“HI

I
3

‘
i

WM

K

NW"

|
‘
1
1
¥

lllklmlh

\
I

1
l

W

—_——
—_.

 

CONDUCTANCE OF AQUEOUS
SOLUTiONS OF BARIUM
METABENZENEDISULFONATE

Wurst: for Hm Degree of M. 5.
MICHIGAN STATE UNIVERSITY

David. Rablen

1960

L133 EAR Y
Michigan State
University

  
   

 

L1

~ .~.
Ix”,

1'! (K

c“.
.‘ -.

 

n" V‘

pair-Il' " 3 3 3 ' 3
A ‘ ' 3 i ‘-
.“‘ llll\‘f" I. u.

.. v I!"
'A- " . k I," “‘. I ._ . , .‘
9‘... .-,"..-. . L ..,i uF LVN. M-J
L-’-- ' 1‘

ma: L,.1.“.'7»,.N(3. ~‘~'N\3H“3P‘N

IIIIII " "f." ’3'

[RY

ABSTRACT

CONDUCTANCE OF AQUEOUS SOLUTIONS OF
BARIUM METABENZENEDISULFONATE

by David R ablen

The conductance of barium metabenzenedisulfonate in water has
been measured in the concentration range 4 x 10"4 to 6 x 10'2 normal.
The phoreogram is slightly catabatic. The data weresuccessfuIly fitted
up to about 2 x 10'3 normal using the Fuoss-Onsager theory (without
ionic association), including extended terms of the electr0phoretic
effect, and the Einstein viscosity correction for the metabenzenedi-
sulfonate ion. In the light of the behavior of 1-1 electrolytes in water,
this seems to be a reasonable range of applicability of the extended

theory to a 2-2 salt.

CONDUCTANCE OF AQUEOUS SOLUTIONS OF
BARIUM METABENZENEDISULFONATE

By

David Rablen

A THESIS

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

MASTER OF SCIENCE

Department of Chemistry

1960

ACKNOWLEDGMENT

The author wishes to express his sincere
appreciation to Dr. J. L. Dye for his assistance
in the preparation of this work.

*>{<*****

ii

TA BLE OF CONTENTS

I. INTRODUCTION . . . . . . . . ............
II. THEORY.............. .....
A . Introduction .............
B. Interionic Attraction Theory . . . . .....
C. Onsager Theory of Conductance
D. Extension of Onsager's Theory .........

III. EX PERIMENTA L .

A. Preparation of barium m-benzenedisulfonate
dihydrate. . . . . . 7' ......
B. Preparation of Conductivity Water .
C. Apparatus . .
D. Procedure.
E. Reagents. ..............
IV. RESULTS .AND DISCUSSION . . . . . ......

LITERATURE CITED . .

iii

U)

~leer

l4

14
15
15
16
l7

18

28

LIST OF TABLES

TABLE Page

I. Composition of Barium Metabenzenedisulfonate
Hydrate......................... 15

II. Conductance Results, Series 1; Conductance Results,
SeriesZ......................... 22.

iv

LIST OF FIGURES

FIGURE Page

I. Phoreogram of barium metabenzenedisulfonate. . . . . 23
0' o . .
II. /\ - /\ versus normality for barium metabenzene-
disulfonate and several theoretical conductance
equations . ........................ 26

INTRODUCTION

Electrolytic solutions conduct in the presence of an electrical
field because of the existence in the solution of electrically charged
ions. The results of resistance measurements of electrolytic solutions
have shown that the equivalent conductance increases with increasing
dilution. In 1887 Arrhenius (1) first attempted to explain this behavior
by assuming that the change in conductance with concentration was
entirely due to the change in the number of free ions present. While
the behavior of weakly conducting systems tended to substantiate this
idea, strongly conducting systems could not be adequately explained.
This anomalous behavior of strong electrolytes led to the rejection of
the Arrhenius incomplete dissociation hypothesis and adoption of the
modern view that strong electrolytes are completely dissociated and
that the coulombic forces which exist between the ions must play the
dominant role in determining the properties of electrolytic solutions.
Although in the first two decades of the present century attempts were
made to develop an interionic attraction theory, it was not until 1923
that a statistical electrostatic theory of dilute solutions was formulated
by Debye and Hiickel (Z). By assuming complete dissociation and
attributing all deviation from ideality to interionic forces, they were
able to successfully derive the limiting law for the activity coefficients
of strong electrolytes.

