitance. This leakage generally can be represented by a pure

resistance R and a Warburg impedance in series. The Warburg impedance
2

can be considered to be equivalent to a resistance and capacitance in

series with equal impedances at any one frequency. Both impedances

1 /2
vary inversely with wu
19
Feates, Ives, and Pryorl9 have solved the bridge balance conditions

for their model (assuming a negligible Warburg impedance). These

conditions revealed the frequency dependence of Rm, the measured

resistance, to be of the form:


R
R = R + (11)
m I 1 + aw2


where:

R R 2 2
1 2 1
R + R
1 2

and:

a = 2Tr, V being the frequency.

Hoover22 has conoared this model and other theoretical bridge balance

conditions and concluded that equation (11) is sufficiently accurate

for extrapolation to infinite frequency. A more detailed description

of the extrapolation calculations is given in the experimental section

of this work.









Conductivity Concepts
23
Svante Arrhenius was the first to suggest the existence of

unbound ions in electrolyte solutions. These unbound ions are free to

move under the influence of external forces. The concept of ions remains

today as the basis for understanding electrolyte solution theory.

However, it has undergone considerable refinement since its introduction,

and today we have a much clearer understanding of ionic solution

processes. rJeertheless, the picture is still far from complete, and

the present work is an attempt to further the understanding of solution

processes and interactions of a specific solvent system.
24
Kohlrausch2 studied the behavior of the equivalent conductance at

low solute concentrations and observed a linear dependence on the square

root of the concentration, c. Thus the behavior of the equivalent

conductance can be expressed as an equation of a straight line, as shown

in equation (12):

A = A + A/c (12)

A is the limiting equivalent conductance at zero concentration.

Kohlrauschalso advanced the concept of independent migration of

ions, which assumes that ions in their movements do not interact with

each other. This is only true at infinite dilution, and in this limit the

individual contributions of each ion to the total conductance can be

separated, as shown in equation (13):

A = \ + X (13)

Now a term to express the fraction of the total conductance associated

with a single ion can be introduced. This term is called the transference

number, symbolized by t and is related to conductance by:

= t (13a)
1








In tables of single ion conductances, anomalously high values

are noticed ~or hydrogen and hydroxide ions. The reason for these

high conductances is due to the fact that these ions are fragments of

the solvent, -wter. Actual physical transport of these ions in water

is not necess-.=-- due to the existence of a proton jump mechanism. The

proton is transferred from an H 0 group to a neighboring water molecule.
3

No major movement of ions results, but the charge moves rapidly along a

chain of water molecules. Figure 3 shows this schematically.

H H H H
HOH + OH -- HO + HOH
+ +

Figure 3. Schematic of the proton jump mechanism.

A similar process occurs with the hydroxide ion, except that the negative

ion acts as a =roton acceptor rather than a proton donor.

An increase in temperature reduces the anomaly between the

conductance c:f hydrogen and that of more "normal" ions. This suggests

a reduced pruab.hiiity of proton jumping due to the disruption of the

water structu-e at high temperatures. A disruption in the structure of

water by mea:-n other than thermal forces would be expected to result in

a decrease &E the proton jump effect as well.


Variation of Conductance with Concentration

Under :he conditions of infinite dilution,ions are considered to

be far enough apart for their interactions to be negligible. For non-zero

concentrations, ions do influence one another, and the simple infinite

dilution approximations are no longer appropriate to handle these

complex interactions. Ionic interaction theory has made a good start

in quantitat-ic.-Ly explaining ho- conduztance varies with concentrations,

but over only a limited concentration range, up to perhaps 0.1M fr 1:1









electrolytes in aqueous solutions. There are two major effects of ion

interactions: the electrophoretic effect and the relaxation effect.

The electrophoretic effect is the result of solvent flow due

to ion migration. An ion moving in a viscous medium drags along nearby

solvent. The solvent can be directly associated with the ion (that is,

the ion is solvated). Also, nearby solvent is pulled along to some

extent by frictional forces. Hence, neighboring ions experience a net

solvent flow rather than static conditions. This flow of solvent is

either with or against the movement of this neighboring ion, depending

on its charge. This effect vanishes at infinite dilution.

Since distances between ions are involved, Boltzmann distribution

functions can be used to express these effects.* If a single electrolyte

is used, all velocities of ions of the same charge will be equal, and the

Boltzmann symmetry is preserved. It can be shown that the electrophoretic

increment to the velocity of the ion is:


00 (z n- k n-k )
+ +-- +
A = A n (14)
+ n n
n=) a (z z_)


where:

A (-n ( e2 n-1
An =nfl V (Ka)
n n6K 7r EkT n

In these relations, k and k are the forces acting on the ions; a is the

distance of closest approach of the ions. n is a function of Ka only

and defined by:
( ea e
gn(Ka) = (Ka)2 + (Ka)
n (I + a) n


'A detailed description of ionic distribution functions can be found in
Chapter 4 of Electrolyte Solutions R.A. Robinson and K.H. Stokes,
second edition, 1970 revi,.;?n, Butter.orths, London.










SS le2 I 1 '2
Ka = 10OOOkT a


Sn(Ka) is also a function of Ka only, and is given by:

n-2 / -nkr
Sn(Ka) = an2 ---- dr
n-r
Sr


which is in the form of an exponential integral. T is the absolute temper-

ature and N is the Avogadvo number. Other terms have been defined pre-

viously, and the summation over n (all ionic species appears from the

Boltzman distribution, as does the Boltzmann constant, k.

In a equilibrium situation, the average distribution of ions is

spherically symmetric, and there is no net force acting on the central

ion. In the presence of an electric field, the central ion will be moved

off-center from the spherically symmetric distribution. As a result of

this movement, the ion experiences a small restoring force before thermal

fluctuations return the original spherical symmetry. This return to

spherical symmerry is termed the relaxation of the ionic atmosphere and

the average restoring force experienced by the central ion is called the

relaxation effect.

Initial work on the problem of the relaxation effect was done by
25
Debye and Huckel,2 but a somewhat more successful treatment is given
26
by Onsager.6 Onsager's expression for the velocity of an ion, as

modified by the relaxation effect, is given by:

v = v 1 + (15)
3 3 3EkT 1+q

where q is given by:

1 1z21 1/ 2



For symmetrical electrolytes, where z, = z2, q = 1/2.









However, this expression is valid only when Ka is small compared

to unity, which generally occurs only in dilute solutions. Additional

approximations also limit its usefulness to dilute solutions (<0.001 !M)

where the relaxation effect is small. Combining this relation (15) for

the relaxation effect with the electrophoretic effect (14) gives an

expression for the variation of the equivalent conductance with concen-

tration known as Onsager's limiting law:



Iz z le2Amq: F'
A = A + q) -6 (Jz I 12 z )' (16)
3CkT (1 + Vq) 67rf T

Here is of the form:

(8TNe' I
1OOOEkT

where I, the ionic strength, is:

I (V + v z2)
2 1 1 2 2

and u represents the number of moles of ions formed from a mole of

electrolyte.

If symbols are replaced by values of the corresponding physical

constants, and a 1:1 electrolyte is assumed, equation (16) can be

written as:



8.204 x 10 8250(17)
A = A -' + /c (17)
(ET) rn(ET)

Equation (17) has the linear dependence on /c that Kohlrausch first

observed. However, there is now a theoretical basis for this behavior

and a means of calculating the empirical constant A.








Shedlovsky27 has proposed an expression suitable for extrapolation

purposes based on this limiting expression. Putting (17) into a more

symbolic form gives:

A = A B A/c B /c (18)
1 2

and then rearranging (18) yields:



A -- c (19)
1

For strong aqueous 1:1 electrolytes, this calculated value of A varies

almost linearly with concentration up to ~0.1M. One can thus plot this

varying A against c, whereupon extrapolation to zero concentration

gives a better estimate of the true limiting conductance A .

Robinson and Stokes28 have included the finite ion size in a

similar expression:

B A + B
A = A 1 a 2 /c (20)


which can be similarly rearranged to give:

B A + B

1 + (Ba B )/c
1

Where B = K//c. Equation (21) is useful for A determinations by

extrapolation using Shedlovsky's method.


Pitts'Equation

It is clear from the behavior of the A of equation (19) that

data up to -0.1M can be represented by:

A = A (B A + B )/c + bc(l + B ic) (22)
1 2 1

if b is chosen to fit the data. This empirical relation has been shown










to be a fortuitous result of derived numerical values of more complete
29
theoretical descriptions.2

There are two major theoretical equations relating electrolytic

conductance to concentration and other physical quantities: that of

29, 30 31-33
Fuoss, and numerous modifications of his basic equation, and

the relation derived by Pitts34 in the early 1950's. Both theories are

based on the model of a charged sphere in a continuum and they have been
35
put in the same form with only differences in coefficients. The

form is:

A = A S/c + Ec log c + J c J c3/2 (23)
1 2


The S term (Onsager's limiting law slope) and the E term are identical

in the two treatments, but the ion size terms, J J are different.
1 2

The differences arise from the different approaches used by Fuoss and

Pitts and reflect differences in boundary conditions and details in

the application of the model. There has been much discussion recently
35-40
as to which treatment is better. 0 The most frequently cited differ-

ence has been a smaller value for a, the ion size parameter, resulting

from the Pitts' treatment. However, large variations in a from different
40
sets of data for even so well studied a salt as KC140 indicate a strong

dependence on the precision of the data. Present techniques give the

quantity a some of the characteristics of a variable modified to allow a

better fit of the data. This of course limits its theoretical meaning.

