A COIJDUCTIMETRIC STUDY OF SOME ELECTROLYTES 11
ETHYLENE CARBONATE-WATER MIXTURES AT 25 AND 40 C
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
This dissertation is dedicated to my wife, Gaylia, and my son,
Benjamin, for their support, encouragement, and patience.
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
LIST OF TABLES
LIST OF FIGURES
ABSTRACT . .
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 .
. . . .
. . .o
. . . .
. . . . .o
Relevant Properties of Ethylene Carbonate
Mixed Solvent Properties . . . .
Plots of A vs. c . . . . . .
Fit to Pitts' Equation Assuming K = 0
Fit to Pitts' Equation Assuming K / 0
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
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
3. Summary of calculated conductance parameters for NaC1,
NaAc, and HCI at 25 and 40 C assuming K / 0 .... 66
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
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
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
Barry Richard Boerner
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
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
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.
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
in solvent systems because of its high accuracy and general value
in assessing lonic solution properties. It was the najor tool used in
THEORETICAL BACKGROUND AND DEVELOPMENT
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
*For a more detailed description, see, for example, G. Kortum, Treatise
on Electrochemistry second edition, Elsevier Publishing Co.,
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-
F =lz (1)
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
F O zze (2)
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:
F = z.eE (3)
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:
v. = (4)
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:
u. = (5)
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 -. (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)
Now the equivalent conductance can be related to a measurable resistance
and concentration by:
A 1 1000 (9)
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
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
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
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
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:
m s (10)
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
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.
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
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
can be considered to be equivalent to a resistance and capacitance in
series with equal impedances at any one frequency. Both impedances
vary inversely with wu
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 + (11)
m I 1 + aw2
R R 2 2
1 2 1
R + R
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.
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.
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)
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.
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_)
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
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
Initial work on the problem of the relaxation effect was done by
Debye and Huckel,2 but a somewhat more successful treatment is given
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:
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
If symbols are replaced by values of the corresponding physical
constants, and a 1:1 electrolyte is assumed, equation (16) can be
8.204 x 10 8250(17)
A = A -' + /c (17)
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)
and then rearranging (18) yields:
A -- c (19)
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
B A + B
A = A 1 a 2 /c (20)
which can be similarly rearranged to give:
B A + B
1 + (Ba B )/c
Where B = K//c. Equation (21) is useful for A determinations by
extrapolation using Shedlovsky's method.
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
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
put in the same form with only differences in coefficients. The
A = A S/c + Ec log c + J c J c3/2 (23)
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.
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
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
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
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
(1 + y)2(/2 + y)
1 + y
A = H(/2 1)
B = 3H2
G = -m7""C
H = 2 e 2 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)
T = 2 + y)
1 4(/2 + y)
3 3/2e(8+ l)y
+8 /2 + y
Ei ((8 + 1)y)
- 2eyE (y)]
E.(t) = e du
1 t u
( 8~nle2c2 1/2
4(1 + y)
(8( + 2)y)
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
mass balance equation by the use of a:
a 2 2
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
50.29 x 108
Equation (26) gives the activity coefficient, f4, on the mole fraction
scale; it is converted to the molar scale by the expression:
2 = 2
S -0 c(2 lvent olute
where m = moles solute per kg of solvent
M = molecular weight
p = density of the solvent
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
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
sodlum-cotasslun alloy. The devclocment of color has been suggested
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
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
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
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
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
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
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.
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.
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)
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
et al. Two were commercially manufactured by Beckman Instruments. The
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
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.
The reason for the wide placement of the lead wires is to reduce
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.
< m Q M r L0 = M n t -3 E
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
Ethylene carbonate has a tendency to leach ionizable impurities
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
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.
14/24 joint- rubber
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
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 + (28)
measured ohmic 1 + aw2
S W 2 F 2
S2 2 R R
F 3 2 1
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
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
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
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 :
If the assumption is made that R = R (the measured resistance after
frequency extrapolation), equation (30) can be rearranged to give:
R =- (31)
If the experimental R is plotted against K''(which can be calculated
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.
Q i0 run 1
A run 3
500 1000 1500
Measured resistance, R
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
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
the molarity c, is given by:5
c = 10 (32)
1000 + mM
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.
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-
son, and Bates. Some modifications were added to increase program
efficiency and alter the printout format.
The program utilized an iterative procedure of Ives, 0 which
is based on an expression for the dissociation constant Kd:
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)
Hence, one can write:
c. = ac = c (35)
similarly, for c :
c = (1 )c = (A. A) (36)
u A. I
Combining equations (33), (34), and (36) yields:
K = (37)
S A.(A. A)
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
This expression can be rewritten as:
S 1A2Cy+ 2
A A A ---- (39)
which can be reduced to the form:
y = A :< (40)
Y= A A
Equatic, (40) is in the form of a straight line, and A and K
(equal to ) are intercept and slope, respectively. As A is used to
calculate A an initial estimate based on extrapolation of the A against /c
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
values of A and K which were constant.