In 1927, using the results of the interionic attraction theory and
fundamental concepts of hydrodynamics, Onsager derived the limiting
law of electrolytic conductance (3). This theory predicts the limiting
s10pe of the observed conductance curve as a function of the charge type

of the electrolyte and solvent properties. A recent extension by Onsager

and Faloss (4, 5, 6) provides a theoretical expression for conductance
which is applicable to higher concentrations (up to approximately C. 01
normal for 1-1 electrolytes). This extension, involving the inclusion
of finite ionic size and a more complete mathematical treatment, was
developed for symmetrical electrolytes only. The conductance behavior
of a number of 1-1 electrolytes is in good agreement with the extended
theory. Since this theory is also capable of handling 2-2 electrolytes,
an attempt was made by Dye and co-workers (7) to apply the Fuoss-
Onsager theory and higher terms of the electrophoretic effect {8) to
explain the conductance behavior of zinc sulfate. The anomalous re-
sults obtained prompted a search for a strong 2-2 electrolyte which
would be free of the complications of ionic association and hydrolysis.
The electrolyte barium metabenzenedisulfonate seemed to fit these
requirements. The purpose of this research was to determine the
conductance of this salt and establish the applicability of the extended

theory to 2-2 electrolytes.

THEORY

A . Introduction

 

When subjected to a directed electrical field, under conditions
of normal field strength and frequency, electrolyte solutions obey Ohm’s
Law, E = I R, where E is the potential applied across the solution, _I_
the current, and R the resistance of the solution. Since for a homo-
geneous conductor of length L and cross sectional area 5, R 2: p/A, the
specific resistance R can be determined from _I_, A, and the measured
resistance R. The specific conductance I: is given by l/p. For electro-
lytic solutions it is convenient to define the equivalent conductanceA as
the specific conductance divided by the stoichiometric concentration in
equivalents per liter times one thousand: A = 1000 L/c. The
equivalent conductance may also be written as

A :zx. (1)
1

1

since it is made up of the sum of the contributions of all the ions.
For a completely dissociated electrolyte the individual ion conductance

xi may be related to the ionic mobility or velocity per unit gradient

21.,
of potential, by the equation

)‘i = F ui . (2)

Equivalent conductances computed from stoichiometric concen-
trations and measured resistances are found to decrease with increas-
ing concentration. From equations (1) and (2) it is evident that this
change is due to the concentration dependence of the ionic mobilities.

By suitable extrapolation of conductance data, A0, the limiting value

of equivalent conductance at infinite dilution can be determined.

Experimentally resolving A 0 into the cation and anion contributions,

 

x°+ and x°w , requires measurement of the transference number defined
by
U1 X”
ti 2 : 1 . {3)
22 ul 2‘, X1
i i

By extrapolation ti) can also be obtained which with A0 serves to
evaluate the individual ionic conductances at infinite dilution. They are
characteristic of the ion and solvent, depending largely upon the size
and the extent of solvation, and the solvent viscosity. In the develop—
ment of the theory of electrolytic conductance the limiting conductances
are treated as empirical constants, the primary aim being to account.
for the difference between the limiting values and those at non-zero
concentrations as a function of the properties of the ions, the solvent,
and particularly the concentration.

The theory of the conductance of dilute electrolytic solutions is
long and complicated: for that reason the discussion presented here will

be largely qualitative with theoretical results stated rather than mathe-

matically developed in detail.

B. Interionic Attraction Theory

 

The modern theory of electrolytic conductance is based on the
interionic attraction theory formulated by Debye and Hiickel (2) in a
treatment of the equilibrium properties of electrolytic solutions.