It is not yet possible to decide which treatment is superior. The KEQIVES
41
program which utilizes the Pittstreatment was available and was used

for the final analysis of the data.

The form of the Pitts' equation used in the rIEQr/ES program (:.;rtt-en

in Fortran IV and described nore fully in the experimental section) was:










( (1 + y) (v'2 + y) 1


A/c
(1 + y)2(/2 + y)


G/c((+y)


H/c
1 + y


A = H(/2 1)

B = 3H2
EkTHN103
G = -m7""C
z2e2K
H = 2 e 2 c
3EKT/c


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


7/2 e(2 + 8)y
+16 (1 + y)2(/2 + y) E


/2 e(1 + 8)y
+ ( y)E(2 + y) i
16 (1 + y)(/2 + y) 1


(8 + 1)


3
T = 2 + y)
1 4(/2 + y)


3 3/2e(8+ l)y
+8 /2 + y


Ei ((8 + 1)y)


- 2eyE (y)]



E( -u
E.(t) = e du
1 t u


y =

( 8~nle2c2 1/2
lOOOC kT


where:


(24)


4(1 + y)


E.(y)
1


(8( + 2)y)










1
2-

C = speed of light

All other symbols have their lprc:vious meaning.

To make the program nore general, concentrations were replaced

by ac, where a is the degree of disrociation. Correspondingly, equivalent

conductances calculated by the- 1,EQIVES program were multiplied by C to

convert A., the value actually calculated (A. is the conductance if the

electrolyte were completely dissociated into ions of oc concentration),

to the equivalenL conductance, A(that is, A/A. = a).

A value for the association constant K can be derived from the
a
mass balance equation by the use of a:


1 -c
K (25)
a 2 2
c cy4

In this expression, y2 is the mean activity coefficient (molar scale)

of the electrolyte. Activity coefficients at very low ionic strengths

can be derived by the Dchye-H.uckel expression:

2A zz2 1/I

f2 = 10 1 + Ba/I

Here A and B, the usual Dcbye-HIuckel parameters, are given by:

1.82,4G x 10
A =
3/2
(CT)


50.29 x 108
1/2
(CT)

Equation (26) gives the activity coefficient, f4, on the mole fraction

scale; it is converted to the molar scale by the expression:


2 = 2
Y (<27)
S -0 c(2 lvent olute
solvent solute




21




where m = moles solute per kg of solvent

M = molecular weight

p = density of the solvent
















CHAPTER III

EXPERT MENTAL


Material ls

The primary source of ethylene carbonate was Eastman, a division

of Eastman Kodak Company. The ethylene carbonate was obtained in 3kg

quantities; the product, of practical grade, came from two different

lots. Some initial trial experiments were done with ethylene carbonate

from Matheson, Coleman, and Bell (MCB).

The solvent was purified by slow freezing of the 3kg quantities.

Freezing was chosen because of its simplicity. Furthermore, the closely

related compound propylene carbonate, has been reported to decompose at
4, 42
temperatures greater than 110 0C. The purification procedure

involved melting of the ethylene carbonate, followed by filtering

through a fine sintered glass filtering funnel to remove insoluble

material. The ethylene carbonate was then allowed to freeze slowly

overnight. The remaining liquid was removed the following day and the

crystals were remelted and then allowed to refreeze. This procedure

was repeated until the initial color (light yellow) was removed. Despite

an initial difference in color intensity between lots, no significant

difference was observed in the number of melting and freezing steps

required for color removal. A similar color has been reported to appear

in propylene carbonate containing traces of water after contact with a

43
sodlum-cotasslun alloy. The devclocment of color has been suggested







44
to be due to the presence of a polymeric form. Typical yields were

on the order of 60 to 80 percent.

Due tc the nearness of the melting point of ethylene carbonate

(36.4 OC) to room temperature, the process of slow refreezing

approximated the conditions of zone refining. The concentration of the

color into the liquid remaining was readily apparent. This was responsi-

ble for the success of this technique of purification. The specific

conductance of ethylene carbonate purified in this manner was on the
order of 5-10 x -8 -1 -
order of 5-10 x 10 acm as low as, or lower than, values reported

2,5,45
in the literature.2 5 Purified ethylene carbonate showed little or no

tendency to absorb moisture from the air, as reported by Bonner et al.46

47
Its rate of hydrolysis is very slow;47 indeed, it has been reported to

be immeasurably slow.48 Base-catalyzed hydrolysis is much more rapid47

but still not. nianageable in the times and concentrations studied in

this work. Acid-catalyzed hydrolysis is also a potential problem, but

EMF measurements indicate little or no problem up to about 0.1 molar in

49
acid at 20 moli percent ethylene carbonate.49 However, at 40 OC and

high mole fractions of ethylene carbonate (>60 mole percent), the acid-

catalyzed hydrclysis rate has increased enough to become a source of

error.

Conductivity water was prepared by a single distillation of water

which was treated by reverse osmosis followed by deiorization. A

Corning AG-llb Pyrex still was used. Conductivity water thus prepared

had a specific conductance between 0.8 1.2 x 10 6 cm This was

expected, since no protection from the CO2 present in the air was

provided.

The saics *-sed in thL- study were recrystsllized 'tice frc-

conductivity w"_er s 3ing standard procedures. The sodiiu chlorid-e a3









Fisher Certified reagent grade material, while the anhydrous sodium

acetate and potassium chloride (for cell constant determinations) were

Mallinckrodt Analytical Reagent chemicals. After recrystallization,

salts were dried in a vacuum oven (initially at 60 OC, to avoid hydrate

meltingthen at 150 OC) and stored in a desiccator over indicating

Drierite until used.

The glacial acetic acid was also a Mallinckrodt Analytical

Reaaent. Purification of the acetic acid consisted of three fractional

freezing. The final fraction was stored in a desiccator over indicating

Drierite.

Hydrogen chloride solutions were prepared by double distillation

of constant boiling hydrogen chloride-water azeotrope. The final concen-

tration was established by the gravimetric determination of chloride

using silver nitrate. This concentration was found to be 6.053 M.


Instrument Description
20
The conductance bridge was based on a design of Jonz and McIntyre,2

slightly modified by Hoover5051 to allow the use of available capacitors.

A schematic diagram of the bridge is shown in Figure 4.

The major component of the bridge is a General Radio model 1654

impedance comparator, modified by the manufacturer to operate at 1.0,

2.5, 5.0, and 10kHz. The transformer bridge used in this commercial

instrument is of a toroidal design with a center-tapped secondary winding.

The halves of the center-tapped secondary act as inductively coupled

ratio arms of the bridge circuit, and they are equal within one part in

10 The precision of this measurement is thus limited by the precision

of the standard resistance used as a comparison to the unknown resistance.










decade
standards


four-lead
switching


Figure 4. Block diagram of the conductance bridge.

The standard resistance used in conjurtion with the comparator

was a General Radio model 1433-F decade resistor. This model has seven

decades of resistance ranging from lOkQ steps down to 0.01 steps. For

the resistances typically encountered during measurements (>1002), the

precision of the resistance readings was 0.01 percent. A General Radio

model 1412-BC decade capacitcr was connected in parallel with the decade

resistance to allow compensation for the cell capacitance. It is also

possible to measure dielectric constants utilizing the measured capaci-

tance of the cells.








To avoid problems associated with jrreproducible contact resistances

from the connections between the cells and the bridge circuitry, a four-

lead measurement system was used. The four-lead system used is essentially

the same as that employed with four-lead platinum resistance thermometers.

Basically, a four-lead measurement requires two measurements with differ-

ing connections between bridge and unknown. The mean of the resulting

two measurements contains no contribution from the inherent resistance

of the leads. This system is shown schematically in Figure 5.



/^-- tK^i ^ --Il^-
t R (cell) R (cell)

C T
m a m t







Figure 5. Circuit diagram of the two different connections
in a four-lead measurement.


The connection between the conductance bridge and the cells

consisted of printed circuit cards and edge connectors. Standard 15-

contact hardware was used, which allowed three contact surfaces for each

of the four leads. The contacts not used for connection purposes were

utilized as spacers. The redundancy of contact for each lead insured

positive contact and more reproducible connections. Figure 6 shows

the physical arrangement of the system. As shown, this arrangement

allows the measurement of two cells to be made simultaneously. One

cell or the other may be balanced simply byinverting the circuit card

connected to the bridge.

























1 circuit card, 2 circuit cards,
full thickness, 1/2 thickness,
to bridge to cells


Figure 6. Drawing of the card connecting system.



The cells used were similar to the design suggested by Kraus
52
et al. Two were commercially manufactured by Beckman Instruments. The
-1
cell constants were 1.0534 and 0.12041 cm. A duplicate of the cell

with the larger constant was made by the departmental glass shop. This
-i
cell had a cell constant of 0.93943 cm All cell constants were

determined at 25 OC. A drawing of the cell design is shown in Figure 7.


Drawing of a cell of the Kraus design.


Figure 7.