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.
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).
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.
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.
Figure 12. Euhvl-ne carbonate molecule, showing
bond angler ard distances.
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
cell of crystalline ethylene carbonate as determined by Brown62 is shown
in Figure 13.
Figure 13. The unit cell of crystalline
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
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.
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
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
exist as liquids at 25 C.72 The mixtures tend to supercool readily, as
does ethylene carbonate itself.
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
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
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
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,
A. D'Aprano, Gazz. Chim. Ital., 104, 91 (1974).
R. A. Robinson and R. H. Stokes, Electrolyte Solutions, 2nd ed., revised,
Butterworths, London, 1970.
cl--e perc-t:t etihylcn-, carbonate-
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
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
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
20 40 60
Mole percent ethyler.- :crbcnate
Figure 16. Plot of viscosity and excess viscosity vs. the mole percent
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,
R. A. Pobinson and R. H. Stokes, Electrolyte Solutions, 2nd ed., revised,
Butterworths, London, 1970.
Mole percent ethyle:.e carbonaate
0 25 C
o 40 C
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
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
concentration fall on the Onsager tangent. A is easily determined from
this straight-line segment of the plot by simple extrapolation to zero
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
a c 0
0 0 ( a
(- 44 u
low u., ;, 4Jeouy-) nr~uo ;'"'l2.'.T `.
Q Imo )o
S> i- a
O o eo
0 a aj0
H 24 0
I 0 ~c
V~~~u e~u:ruz u.:2Anb2 -
/ 0 u
,-4 o Q 1n
I O I >1
S n u
O 4 J
r 'O N
IC I N
I f i1r
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
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
values). However, the high dielectric constant does not favor triple ion
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
It is interesting to note that this gradual progression from type
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
0 0 0
p O ..
I C ) fa
) c u
C) CJ. f
I I I I
0 a 0 0
1 '1 r') a,
I Q ?
I / c*
In / ("
/0 a piQ <
/ P au~~~~ >,ae;T 1
0 U) z.
0 0 (
.4 C )
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
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-
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,
the program still produced non-zero values for K
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
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
associated with the data for 2. mole percent ethylene carbonate.
Summary of calculated conductance parameters for NaC1, NaAc, HC1 in
20 mole percent ethylene carbonate at 25 and 40 OC assuming K = 0.
A (Q-1 cm2 mol-1) K (liter mol-1)
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
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
Summary of calculated conductance parameters for HaCl, NaAc, and HC1 at
25 and 40 C assuming K / 0.
M A' (Q' cm2 mol ')
25 OC laCl
K (liter mol-I)
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
40 OC HaCl 20
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
least by the inclusion of poor data, remaining essentially the same.
The calculated values of K changed by a greater amount, but, in general,
the standard deviations of K values were greater than those of A and
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
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
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-
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
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
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
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 o C
n 0 II
I .-. s
U U C
o a 0
/ f c
---I-c^-------- <----------- ;o aT'uT
of equivalent conductance and viscosity, called the Walden product,
symbolized by A T. The Walden product was initially assumed to be
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
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
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
It is also intereszInq to compare the behavior of hydrcqe:i
chloride with the salt. At lo. concentrations of ethylene carbonate
UV I-n:oid uaprvbl
0 O -0
U U U U.O
o U 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-
LiV 'a 0n o ad u .p I: ,
o 1C .3
- s 0
the K 's are lower for hydrogen chloride than for the salts. As the
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
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
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
S iz z le2
N = 4 n.exp .- T2 r2dr (44)
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)
z z2 le2
Q(b) = x- edx
In this case:
|z z le
2 = 1 2
zI z 2e2
x = r
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
Values of the integral Q(b) have been tabulated, and a
more recent statistical treatment results in an asymptotic expansion of
S4TNa eb (49)
a 1000 b
Fuoss, however, suggests that only ions In contact can correctly
be considered associated. His analysis of the problem results in:
K = (50)
Experimentally,determined K values for the electrolytes are
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
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
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
solvation, E The derived relation by Gilkerson is:
Comparison of calculated and experimental Ka values.
K (liter mol-')
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).
F Value of K calculated using Fuoss' equation (50).
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)
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
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
Sellers, Eller, and Caruso. While the method is not original with
them, they have provided a strong theoretical background for the original
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 .
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.
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
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
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 2 1
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)
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 -
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
the log-log C-i=ts. Table 6 summarizes the results of such calculations.
Halle has determined the value of K for acetic acid in 50 weight
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
Summary of calculated conductance parameters for HAc at 25 and 40 C.
M Ac (-] cm2 mol-1)
K (liter mol- )
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
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
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
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.