Debye and Hiickel assumed that the solute of an electrolytic solution
consists entirely of ions which may be treated as a dilute solution of

point charges or charged Spheres in a structureless medium of uniform
dielectric constant. These assumptions allow the application of Poisson's

equation of electrostatic theory:

Av=———p <4)

where}? is the dielectric constant of the solvent, 1’ the electrostatic
potential, and E the charge density at the point considered. Due to the.
complexity of an electrolytic solution the theoretical approach is
necessarily statistical, the function of interest being the time average
potential with respect to a given type of ion, say ail-type, chosen as
origin. The calculation of Lusing Poisson's equation requires that
the time average charge density, hence the time average ionic distribu-
tion about the _j_:ion be known. The dependence of the distribution upon
position is due to the mutual attractive forces between oppositely charged

ions and mutual repulsive forces between like charges. The distribution

is assumed to be given by the Boltzmann equation

njicfir) :: ni exp - ei \Vj(r) /kT (5)
where the quantities in the equation are defined as:

no.

31 is the local concentration of i-uions about a j-ion;

 

ni is the bulk concentration of i-ions;

ei is the charge on an imion;

is the electrostatic potential at a distance r from a j uion
due to the presence of the j-ion and the ions assembled
about it;

Vl-(r')

k is the Boltzmann constant;
T is the absolute temperature.

The charge density is then given by

pj 2' Z ej‘niexp [ -ei \I/j /k.T] . (6)
1

Substitution of this expression for charge density in Poisson' 5 equation

yields a non—linear differential equation for which no general solution is

known and which implies a contradiction of the linear superposition of
fields principle. However, by restricting the results to dilute solution
where ei VJ- ’<‘ kT, the exponential can be expanded and terms quadratic
and higher neglected. A linear differential equation results which when

integrated using boundary conditions which consider the ions as hard

it. 4;: i<e-xr><a—:;>

for the potential. The quantities in the equation are defined as:

Spheres yields

 

r is the distance from the j-ion;
ej is the charge on the j-ion;
D is the dielectric constant of the medium (solvent);

a is the mean distance of closest approach of. the ions;

4 Z ,
K2 : 1.3.31.3... E ciziz, (8)
DkT 10 i

where

e is the electronic charge;

zi is the valence of an i-ion;

Ci is the equivalent concentration of the i-ions;

l_\I_ is Avogadro's number.

The potential has been written as the product of three factors.
The first is the potential due to an isolated j -ion at the origin, the
second factor represents the electrostatic screening which arises

between two ions due to the presence of the other ions in the system,

and the third factor gives the effect of finite ionic size.

According to the interionic attraction theory picture the compen—
sating charge of a reference ion of charge if is a Spherically‘ symw
metrical, continuous distribution of total charge :3 which is called the
ion atmosphere. The radial charge density can be shown to have a
maximum at l/K' which is considered to be the mean diameter of the
atmosphere and is of the order of magnitude of. molecular dimensions.
This preponderance of opposite charge "up close" is a natural conse-
quence of the coulombic attractions between unlike charges and repulsions
between like. charges.

. Using the above expression for VJ and assuming all nonwideality
could be attributed to interionic forces, Debye and Hiickel successfully
predicted the limiting law for the activity coefficients of strong electro-

lytes.

C. Onsager Theory of Conductance

 

Upon the basis of their interionic attraction theory Debye and
Hiickel (Z) deduced a simple theory of electrolytic conductance which
was not completely satisfactory. The necessary refinements of the
DubyewHiickel treatment were made by Onsager (3) who first successfully
derived the limiting law for electrolytic conductance.

At equilibrium the average ionic velocities are zero. The appli-
cation of a directed external field initiates ionic motion parallel to its
direction. At infinite dilution the only forces exerted on an ion are
the external field and the frictional resistance of the solvent. The
equation-of motion is then simply

Vi = Xeiu'i’ (9)

where

v1 is the velocity relative to an external observer;

I><|

is the external electric field;

ei is the ionic charge,

119 is the limiting ionic mobility, the reciprocal of which is the

—- ionic coeff1c1ent of fr1ct10n.