The reason for the wide placement of the lead wires is to reduce
53
the Parker effect. This effect is the result of capacitance formed by

the leads as they pass through the electrolyte solution. These capaci-

tances produce a frequency dependence of the measured resistances. The

electrodes are of shiny platinum, spot welded to platinum wire. The

platinum wire is welded to tungsten for sealing purposes. Heavy gauge

copper wire is brazed to the tungsten, and the copper is doubled at the

top of the glass for four-lead measurements.

The constant temperature bath was constructed by the department

machine shop. The bath itself is of stainless steel, with welded seams.

The bath is insulated with Styrofoam, and supported by a phenolic board

box frame. The box frame is secured in a welded angle iron cart.

Circulation for temperature uniformity is provided by two 1.3-ampere

American Instrument Company circulating pumps. The bath liquid was BP

food grade white oil. This white oil, of low dielectric constant, was

used to reduce further the lead capacitance effects mentioned previously.

Temperature control to 0.002 'C was obtained by a Yellow Springs

Instrument Company model 72 temperature controller. A 10-turn potentio-

meter was substituted for the standard three-quarters turn potentiometer

to permit more precise control of the temperature setting. The tempera-

ture controller was used with a thermistor probe and two immersion

heaters. One of the imrrersion heaters used was a standard 500 watt

Vycor sheathed immersion heater. The other was constructed of Nichrome

heating wire wrapped on a Plexiglas frame. This heater was placed to

take advantage of the flow from the two circulation pumps. Cooling water

was circulated through copper tubing immersed in the oil as an aid in

temperature control. This water was cooled by a Blue M Constant Flow








cooling unit i-mmersed in a auxiliary water bath. This cooling was in

opposition to the immersion heaters used in conjunction with the tempera-

ture controller and allowed continuous control rather than cycling.

As a further aid in temperature control, and to keep dust and

other debris out of the constant temperature bath, a Plexiglas cover,

constructed by the departmental machine shop, was provided. A hinged

box lid with an additional door was placed over the area where the cells

were positioned. This simplified the addition of stock solution and

manipulation of the cell assemblies.

Stirring for the cells was provided by a variable speed Poly

Science Corporation model RZR-10 stirrer motor. This stirrer motor was

connected to a Pic chain and sprocket mechanism by two Sears Craftsman

right angle drv.'.s. The chain sprockets turned two large Teflon stirbars

to provide stirring for two cells. Figure 8 shows a cross-sectional

view of the constant temperature bath and the placement of the various

components associated with it.

Densities were determined by three Fisher pycnometers with volumes

of approximately 25 ml. Pycnometers were calibrated by multiple weighing

of conductivity water. The values obtained from the three pycnometers

were averaged together to get mean values for the densities.

Viscosities were determined with viscometers of the Cannon-Fenske

design; they were also calibrated with conductivity water.

































.Q











0
CO
3













0
ca










C




OA
a








4U
0





o
a

4,-I




0
0)




C

I-Jo
00
(U






*3
0

*C


-'4

0





0
0)

C0

U)
u

0


'0






0 -
o










--I









-a

.4
u) .

m m












,O -I
aJ





3 0
0E-4




'/1 U
* 4
(J' 4
C D
*^ C
1^ CT


< m Q M r L0 = M n t -3 E


'U
*-'-









U) U
r 0

0 m

So
S O
0 0





U 0







r_
Uo 0








0


0> "
0 0

u c
P 4-1










x -4
C 0










-4 0
U 0
C^ C
0
-I



u a







0 C
cf U)




































* 41
I I
I I
I I
* I

* I
* I
* I
* I
* I
I I
I I
* I
L g


0000000





0000000
< 0000000















CHAPTER IV

METHODS


Method of Experiment

The properties of ethylene carbonate-water mixtures are such as to

require pretreatment and conditioning to insure reproducible results.

However, the experimental procedure followed was basically a stepwise

addition method utilizing weights rather than volumes for higher accuracy.

Thus, solute concentrations were initially low. Concentrations greater

than that of the addition solution were produced by the addition of the

electrolyte itself.

Ethylene carbonate has a tendency to leach ionizable impurities
4
fro glassware. To reduce the magnitude of this problem, cells and other

glassware in contact with ethylene carbonate during the experiments were

filled with conductivity water when not in use. This was not sufficient,

as a decrease in resistance with time was still observed when solvent

was added. Thus, before starting a run, it was necessary to allow the

cells to equilibrate overnight with solvent of the same composition as

that used in the experiment. The ellss were then rinsed and refilled

with fresh solvent, and its specific conductance determined (for use in

making solvent corrections).

The first addition of electrolyte after this pretreatment step

exhibited behavior opposite to leaching. Drift of the measured resistance

in this case was upward, in.plying a gradual loss of ions. The cell

surfaces now had t-o come to equilitri-um with the solute at its initiall







































































































low z WO "J) V UU.)flpJ'.) 9J In'At7LLD


0(
0


0

'-4
x






0
C)

0-

41)
0
14I



0
4
0
0

a)

C/


0*
N


>)

.C
41


C.)










U
M)








04
a)
44










0



0


U
(a
0








0


U












0 4
(n 4





r -
co












C4)
0







ru
4-4

u,4-
-rl

Ut)


0

-4
CW









concentration. This problem was more pronounced for the acids than for

the salts. Equilibrium was generally reached in 18 hours, as evidenced

by a constant value of the measured resistance. The initial conditioning

solution was then discarded; fresh solvent was added without rinsing and

the weight of the cell and solvent determined. The first weighed

increment of addition solution was added at this time. The cell was then

placed in the constant temperature bath and allowed to reach thermal

equilibrium. Figure 9 shows the difference between conditioned .and

unconditioned runs. The solution was indeed stable thereafter, as

evidenced by relatively minor changes in measured resistance (<0.01%)

which occurred overnight.

Addition of solutions directly into the cells resulted in splashing,

and drops of more concentrated solution collected on the sides of the

cells. The entire cell then had to be shaken to wash these drops into

the bulk of the solution. When using two cells, however, the possibility

of cell damage from shaking was significantly increased. To eliminate

the necessity of shaking the cells, a special filling cap was designed,

as shown in Figure 10.


rubber
14/24 joint- rubber
3-way bulb
stopcock





45/50 joint_



filling tube


Figure 10. Drawing o: a special filling cap.









The long fill tube extending to the solution level prevented splashing,

and the bulb and three-way stopcock allowed solution to be pushed up

into the fill tube to rinse it out. Both caps and stirbars were stored,

as were the cells, in conductivity water. They were also subjected to

the pretreatment and conditioning steps.

Addition solutions were kept in a weight buret or capped polyethy-

lene wash bottle. In earlier experiments, the ground glass joints of

the weight buret were frequently covered with crystals, causing potential

weighing problems. This "creeping" was the result of evaporation of

water from the solution. The crystals resulting from this evaporation

formed capillaries which then drew more solution up, leading to further

evaporation. Crystals would frequently cover the entire bottom of the

buret. This experience made it necessary to find alternatives to the

weight buret. The use of polyethylene wash bottles eliminated this

problem and offered other advantages as well.


Preliminary Data Handling

As the conductance bridge was designed to use the four-lead

technique, all resistance data are the means of the resulting two

readings. Measurements were made with alternating current rather than

direct current to eliminate composition changes resulting from electrol-

ysis. Hence, provision had to be made for separating the ohmic resis-

tance from capacitance effects ani other frequency dependent terms.

This is generally done by taking measurements at various frequencies

and then extrapolating to infinite frequency. Many of the various methods

of frequency extrapolation have been discussed by Hoover,2 and his

recommendations were followed. T.e :achnique used is also discussed by








54
Robinson and Stokes,54 who consider it applicable to bright platinum

electrodes in aqueous solutions. It is based on an equation of the form:

R
R R + (28)
measured ohmic 1 + aw2

where:


F -1
S W 2 F 2
3 2

and:

F 2
S2 2 R R
F 3 2 1
2 9
W 2 R R
1 2 3 1


w has the usual form of 2TTJ. The measured resistance was plotted against

(1 + aw )-1, and the intercept at infinite frequency (where the second

term on the right of equation (28) = 0) gave the value of the ohmic

resistance.

Equation (28) was cnly useful over a limited resistance range,

however. When the measured resistance is very high (as with pure solvent

or very dilute solutions), resistance increased with frequency rather

12,15
than decreased, which is considered normal.1 Application of

equation (28) to these anomalous frequency results caused a reversal of

the u2 dependence. This reversal of the dependence resulted in an

intercept of unknown meaning. The effect has been described by Mysels

et al., and is attributed to leakage to ground along a resistance and

capacitance in series. They conclude that extrapolation to =ero frequency

is the correct procedure for extracting the ohmic resistance of the cell.

This was the procedure followed in this work.

To convert the value of the ohnic resistance to the specific

conductance, a knowledge cf rhe cell constant is required. The cell









constant was determined by measuring the resistance of a solution of

known specific conductance. The accepted standards for cell constant

determinations are aqueous solutions of potassium chloride as described
14 56
by Jones and Bradshaw.14 A more recent work by Fuoss et al.56 gives an

expression which allows the calculation of the equivalent conductance of

aqueous potassium chloride at 25 OC at any concentration up to about

0.04 M. Their equation is:

A = 149.93 84.65/c + 58.74clogc + 198.4c (29)

where c is the concentration in moles per liter.

The experimental procedure of the usual runs was followed in its entirety.

This produced a set of measured ohmic resistances and concentrations.

From equation (7), we can write an expression relating the specific

conductance Kto the cell constant 6 (equal to A ) and the solution

resistance R :
s
K (30)
R
s

If the assumption is made that R = R (the measured resistance after
s m

frequency extrapolation), equation (30) can be rearranged to give:


R =- (31)
m K

If the experimental R is plotted against K''(which can be calculated
m

using equation (29) and equation (8)), the slope of the line will be the

cell constant. As many points will be used in the determination, a

linear least squares fit can be used. An example of such a plot is given

in Figure 11. This plot includes data from three separate runs and

demonstrates the reproducibility of the technique.

No definitive standards for solution conducti'.ity have been

proposed for tem-pratures other than 0, 16, and 25 'C. Thus, -el.




















U

1500


C


0
U


04
U
U















Q i0 run 1
E4
w



-4
it








A run 3

500







500 1000 1500
Measured resistance, R
m

Figure 11. Plot of the inverse of the calculated specific conductance vs.
the measured resistance.









constants at 40 OC were determined by calculations based on cell design

and the coefficients of expansion of Pyrex glass and platinum. This
57
calculation is described in detail by Robinson and Stokes. The cell

constants thus calculated were on the order of 0.02 percent less than the

corresponding values at 25 OC.

The concentrations of the individual solutions were determined

on the basis of the total amount of addition solution used and the

initial weight of solvent present in the cell. Since all additions were

in terms of weight, it was most convenient to use molality (moles per

1000 g of solvent) for these determinations. In calculating the

equivalent conductance, however, the concentration is expressed in terms

of moles per liter. A convenient relation between themolality, m and
58
the molarity c, is given by:5


1000pm
c = 10 (32)
1000 + mM
solute

To apply this equation one needs a knowledge of the solution density, p.

Densities of the various solutions were determined at a single concentra-

tion. Densities at other concentrations were assumed to lie on the

straight line defined by the measured solution density and the pure

solvent value. Once the concentration was known,the equivalent conduc-

tance could be calculated using equation (8).

Calculations up to this point were all done on a Hewlett-Packard

model 55 programable calculator. (Power series fits of mixed solvent

parameters and the linear least squares fits of the potassium chloride

cell constant determinations were done on a Wang 600 series programable

calculator.) Several "programs" were written especially for the

calculation of these results.




40



KEQIVES Program Description

The facilities of the Iortheast Regional Data Center of the

University of Florida were used for more complex calculations involving

Pitts' relation (equation (24)). The Fortran IV program used for the

final analysis of the equivalent conductance data was that of Duer, Robin-
41
son, and Bates. Some modifications were added to increase program

efficiency and alter the printout format.
59,60
The program utilized an iterative procedure of Ives, 0 which

is based on an expression for the dissociation constant Kd:


C 2Y2
c.y
d (33)
d c
u


Here the subscript i denotes quantities based on the ions present in

the solution. The subscript u denotes undissociated molecules of

electrolyte (the activity coefficient in this case is assumed to be equal

to unity). The degree of dissociation can be expressed as:


S= A. (34)
1

Hence, one can write:



A
c. = ac = c (35)
1 A.


similarly, for c :



c = (1 )c = (A. A) (36)
u A. I




41




Combining equations (33), (34), and (36) yields:


A2cy+ 2
K = (37)
S A.(A. A)
1 1

59
In Ives' paper, the theoretical basis for determining A. was Onsager's

limiting law, equation (161. In the present program, however, Pitts'

equation is Lused. If A symbolizes Pitts' theoretical expression for

determining A. frcm A equation (37) becomes:

A cy, 2
K = (39)
S A. (A + A ) A
I r



This expression can be rewritten as:

S 1A2Cy+ 2
A A A ---- (39)
r A.K
i d



which can be reduced to the form:

= A1
y = A :< (40)
Kd



where:


Y= A A
r

A2cy2
X A
A.,2



Equatic, (40) is in the form of a straight line, and A and K
a

(equal to ) are intercept and slope, respectively. As A is used to
d
calculate A an initial estimate based on extrapolation of the A against /c
r

was .rovidd. z-..f-r following the above procedure, least squares









analysis gives a new estimate of A The procedure is repeated with

this new A generating another set of X and Y values and another A

and K Five of these interactions were more than sufficient to reach
a
values of A and K which were constant.
a
In Ives' paper, the Debye-Huckel limiting law expression:

log f2 = -2AzIz2 1/I (41)

was used to determine the activity coefficients. However, the more

complete expression (equation (26)) was used in the KEQIVES program.
61
As a check of the program the data of MacInnes and Shedlovsky1

for acetic acid in water at 25 *C were analyzed. Table 1 compares the

accepted values of A and K with those determined by the program (the

ion size parameter in each case was 4 1).



TABLE 1


Comparison of the accepted values of limiting
equivalent conductance and association constant
to the values determined by the F-EQIVES program
for acetic acid in water at 25 "C.


A (P-1 cm2 mol-') Ka (liter mol- ) x 105

Accepted 390.71 1.753

KEQIVES 390.59 1.750


a = 4.0, Azcepted values from Pobinson, R. A. and
Stokes, R. H., Electrolyte Solutions, 2nd. ed., revised,
Butterworths, London, 1970, pp 336, 339.
















CHAPTER V

RESULTS AND DISCUSSION



Relevant Properties of Ethylene Carbonate

Ethylene carbonate is an interesting solvent with many unusual

properties. It is generally considered to be a cyclic ester, and has

been listed in Chemical Abstracts under the heading: Carbonic acid,

cyclic ethylene ester. Since volume 76, it has been listed as 1, 3-

dioxolan-2-one. The common name, ethylene carbonate, has been used

throughout this study.

The structure of ethylene carbonate is that of a heterocyclic

five-membered ring incorporating a carbonyl group. Bond lengths and

angles have been reported by Brown62 and are reproduced in Figure 12.


0
3



1.15A

C
o 3
111 o
1.33A
0
O 109








2 1


Figure 12. Euhvl-ne carbonate molecule, showing
bond angler ard distances.

43
43








The large permanent dipole noment of 4.87 debyes3 is responsible for

its large dielectric constant: (90.36 at 40 OC).

X-ray diffraction studies show that solid ethylene carbonate

consists of layers.62 The c.rbonyl groups are parallel in any given layer,

but in alternate layers they are opposite in orientation. The unit
62
cell of crystalline ethylene carbonate as determined by Brown62 is shown

in Figure 13.










3.541A

0
3.11A












Figure 13. The unit cell of crystalline
ethylene carbonate

The closest intermolecular distances between layers are associated

with carbonyl oxygens and et.ylene hydrogens. Various other C-H-0

alignments occur as well, some of which are indicated in Figure 13.

This close approach is an indication of strong dipole interactions, or

possibly the presence of scene hydrogen bond character.

In the solid state, --he carbonate group is planar, with the C -C

bomd forminganangle of 20" to tt.!e carbonate plane. In the licuid scate,
b n ~\ fein anage f2T \








there is evidence that ethylene carbonate is planar except for the
64,65 66
hydrogen atoms, as postulated by Angell.66 A more recent study

concludes that the carbonate group remains planar, but there is a small

nonplanar ring-puckering motion of the ethylene group.6

Ethylene carbonate is generally considered to be slightly associated.
68
Values of the Harris-Alder correlation parameter68 and the Kirkwood

parameter69 indicate slight association. Bonner and Kim70 have studied

osmotic coefficients of ethylene carbonate in benzene, and observed

non-ideal behavior. They conclude that the primary reason for this

non-ideality is association. They also report "clusters" in ethylene

carbonate averaging 8.3 monomer units in size, and that the carbonyl

group is involved in the association. However, the expected carbonyl

association would result in a major cancellation of the dipole moments.

The high dielectric constant is evidence against structures similar to

those present in the solid state. An alternative possibility is the

presence of hydrogen bonds, although this is also unlikely, as carbon

is not considered electronegative enough for their formation. This would

be an interesting area to investigate in future studies.

As an electrolytic solvent, ethylene carbonate is unusual. The

alkali metal chlorides are almost insoluble, as mentioned previously.

The chlorides of Hg(II), Fe(II), and other heavy metals are soluble,45

as are alkali metal perchlorates and tetraalkylammonium halides.5

This behavior is a result of poor anion solvation and the greater

degree of salvation of the larger, more polarizable cations. Ethylene

carbonate can be classified as a dipolar aprotic solvent using Kolchoff's7

extension of Davis' classification scheme, and has moderate Lewis base

properties.









Mixed Solvent Properties

Ethylene carbonate has a relatively high cryoscopic constant of

5.40 C/mol.47 Hence, mixtures with relatively small amounts of water

should remain fluid at 25 C. This behavior was observed, and composi-

tions up to about 90 mole percent ethylene carbonate have been reported to
72
exist as liquids at 25 C.72 The mixtures tend to supercool readily, as

does ethylene carbonate itself.
70
Bonner and Kim report self-association of ethylene carbonate in

benzene but note that in solvents of high dielectric constant the

association is much less. Hence, little self-association of ethylene

carbonate in water mixtures is expected until the fraction of ethylene

carbonate is quite high.