At non-zero concentrations the ions influence the motion of each)
other because they are coupled through their electrostatic fields.
A retarding effect arises in the following way. When an electric field
is applied a given reference ion starts to move. If the ions of its
atmosphere were able to immediately redistribute themselves, the
spherical symmetry of the equilibrium state would be retained.
However, due to the non-zero coefficients of friction of the ions, the
atmOSphere lags behind the central ion giving rise to an asymmetry in
the distribution. In effect there is more opposite charge behind the
reference ion than in front. -As a result a local field exists about the
central ion which opposes the external field which produces it. As a
consequence the force felt by the reference ion is less than that for the
isolated ion and the ionic velocity is necessarily decreased. Due to its
connection with the finite time required for a perturbed state to decay
to an equilibrium state, this effect is referred to as the relaxation field.
The non-equilibrium potential may be expressed as the sum of the
equilibrium value calculated by Debye and Hiickel, and a small per-

turbation term \yJ-z

o
. = . + ' (10)
VJ \ifJ Yj

!

The problem is to calculate Wj , the gradient of which gives the magni-
tude of the relaxation field. This is a more difficult task than the

equilibrium problem because the local concentrations about a reference

ion are a function of direction as well as distance. Essential to the
formulation of the solution are the symmetrical distribution functions

where nJ- is the average concentration of j type ions, and nji is the local

 

concentration of i type ions located by a vector 3,, with respect to a j
ion as origin. The quantity fji (rig) is proportional through l/V to the
total number of i ions in the atmosphere: ofj ions. These distribution

functions satisfy the conservation condition

V,- ii). vi,- + V2. fji €in = o (12)

which is the equation of continuity for ion flow. In the equation Gij is

 

the time average. velocity of a i ion located at r12. The distribution
functions can be related to the potentials through the Poisson equation.
Once the internal forces in the equations of motion for the ions have been
expressed in terms of the unknown potentials, the equation of continuity
and the Poisson equation constitute the system of equations necessary
for the evaluation of 1):; .

A fourth order nonnhomogeneous differential equation is obtained
for Hij— which in the original treatment was greatly simplified by
neglecting all terms of higher order than first in the ionic charge. The
differential equation was then integrated subject to boundary conditions

for point charges. Onsager's final result for the relaxation field is

I
41—33,— : A X = X eie; qzfl (13)
a 0 ° 3 DkT(1 + q)
r:

where q = 1/2 for symmetrical electrolytes. The ”corrected” field

at the reference ion is then

Bjeix
X + AXO = x 1+ —-———— , (14)
lBDkT

10

When an ion moves in an electrical field it pushes solvent away,
directly in front, and also drags it along, from behind. Oppositely
charged ions move in opposite directions. As a consequence a given
reference ion finds itself swimming upstream in a counter current of
solvent produced by its Oppositely charged atmOSphere. This is called
the electrophoretic effect and obviously leads to a decrease in the ionic
velocity relative to an external observer. The magnitude, Avj , of
the solvent counter velocity can be calculated in the following—manner.
If the ion atmosphere about a reference ion of charge _e_J-_ is represented
as a spherical shell of radius l/H~ with the charge -ej uniformly

distributed over its surface, it will be subjected to force —Xej . The

 

velocity of this Sphere can then be calculated by applying Stoke's law

of hydrodynamics, F = v/61rnr which is the equation of motion for a

 

sphere of radius r traveling in a hydrodynamic continuum of viscosity 1).

The counter current velocity is given by

-Xe' H.
D : ——4—
AvJ 61in . (15)

This is the limiting form of

-Xe°
AV“ : J __‘!_(___
J <67”) )<1+ 3(a) ’ (16)

the electrophoretic effect obtained by more rigorous methods (3).

 

Combining the two retarding effects, the velocity of an ion may be

 

 

 

written
_. AXo o
Vj - Avj + eJX(l+ X )uj
X - . . o
- CJK+ er (1+ + eJel > uj (17)
6Trr) 18 DkT

or in terms of equivalent conductance

A :2 A0 - (GAO +6) Cl/2 (18)

11

which is the Onsager limiting law for electrolytic conductance. The
constants 2 and E are completely determined by the absolute temperature,
the dielectric constant, and viscosity of the solvent, the valency type of
the electrolyte, and universal constants. The only arbitrary constant is

A0 . The Onsager limiting law has been extensively tested by precise

 

experimental data and has been shown to be the exact expression for the

tangent to the conductance curve for many systems.