A plot of density vs. mole fraction is shown in Figure 14. The

plot exhibits positive deviation from ideality, which usually indicates
73
association between the two components. Geddes has indicated that the

composition at zhe maximumdeviation from linearity is that of the

associated species. As an aid in determining this point of maximum

deviation of linearity, the excess density, Ad, is plotted with the

density. The excess density was calculated from the expression:

Ad = dm (x d + x d ) (42)
1 1 2 2

Here dm is the experimentally determined density at a given mole fraction,

while d and d are the densities of the two pure components of the
1 2
mixed solvent system. x and x are the mole fractions of the two

components. The excess density is plotted in the lower part of the figure

using the same mole fraction axis as for the density. It displays a broad

peak with a m.-ximu. at a mole percent of approximately 33 at both 25 and

and 40 'C. This ccrresco.ds to an association between one ethyle'e






























Figure 14. Plot of density and excess density vs. the mole percent
ethylene carbonate.


Note: data for this plot were obtained from the following sources in
addition to this work.

G. P. Cunningham, G. A. Vidulich, and R. L. Kay, J. Chem. Eng. Data, 12,
336 (1967).

A. D'Aprano, Gazz. Chim. Ital., 104, 91 (1974).

R. A. Robinson and R. H. Stokes, Electrolyte Solutions, 2nd ed., revised,
Butterworths, London, 1970.



























































40


60


cl--e perc-t:t etihylcn-, carbonate-


1.3







1.2






I.I
cn
a











1.0




0.10
J.J
Ln
C
c
ra
Un

I 0.05






0.0O


20


80








carbonate molecule and two water molecules, most likely by hydrogen

bonding involving the carbonyl oxygen. However, the peaks are broad and

it is doubtful that any definite composition is present.

The change of the dielectric constant with composition also shows

positive deviations. However, the corresponding excess values exhibit a

shift with temperature, as sho.rn in Figure 15. At 25 OC, the excess

dielectric constant is a maximum at about 20 mole percent ethylene

carbonate, while the maximum at 40 OC corresponds to 40 mole percent.

The'data for the dielectric constant appear less precise than those for

the density. This fact must be taken into consideration when conclusions

are drawn relating to the plot. Nevertheless, the possibility of some

form of association with water exists. When the temperature is as high

as 40 OC, the association is reduced through thermal agitation, and a

composition closer to a 1:1 ratio may be favored.

As shown in Figure 16, the plot of viscosity vs. solvent composition

also exhibits interesting behavior, again best illustrated by the excess

quantity. While the viscosity does not go through a maximum as observed
74
in the strongly associated dimethylsulfoxide (DMSO)-water system, there

is a point of inflection. In the region of low mole fractions, the plot

behaves in the same manner as the previous two, a fairly rapid rise being

followed by a slight leveling, which is earlier in this case. As the

concentration of ethylene carbonate increases, a reduction in viscosity

occurs possibly due to formation of the 1:1 species. This 1:1 species

probably has less structure than either pure water or pure ethylene

carbonate. However, the compositions with more water retain more of

their structure than the compositions with higher ethylene carbonate

*:Cncentra.tion. This is evidn.nced by the negative. dev'.iations of -he








































Figure 15.


Plot of dielectric constant and excess dielectric constant
vs. the mole percent ethylene carbonate.


Note: data for this plot were obtained from the following sources.

R. A. Robinson and P. H. Stokes, Electrolyte Solutions, 2nd ed., revised,
Butterworths, London, 1970.

R. P. Seward and E. C. Vieira, J. Phys. Chem., 62, 127 (1958).

























0 25 C

D 40 C


0
o


20 40 60
Mole percent ethyler.- :crbcnate


80


90


85


75




2.0


1.0


100





































Figure 16. Plot of viscosity and excess viscosity vs. the mole percent
ethylene carbonate.




Note: data for this plot were obtained from the following sources in
addition to this work.

G. P. Cunningham, G. A. Vidulich, and R. L. Kay, J. Chem. Eng. Data, 12,
336 (1967).

R. A. Pobinson and R. H. Stokes, Electrolyte Solutions, 2nd ed., revised,
Butterworths, London, 1970.








2.5







2.0




>1
4-1
.,I
Ul

- 1.5







1.0







0.2


40 60
Mole percent ethyle:.e carbonaate


0 25 C
o 40 C


0.I



0.01


-0.1


20


80


100








excess function at the ethylene carbonate end of the plot. Apparently

water is better at destroying the existing ethylene carbonate structure

than ethylene carbonate is at breaking up the hydrogen bonded water

structure.

Bonner and Choi75 present evidence that propylene carbonate-water

mixtures of Low water concentrations (mole fraction less than 0.1) contain

both a 1:1 species and a 1:2 species (one water molecule to two propylene

carbonate moLecules). This is perhaps the case with ethylene carbonate

as well. The 1:2 species would be less likely to participate in further

hydrogen bonding, and its formation is probably associated with the

ethylene carbonate structure breakdown. As the concentration of water is

increased, tri-e 1:1 species would predominate, and the increased chance

of hydrogen --.nnded chains would be less disruptive to the water structure.

As concp-:ed to other mixed solvent systems containing ethylene

carbonate, the relatively small positive deviations from linearity are

significant. Cne would expect that the addition of an-organic species

would disrupt tzhe structure of the water. The lowering of temperature

when the aixed solvent is prepared would be experimental evidence for

such a breakoAwn of the water structure. Heat must be extracted from

the solution to break the hydrogen bonds present in the water. Indeed,

on mixing ettpylene carbonate and vater, the temperature was reduced

sufficiently bt cause the formatic*- of crystals of ethylene carbonate.

Considering ti:1s reduction in structure, large negative deviations

from linearit.rr would be expected, rather than the small positive devia-

tions actually observed. Similar behavior has been observed in the

DMSO-water system and attributed to a strong interaction between the

two components' Perhaps at lower mole fractions of ethylene carbonate,









the ethylene carbonate molecules can fit into the larger gaps of the

diffuse quasi-lattice of water77 with minimal disruption. However,

as more ethylene carbonate molecules are added, smaller caps must be

used resulting in more structural breakdown- and more association between

the two species.


Plots -f A vs. /'c

The usual method of presenting conductance data is by plotting

the equivalent conductance, A, vs. the square root of the molar concen-

tration, c. Strong electrolytes w:th little or no association give linear

plots, and extrapolation to the limiting equivalent conductance, A ,

at zero concentration is straightforward. Data for electrolytes with

higher association constants exhibit curvature at the lower concentration

regions when treated in this manner. In this case, extrapolation becomes

more difficult without the aid of additional manipulations of the data.

Puoss and Accascina7 describe the changes in; the conductance

curves as the electrolyte is chanLeiS from one which is completely

dissociated to one which is stro-lyv associated. The curvatures

described are arbitrarily divided into six types. As an aid to classifi-

cation, the Onsager tangent is included with the conductance curve. The

numerical value of the Onsager tangent has been given previously as the

factor in brackets in eauation(171:


A A.2S-204 x 10 m 82.501 /
A = A 4 x 10 -c (17)
(CT) / 1/2


The line showing the Onsager tangent in the following plots was generated

by utilizing the experimental A and calculating the value of A at a

concentration of 0.01 molar accord:'._ to equation (17).









Figure 17 is an example of type I. This behavior is typical of

the majority of 1:1 salts in water and other solvents of high dielectric

constant. Type I plots exhibit increasing positive deviations from the

Oisager tangent as the concentration is increased. The data of low
CO
concentration fall on the Onsager tangent. A is easily determined from

this straight-line segment of the plot by simple extrapolation to zero

concentration.

Behavior intermediate between Fuoss and Accascina's types I and II

was exhibited by some of the data in 20 mole percent ethylene carbonate

(see Figure 18). The experimental points fall on the Onsager tangent up

to relatively high concentrations. A is again easily determined by

extrapolation to zero concentration.

Type II is shown in Figure 19. It is characterized by a straight

line with a slope somewhat less than the Onsager tangent. A can still

be determined by extrapolation to zero concentration. Type II is

generally characteristic of solvents with moderately low dielectric

cznstants. Due to this decrease in dielectric constant, ion pairing is

beginning to occur.

The majority of the data in this study exhibit type III behavior,

as exemplified by Figure 20. The conductance curve is straight or

concave to the Onsager tangent at relatively high concentrations, and

approaches the tangent only at very low concentrations. A linear

extrapolation to zero concentration will result in a value for A which

is high. In this case, ion association has increased sufficiently to

bring an inflection point with an associated linear behavior into the

usual experimental region. With this behavior, it is suggested that the

ir.acrpnraticn of 2, the degree of dissociation, into the theoretical












0 -
N -4

O
0


0
-.1






0


0



0 O





-I 0

a c 0
0 0 ( a




(- 44 u
0I
1-U 1



0 0

O Oo
O U
0
4CN
a) 4)




W Q0
S1 >a
S*H 4






ra

0


















low u., ;, 4Jeouy-) nr~uo ;'"'l2.'.T `.
















Ua)
Sc




C




Co
>1
u








OL
u








o
S0
(



1LI
C 40
Q Imo )o




S> i- a


O 3C
O CO)











4 .Q
CC
00 2
S0 r_





















OOi
-1
















.C C
Jc cra




r_ a
141 O






















) 4
0 0
Ei


O o eo






0 a aj0




c!



S0 u




ui 0




59















U')
Jo
N









CI)
a0

0

:4

0
Hc


H 24 0
.4.
m0



00










0











)e
I 0 ~c
LO,


















V~~~u e~u:ruz u.:2Anb2 -




60





6O
--1T

0
4-I
C

Li


C
J .0
/ 0 u




o



-' 0


,-4 o Q 1n
0O


I O I >1
0


S n u
I H


O u
U r(
L r-





o 0

C 0*




r-.
0c u

..-i
O 4 J
r 'O N
O U














LO
0 0
















0 0
ar















N -
IC I N
S0 *a
I f i1r
V ' P If 1-l
/ _/ -< 1
/ 0 &

I f <"








expression is necessary to accurately describe the behavior of the

curve. This is done simply by replacing the concentration c by ac. One

should recall, however, that this results in calculation of A.. To
1
generate a calculated A, it is necessary to multiply A. by a.

Type IV behavior occurs when ion association moves the inflection

point to the low concentration region of the plot. An example is shown in

Figure 21. Large errors in A result from linear extrapolation to zero

concentration. Ion pairing is extensive, and the use of the mass action

relation (equation (25)) is recommended.

All of the data for acetic acid exhibit type V behavior, as shown

in Figure 22. As can be seen, type V typically exhibits extremely low

values of the equivalent conductance and high curvature. However,

type V usually goes through a minimum which is a result of triple ion

formation. No such miniinum was observed for either acetic acid data or

hydrogen chloride data at any composition, including pure ethylene

carbonate. Hence, it appears obvious that the solution properties of

ethylene carbonate permit ion pairing to occur (producing the large K
a

values). However, the high dielectric constant does not favor triple ion

formation.

None of the data in this study are representative of type VI.

This behavior is usually associated with the very low dielectric

constants of hydrocarbon solvents and with complex structures due to

multiple clustering.

It is interesting to note that this gradual progression from type
78
I to type V (or VI) was attributed by Fuoss and Accascina78 to decreasing

dielectric constant. In the case of ethylene carbonate-water, the

progression follows the increasing, ethylene carbonate ccn:entration, or











C-


u
0
44i

0

J












0 0 0
U








I
0

0








0 0




,Li a

o '%
O
p O ..






0 0.
DC 0





0 0
I C ) fa









0n0 :
) c u






4 r:
/u O



C) CJ. f












(>00
UO











W E
I I I I






















0 a 0 0








1 '1 r') a,
x








I Q ?
%4 1
V
I / c*
In / ("
/0 a piQ <
/ P au~~~~ >,ae;T 1




63







0 u


4-4
0


0
4-J








0
0








x
0



o O
to


x u









o (d
4-

4J >
0 0
O U



0 'u
C (U



0 o



o o
d4-

















I I
0 U) z.



v0


0 0 (






4-



0)


-40





.4 C )
/aulopo zur*1u%7nc3









increasing dielectric constant. The experimental data thus provide

additional evidence that the patterns of ionic dissociation and

association are as profoundly influenced by ion-solvent interactions

as by changes in the electrostatic (Coulomb) forces between oppositely

charged ionic species.


Fit to Pitts'Equation Assuming K = 0
a

As evidenced by A vs. /c plots, the data at 20 mole percent

ethylene carbonate suggest that little or no association is present for

the salts or for hydrogen chloride. Accordingly, the program was modified

to fit the A c data assuming a = 1.0 and K = 0. However, no satis-
a

factory fits were obtained using this procedure. The criterion usually

used to determine the best fit (and consequently the best value of a,

the ion size parameter) is the minimum value of the standard deviation

between the experimental t\ values and calculated A values. The calculated

A values are determined using the Pitts'equation and the A value deter-

mined by the coordinate transform line. The general trend of results

using the modified program was increasingly poorer fits as a was increased,

with no minimum observed (except perhaps, at unreasonably small values

of a). The results for a = 3.0o, a reasonable value based on Bjerrum's

theory, are sutmnarized ir- Table 2 Despite initially setting K = 0,
a

the program still produced non-zero values for K
a
79
As a check of the program, the data of Prue et al. for lithium

perchlorate i-r hexamethyLphosphotriamide (H.PT) were treated by the

program under the same conditions. In this case, the results were more

reasonable. Values generated for K as the ion-size parameter was

chan at rst. However, as 3 was creased, cam
a









positive, and was equal to zero when a was at the value reported by

Prue et al. Hence, it appears that there is a nonzero value of K
a

associated with the data for 2. mole percent ethylene carbonate.


TABLE 2

Summary of calculated conductance parameters for NaC1, NaAc, HC1 in
20 mole percent ethylene carbonate at 25 and 40 OC assuming K = 0.
a

A (Q-1 cm2 mol-1) K (liter mol-1)
a

250 NaCl 73.26 0.02 1.35 0.06
NaAc 55.99 0.01 1.78 0.07
HC1 199.08 0.03 0.346 0.003


40 NaC1 98.70 0.01 1.08 0.02
NaAc 77.31 0.04 2.11 0.46
HC1 248.26 0.03 0.587 0.007

0
a = 3.0A, 95 percent confidence levels.


Fit to Pitts'Equation Assuming K a 0


Treatment of the data with the full, unmodified KEQIVES program

(see appendix) gave satisfactory results for both salts and hydrogen

chloride. Results of the data for acetic acid were unsatisfactory,

with the only reasonable fits occurringat a composition of 20 mole

percent ethylene carbonate. The analyses of the acetic acid data and

the hydrogen chloride data in 80 mole percent ethylene carbonate and pure

ethylene carbonate are discussed in a later section.

The results of the computer analysis for sodium chloride, sodium

acetate, and hydrogen chloride are summarized in Table 3. The value of

the ion size parameter a corresponding to the minimum in the standard

deviation of the calculated and experimental equivalent conductances

was taken to be the correct distance of closest approach. However,

the fit is so..ewhat sensitive to experimental errcrs in the data. Of

the calculated parameters, the value of A generally is changed the









TABLE 3


Summary of calculated conductance parameters for HaCl, NaAc, and HC1 at
25 and 40 C assuming K / 0.
a


M A' (Q' cm2 mol ')


25 OC laCl


73.15
51.765
46.477
42.880


0.02
0.004
0.002
0.005


K (liter mol-I)
a


1.06
3.30
5.53
7.93


0.03
0.01
0.01
0.01


NaAc 20 55.93 + 0.01 4.38 + 0.02 13.4
40 41.413 0.003 10.33 1 0.01 17.0
50 37.82 + 0.01 14.2 1 0.03 >24
60 35.95 0.01 19.7 + 0.06 124


HCI 20
40
50
60


40 OC HaCl 20
40
50
60


198.S0
102.06
75.96
58.75


98.69
71.33
63.20
58.09


0.01
0.01
0.01
0.02


0.01
0.01
0.03
0.01


1.35
2.53
5.67
9.65


1.01
3.53
6.47
8.31


0.01
0.02
0.07
0.07


0.02
0.01
0.03
0.02


10.5
2.40
2.90
2.70


2.80
3.90
13.5
16.5


NaAc 20 77.05 z 0.01 6.15 0.04 >24
40 58.15 0.01 9.98 0.01 17.8
50 52.81 0.01 14.26 0.01 >24
60 49.21 0.02 18.2 0.1 >24


HC1 20 248.26 0.03 0.44 0.02 2.50
40 130.76 0.06 2.09 0.04 2.35
50 97.28 0.02 4.79 0.03 2.40
60 76.41 0.04 8.21 0.10 2.90
80 49.39 0.08 49.1 0.5 5.10


95 percent confidence levels

M mole percent ethylene carbonate


o
a(A)

2.85
2.88
5.55
10.3









least by the inclusion of poor data, remaining essentially the same.

The calculated values of K changed by a greater amount, but, in general,
0O
the standard deviations of K values were greater than those of A and
a
changes were less than the standard deviations. The value of a, the

distance of closest approach, was much more significantly affected by

the inclusion of poor data. The changes in A and K above reflect
a

the change in the minimum point rather than the change in the data.

For the same a value, for example, the A and K values for data sets
a

with slightly different groupings of the total number of data points

generally would be changed by an amount of the order of the standard

deviation of the two parameters. At this point, then, it is possible

that the variable parameter a has more of the character of an empirical

fitting variable than that of a true physical parameter.

The sodium chloride data sets appear to be the best behaved. This

is due to the fact that the solvent correction in the case of sodium

chloride is unambiguous, and there is no possibility of reaction. The

values of the parameter for sodium chloride are most likely to have

a precise physical meaning, corresponding to the distance of closest

approach of free ions.37 Ions of opposite sign approaching closer than

the association distance are assumed to be paired and do not contribute

to the conductance. At this point, there is some ambiguity as to inter-

37
pretation. Prue et al. equate the a parameter generated by the Pitts

expression (and other similar expressions) to a so-called "association

distance" d. This is not the ion contact distance, which they symbolized by

a. It is not clear if the association distance d is that of solvated ions

in contact, or merely indicative of the fact that ion pairs can exist

as stable entities while nct in ccn.act with each other. Howeve-r, -he








a parameter is generally taken as an ion size parameter. From the

data in Table III, we see that the size of the sodium chloride ions

increases with increasing concentration of ethylene carbonate in the

solvent mixture. This is expected, since solvation by the larger

ethylene carbonate molecules would increase as the concentration of

ethylene carbonate increases.