D. Extension of Onsager's Theory

 

1. Higher terms of the electrOphoretic effect—~In the original calcu-
lation of the electrophoretic correction by Onsager (3), the exponential
distribution function was approximated by expansion and retension of
only the linear term. Dye and Spedding (8) have pointed out that it is
invalid to neglect the higher terms for ions of high charge even at quite
low concentrations. In their treatment they have evaluated the integrals
approximated by Onsager by retaining the complete exponential. The
integrals have now been evaluated by numerical methods using a high
speed digital computer for a range of concentrations, charge types, and
ion sizes (9).

Z. Fuoss-Onsager Theory--An extension by Fuoss and Onsager
(4, 5, 6) involves both an improvement in the model and the mathematical
approximations used in the calculation of the relaxation field. In expand-
ing the equation of continuity, all terms were retained except those
quadratic in field which by hypothesis were negligible. This gave rise
to five higher order terms in the differential equation which had been
neglected in the original derivation of the relaxation field by Onsager.

As a first approximation only the terms originally retained were used
but subject to boundary conditions for spherical ions of radius 3 instead

of for point charges.

12

These boundary conditions are: the field must vanish at infinity;

the potential and field must be continuous at r z: a; the ions are im-

 

penetrable. The last condition was fitted by requiring that the radial
components of the relative velocity of any two ions vanish at contact
(:3). The first order solution was then substituted into the higher
order terms in the differential equation for ___\V_'_ which was then resolved
as a perturbation problem.

The resulting relative relaxation field can be written symbolically

 

as
-- l
———§X : (QC /2> (1 -A1+Az+ Axv) (19)
X
in which
1/2 . . . . . .
a c is the limiting value of the relaxation term for pOint

charges;

A1 involves terms which allow for finite ion size;

A2 includes all the effects of the perturbations in the relaxa-

—— tion field except those due to AXv , a hydrodynamic term
which is more conveniently coin—Sined with the electro-
phoresis term in the conductance equation.

Another effect which causes conductance to change with concen-
tration was pointed out by Onsager (10). Mutual attractive forces
naturally lead to cation-anion collisions. As previously mentioned, in
the presence of an external field the distribution of anions about a
reference cation is asymmetric with an excess of anions behind it. As a
result the cation will be struck more often from behind giving it a com-
ponent of velocity in its normal direction of motion. The virtual force
£1 on the reference ion due to this effect is calculated by integrating
the directed component of the local osmotic pressure over the surface of

the ion. The solution is of the form

A Pj = XeJ'C {(D, T, a) . (20)

13

The conductance equation including all of the above mentioned

effects may be written

 

1/2 '
A :<[\.0 - “if: a><1+Ax +——-Ap‘ .(21)

x x
3/2

The expansion of this product, dropping all terms of order c and

 

higher is
0 0 1/2
A zA —(a./\. + MC +Ec logc+ Jc (22)
in which
(GAO + B) is the limiting law coefficient;

:1 is an explicit function of _a, A0 , and the prOperties of
the solvent;
0
E is independent of 3, depending only on A and the

prOperties of the solvent.

The two parameters :4}: and a must be evaluated from the experimental
data.

When the ions are large compared to solvent molecules their
influence on the viscosity of the solvent must be considered. This is

taken into account by including Einstein's viscosity equation

n = flo(1+%(p) (23)

where n is the viscosity of a solution in which a volume fraction, m,
of solute molecules is present in a solvent of viscosity _n_9_. This leads
to another linear term in the conductance equation and, includes another
parameter, the hydrodynamic radius, which must be evaluated from
experimental data.

The results of the Fuoss-Onsager theory are limited to symmetri-
cal electrolytes and to concentrations less than about . 01 normal. This
extension of the relaxation field offers a ready explanation of the anabatic

phoreograms exhibited by electrolytes such as the alkali halides.

EXPERIMENTAL

A. Preparation of barium gi-benzenedisulfonate dihydrate

 

Barium m-benzenedisulfonate was prepared by the neutralization
of an aqueous solution of m—benzenedisulfonic acid with barium hydroxide.
Due to the presence of sulfuric acid in the technical grade {ii-benzene-
disulfonic acid employed, a precipitate of barium sulfate formed which
was removed by filtration. The resulting solution was concentrated by
evaporation and the barium m—benzenedisulfonate precipitated by addition
of ethanol. Five to six recrystallizations were carried out from con-
ductivity water and ethanol. The salt obtained in this manner was hydrated
to an unknown extent.