The data for hydrogen chloride are less consistent than those

for sodium chloride. However, the trend is for a to remain essentially

constant throughout the entire composition range, rather than the

increase observed with sodium chloride. This is due to the different

natures of the hydrogen and sodium ions. The hydrogen ion is smaller

than the sodium ion, and thus size would place steric limitations on

solvation by large, bulky molecules. The larger sodium ion is more

polarizable than the hydrogen ion, and the effects of size and polarization

imply more solvation of the sodium ion. There is evidence that in the

propylene carbonate-water system, water is strongly bound to the chloride
80
ion. One would expect similar behavior for ethylene carbonate, and

the size of the solvated chloride ion is probably constant over the

composition range of Table 3.

The poorest consistency is with the data for sodium acetate. This

is possibly due to problems associated with solvent purity and the solvent

correction. The purpose of the solvent correction is to eliminate the

conductance of the solvent from the experimentally determined solution

conductance. For sodium chloride, the normal solvent correction would

simply involve the subtraction of the conductance of the solvent from

the experimental conductance. For acids and bases, however, the appli-

cation of the correction is not as straightforward. The major security









in the solvent mixture is the carbon dioxide present in the conductivity

water. The recommended procedure for acid measurements in this case is
81
to make no correction, and this was followed for the measurements of

hydrogen chloride. For salts of strong bases and weak acids (sodium

acetate), a pcitive correction is recommended,81 but its magnitute is

not easily determined. However, the use of the normal correction appeared

to be more satisfactory, and this procedure was followed. Possibly the

data at low salt concentrations, where the solvent correction has its

greatest effect, are responsible for the deviant a values. However,

the values are consistently high, and some form of solvation involving

the carbonyl groups cannot be ruled out at the present time.

Figures 23, 24, and 25 show the behavior of the limiting equivalent

conductance of hydrogen chloride, sodium chloride, and sodium acetate,

respectively, as changes of solvent composition take place. The general

trend of a rapid decrease as the concentration of ethylene carbonate

increases is evident. The major portion of this decrease is probably

a result of the reduction in ion mobilities due to the increase in

viscosity of the solvent, as well as a reduction in the number of ions

due to increasing association constants. The much larger drop-off

observed for hydrogen chloride is the result of the high initial

conductances in water, presumably due to the proton jump mechanism.

The water structure favoring the jump mechanism is disrupted by the

addition of the ethylene carbonate to the water. Hence, hydrogen ions

behave more "normally" in solvents with large amounts of ethylene

carbonate present.

A convenient param.cter which allows one to remove the influence

of the viscosity : on- t.he variations in ion ccnductance is the produce:










O u

0
ao









-i



a


U U3

U .






o o C







I2 0
n 0 II













I .-. s
00 0









.Q U






4J











0
4Li










-4
..o r.















0 0





'A





0
n0





-,4
0 c'J
*-I


-1.




71


o0 u
0 0
oo
0





CN
Jj
I-,



z
r-
U
0 i(


'4-4
) 0
4.
U U C
o a 0
.Q


SC






0 0






0
0) 0








0




0
SI.








lo
c1















0 0
C 0
*r C)
.) ".
















/ f c
0
-I





'4-J










---I-c^-------- <----------- ;o aT'uT


rj-
c









0
o





c)
CM



41






V



L0
Co 3




a4









QIV


C00
L"O
SC: a,

U4 U








OI 0
Ila C:
U









00
4J 04









Ov E
J >
U 1)























0.
-0J












C J



*0
*-4

















I 00
Li












-J'(








of equivalent conductance and viscosity, called the Walden product,

symbolized by A T. The Walden product was initially assumed to be
82,83 84
constant283 for different solvents, but later work revealed variations.84

While today it is not considered quantitatively reliable, it is useful

for limited comparison studies. As shown in Figure 26, a plot of the

Walden product vs. solvent composition for the two salts does reveal

approximate constancy. However, the Walden products for hydrogen chloride

data show a decrease from an initial high value which is evidence for the

disruption of the proton jump mechanism.

A somewhat clearer picture emerges if we plot the Walden product

against the solvent parameter 100/E, where E is the dielectric constant

(see Figure 27). The conclusions reached above are still valid, but

it is more apparent that the value of the Walden product for hydrogen

chloride is approaching that for the salts as the fraction of ethylene

carbonate increases. It also appears that each salt reaches a constant,

though different, value of A T.

The association constant, K behaves very much as expected as
a

solvent composition is changed. As the mole fraction of ethylene

carbonate is increased, the association constant increases, due to the

decreased solvating power of the solvent system, as shown in Figure 28.

Sodium acetate is apparently the most affected by the addition of

ethylene carbonate, since its K increases more at lower concentrations
a

than does that for the other electrolytes. This is due to the fact

that the chloride ion is more easily solvated by water and perhaps

also indicative of a specific interaction between ethylene carbonate and

sodium acetate.

It is also intereszInq to compare the behavior of hydrcqe:i

chloride with the salt. At lo. concentrations of ethylene carbonate





























u 0
0 0
U, Un
r' CN


UV I-n:oid uaprvbl


U 0
0 a
LIn 0
CN *


u 0i


0 O -0


0
0













0













Oc
(D 0
a,
(~g


C,




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C,

U)
0r




0
Nk


-Jo
0
.F,












U U U U.O
o U 0 0 0 0
0 0
L0 o o o

-n o 0r



u u ru TO r.
= z z z z

S-0 -0 0- uD-


S


LiV 'a 0n o ad u .p I: ,


i-q


-IT
u








o









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a
rl


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.-



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C.,
















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*
00
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2 r




u





a)
3r~
ScT

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'Ije2:so03 uoll0t:OSsv


SC~J <
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o 1C .3
X- z

0-0 0-


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co




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cf
C-


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u










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-,













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01.
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the K 's are lower for hydrogen chloride than for the salts. As the
a

mole fraction of ethylene carbonate continues to increase, the hydrogen

chloride curve crosses the sodium chloride curve and perhaps even the

curve for sodium acetate. This is a further indication of the basic

difference between the hydrogen ion and the sodium ion. It is the

result of the greater ease of solvation of the sodium ion and the

consequent increased probability that dissociation will occur.

Plotting the association constant vs. the parameter 100/E, as

before, reveals a clear distinction between the behavior at the two

temperatures (see Figure 29). At each temperature, the sodium acetate

curves are higher than the others, supporting the conclusions made

earlier, although this method of presentation perhaps makes the distinctions

clearer. However, in general the slopes are positive rather than negative.

Thus, another example of a reversal of the usual dependence on dielectric

constant is illustrated by these results.


BjerruT Theory of Ion Association

One of the problems relating to ion association concerns the

definition of an ion pair. The problem is basically whether or not

actual physical contact between ions is necessary for association. The

basis for most of the relationships concerning ion association is the

85
work of Bjerrum.8

By definition, ion pairs must retain their identity for a long

enough time for their exLstence to affect the surrounding solution.

Bjerrum proposed that all oppositely charged ions within a certain

critical distance be considered associated into ion pairs. Based on

considerations of the Poiszon-Boltz.manr. distribution of electrostatic

forces, this critical Jist.-nce, q, is found to be the distance w..:re








the electrostatic potential energy of the two ions is 2kT. Hence, the

expression for q is:


Iz z |e2
q (43)
2EkT


Bjerrum, using standard procedures, formulated an expression for

determining the number of ions N of opposite charge about a central

ion in a shell of thickness dr, at a small distance, r, from the central

ion:

S iz z le2
N = 4 n.exp .- T2 r2dr (44)
1 EkTr


where n. is the number of ions per cc. The interplay between nearness

to the central ion (where one would expect to find more ions due to

attractive forces) and the increase in the shell volume as r is increased

results in a minimu-n. The expression for q, the critical distance, can

be derived frcon equation (44).

The degree of association, (1-a), can be determined by finding the

number of ioirs in the shell starting at the distance of closest approach

to the critical distance. This is a simple integration, as shown:


/ / z Je2
(1 ) = 4n. exp (- 1 r dr (45)
a EkTr /


Using suitable transformations, equation (45) becomes:



(1 C) = 2 Q(b) (46)
1000 EkT




80




where:

z z2 le2
b =
EkTa


and:

b
Q(b) = x- edx



In this case:

2Z2
|z z le
2 = 1 2
EkTq


and:

zI z 2e2
x = r
EkTr


From the law of mass action, one can write:


K = (47)
d 1 -c


If the assumption is made that the solutions are very dilute, = 1

and y 1. Now, combining (47) and (46) results in:


1 Ct 4T (T z Iz 2e Q(b) (48)
K a c 1000 AkT


85,86
Values of the integral Q(b) have been tabulated, and a

more recent statistical treatment results in an asymptotic expansion of
87
Q(b) giving:8


S4TNa eb (49)
K -
a 1000 b

88
Fuoss, however, suggests that only ions In contact can correctly

be considered associated. His analysis of the problem results in:










3b
4TNa e
K = (50)
a 3000


Experimentally,determined K values for the electrolytes are
a

compared with the calculated values in Table 4. Equation (49) is

used rather than Bjerrum's original expression, as the high dielectric

constant resulted in values of b less than 2, the lower limit of the

tables. B. is the value calculated using Bjerrum's expression, while

F is the value resulting from Fuoss' expression, equation (50). The

value of the ion size parameter a for HC1 appeared to be constant, and
0
hence a was arbitrary set equal to 3.0A. Table 5 shows the results

if the Bjerrum critical distance is used as the ion size parameter.

The ion size parameter is approximately constant for the HC1

data in Table IV and for all electrolytes in Table 5. In this case,

when the experimental values of K are increasing, the calculated values
a

are decreasing. Indeed, only a change in the ion size parameter can

counteract the increasing dielectric constant. The NaCl data are an

example of the behavior as the ion size increases. However, even in

this case, agreement is not good, with Bjerrum's expression greatly

overcompensating at high values for a. The existence of the minimum

in the sodium chloride data at 25 OC is also a result of a constant

value for a. This reverse behavior has been reported previously.8

It is obvious from these calculations that a simple electrostatic

model of ion association is totally inadequate to deal with the complex

interplay of forces present in electrolyte solutions. Factors relating

specifically to ion-solvent interactions must be considered. A solvation

term has been proposed by .joss, 90 based on the m-olar free er.ergy of
91
solvation, E The derived relation by Gilkerson is:
a









TABLE 4

Comparison of calculated and experimental Ka values.
a


a (A)


K (liter mol-')
a


25 OC NaCI 20 2.85 1.06 0.79 0.63
40 2.88 3.30 0.77 0.59
50 5.55 5.53 3.56 1.38
60 10.3 7.93 24.8 5.11

HC1 20 10.5 1.35 25.9 5.56
40 2.40 2.23 0.59 0.54
50 2.90 5.67 0.77 0.57


40 OC NaCI 20 2.80 1.01 0.79 0.64
40 3.90 3.53 1.44 0.81
50 13.5 6.47 62.7 10.0
60 16.5 8.31 130.5 16.7

HC1 20 2.50 0.44 0.67 0.67
40 2.35 2.09 0.58 0.54
50 2.40 4.79 0.58 0.52
60 2.90 8.21 0.75 0.55
80 5.10 49.1 2.78 1.11


B. value of K calculated using Bjerrum equation (49).
3 a

F Value of K calculated using Fuoss' equation (50).
a


TABLE 5

Comparison of calculated and experimental K values using the Bjorrum
distance as the ion size parameter.

M a (A) NaCI NaAc HC1 B F

25 OC 20 3.38 1.25 2.01 0.23 1.08 0.72
40 3.28 3.45 7.53 2.43 0.99 0.66
50 3.22 4.93 9.98 5.76 0.93 0.62
60 3.18 6.27 15.5 9.80 0.90 0.60


40 OC 20 3.43 1.23 2.20 0.72 1.13 0.75
40 3.30 3.37 7.98 2.36 1.00 0.67
50 3.24 5.77 10.8 5.05 0.95 0.63
60 3.18 6.27 13.9 8.30 0.90 0.60
80 3.06 48.4 0.80 0.53










4rNa3 b s/R
K = e e (51)
a 3000


This expression should take into account specific solvation in the

association process. Unfortunately, almost no work has been done with

ethylene carbonate-water mixtures, and values for the parameter E have
s

not been found to date.


Treatment of the Acetic Acid Data

The KEQIVES program was unable to calculate convergent values for

the various parameters for either the data for acetic acid at ethylene

carbonate concentrations greater than 20 mole percent or for hydrogen

chloride at 100 mole percent ethylene carbonate. The problem was

associated with an iterative procedure that determined the value for a,

the degree of dissociation. An alternative method was therefore used

for the analysis of these data. This method was based on a procedure of
92
Sellers, Eller, and Caruso. While the method is not original with

them, they have provided a strong theoretical background for the original

technique.

The procedure involves plotting log A vs. log c. The resulting

plot is generally a straight line whose slope gives information concerning

the type of association present in the system. The intercept gives

quantitative information about K and A .
a

The data for solvents containing large amounts of water have

slopes with a value of -0.5, with deviations from a straight line

present only at low concentrations. This behavior is consistent with

simple dissociation into ions,


14.Ac H + Ac









which is the dissociation process in water. A plot exhibiting this

behavior is shown in Figure 30. An increase in temperature results in

a downward shift in the plot, with no change in the slope. This is a

result of the changes in K due to thermal and kinetic processes.
a

As the concentration of ethylene carbonate increases, the slope

increases to more negative values. AL 60 mole percent ethylene

carbonate at 25 OC, the slope is still -0.50. At 40 C, however, the

slope has increased to -0.75. This slope corresponds to the formation

of acetic acid dimers. It thus appears that dimer formation is enhanced

by an increase in temperature, an unusual occurrence.

However, there is some ambiguity in the interpretation of results

using this method. A slope of -0.50 may also correspond to dimer forma-

tion coupled with triple ion formation, as shown below:


(HA) = H + AHA
2


Since the slope increases slightly at lower concentrations as well,

this would imply dimer formation rather than simple ionization. This is

because increasing solute concentration would favor triple ion formation

rather than simple ionization and result in the behavior observed.

However, there was no increase in A as solute concentration was

increased, a characteristic of triple ion formation. Therefore, it may

be that the small increase in slope at lower solute concentrations is a

result of impurities and the fact that no solvent correction was

employed.

At 80 and 100 mole percent ethylene carbonate at 40 oC, the slope

has increased further to a value of -0.84. A negative value of the

slope of this magnitude 'theoretical'/ -3.833) corresponds :o :river

formation, coupled with sirile association.








u

rl


C


0
H


J
C
i
i)
u
C



















0 0
u















C"
r- u





0






0
Li













C












r'2
S -



























U
SC
u 2 1

C d






































4o *-
C;


<> 0
0 C





rr4

3aU



5C '2


0 C




0 '



Q H




Li













































































V O6T -










For hprogen chloride in 100 mole percent ethylene carbonate at

40 OC, the picture is more complex, as shown in Figure 31. There appear

to be two linear regions present. At the lower concentrations of

hydrogen chloride, the slope is again around -0.75, consistent with

dimerization a.d simple dissociation. At higher concentrations, the

slope lessens to a value approximating -0.25. This behavior corresponds

to dimer formation, but now coupled with the more complex dissociation:

+
3(HC1) T= 2H + 2C1(HC1)
2 2

The difference in behavior between the two acids is probably due

to the presence of the carbonyl group in acetic acid. This permits more

extensive solvation for acetate ion than for chloride ion by a dipole -

dipole interac~:icn.

As the values of the intercepts are combinations of the magnitudes

of A and K some idea of the magnitude of these parameters can be

gained. If we. assume that Kohlrausch's law of independent migration holds,

A for acetic acid can be determined from the values for the other

electrolytes by the simple relation:


HAc = HC NaC + NaAc (52)

The data at 20 mole percent confirm that this relationship holds at this

solvent composition. Thus, we now have a means of extracting K from
a

the log-log C-i=ts. Table 6 summarizes the results of such calculations.
91
Halle has determined the value of K for acetic acid in 50 weight
a

percent ethylene carbonate at 25 and 40 oC by EMF measurements. 50 weight

percent is approximately 20 mole percent, and his value for the pK, 5.65,

is in good agr~e.ement with the experimental value determined in this work

(5.S4).
























TABLE 6


Summary of calculated conductance parameters for HAc at 25 and 40 C.


M Ac (-] cm2 mol-1)


Slope


K (liter mol- )
a


25 C 20 181.77 -0.50 6.9 x 105

40 91.71 -0.51 6.4 x 106

50 67.30 -0.50 2.0 x 107

60 51.83 -0.52 9.8 x 107





40 OC 20 226.62 -0.50 7.8 x 105

40 117.58 -0.50 7.7 x 106

50 86.90 -0.51 2.5 x 107

60 67.54 -0.75 2.4 x 108

80 -0.84

100 -0.8.1














CHAPTER VI

CONCLUSIONS


In general, ethylene carbonate can be considered to be a dipolar

aprotic solvent of high dielectric constant with minimal self-association.

It may be that ethylene carbonate has a better claim to being a nearly

ideal solvent for ions than has propylene carbonate, as discussed by
94
Friedman. When mixed with water, solvent mixtures result which have

solvating powers intermediate between the two pure solvents. Experimental

results from this study and others 70 support the idea that the water

structure is broken down by the addition of ethylene carbonate.

Based on the general behavior of the A vs. /c plots and the
78
discussions of Fuoss and Accascina, it appears that ion association

becomes evident for the stronger electrolytes (soldium chloride, sodium

acetate, and hydrogen chloride) at solvent compositions about 40 mole

percent ethylene carbonate. Problems associated with the computer fit at

20 mole percent ethylene carbonate, assuming K = 0 and a = 1, indicate

that ion association was important even at this composition,except

perhaps at concentrations below 0.01 molar.

Hydrogen chloride was the least associated of these three stronger

electrolytes, followed by sodium chloride and finally by sodium acetate.

However, hydrogen chloride became more associated than sodium chloride

at a solvent composition of approximately 50 mole percent ethylene

carbonate. This was probably due to the higher polarizability of the

sodium ion, which resulted i: the sodii:m ion becoming more sol.':aed th.:l

the smaller hydrogen ion.




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