In order to calculate stock solution molalities it was necessary to
prepare a form of the salt suitable for weighing. The possibility of
preparing a stable hydrate was explored. A two gram “sample was dried
in a desiccator over phOSphorous pentoxide after which it was transferred
to a second desiccator containing a 100 milliliter beaker of saturated
solution of the salt. Successive weighings showed that the sample weight
initially increased but reached a constant value after a few hours. When
this sample was again placed in the ”drying desiccator" a weight loss
occurred. When the drying agent was replaced with the saturated solution
the initial constant weight was again attained, which furnished convincing
evidence that a stable hydrate had been prepared. The results of a
Fischer titration and a hydrogen analysis established that the salt in
equilibrium with the saturated solution was the dihydrate.

All stock solutions were prepared from barium {n_-benzenedi-
sulfonate treated in a similar manner. The molalities of the stock

solutions were calculated directly from the weight of salt and water used.

14

15

TABLE 1. Composition of Barium _1;n_-Benzenedisulfonate Hydrate

 

 

Hydrogen analysis (percent by weight):

found theoretical (dihydrate)
1. 91% 1. 97%
1. 94%

Fischer Titration:

l. 85 moles water per mole of salt
lo 92

 

B. Preparation of Conductivity Water

 

The distillation of an alkaline permanganate solution of demineral-
ized water yielded water reasonably free of contaminants except for
atmospheric carbon dioxide. This water was then transferred to a second
distilling flask and redistilled in a stream of nitrogen. The nitrogen was
purified before entering the distillation system by passage through gas-
washing towers containing concentrated sulfuric acid and an aqueous
solution of potassium hydroxide. The conductivity water prepared in

this way had a Specific conductance of about 0. 6 x 10"6 ohm"1 cm'l.

C . Apparatus

 

1. Bridge--The resistance measurements were made using a.
modification of the Jones bridge described by Thompson and Rogers (11).
It consisted of an audio frequency oscillator, an amplifier, and a cathode
ray tube null point detector. . The apparatus permitted resistance read-
ings to be made at five frequencies over the range 400 to 5,000 cps. and
gave results reproducible tod: . 01%.

2. Bathw—A constant temperature bath was used for all conductance

measurements. It consisted of a 12 inch diameter by 18 inch Pyrex glass

l6

cylinder filled with oil which was circulated with a centrifuge pump.

The temperature of the bath was determined using a platinum resistance
thermometer and was maintained at 25 i . 010C. by means of a thermo-
regulator-and a heat lamp.

3.. Conductivity Cells-—For high concentration conductance
measurements, a Leeds and Northrup type B conductivity cell was used.
The"low cell"employed was similar to the erlenmeyer type used by Kraus
and co-workers (12). It consisted of a Leeds and Northrup type A cell
which was sealed to a 500 milliliter flask fitted with a standard taper
cap. The flask had two stopcocks, one mounted on a side arm and the
other on the cap. This arrangement permitted the introduction of con—
ductivity water under nitrogen pressure and for a flow of nitrogen over

the solution when additions of stock solution were made.

D.) Procedure

 

1. Low Cell--Before a run, the cell was cleaned with hot fuming
nitric acid, rinsed, and allowed to soak overnight filled with conductivity
water. After drying the cell in an oven the cap was lubricated, inserted,
and the cell was weighed. About 300 grams of conductivity water was
transferred into the cell under nitrogen pressure. The filled cell was
then reweighed to determine the weight of water. For these weighings
a torsion balance, accurate to :h . 05 gram, was employed. The cell was
placed in the oil bath for one-half hour before resistance readings were
taken. A reading was recorded when mixing gave results reproducible
to :I: . 01%. Due to the high resistance of the conductivity water, a 20,000
ohm shunt was used in parallel with the cell. From the resistance
readings of the shunt and the parallel combination, the conductance of the
water was computed. . This solvent conductance measurement was neces-
sary in order that the total conductance could be corrected for the

contribution of the solvent.

17

Using a weight buret, successive small portions of stock solution
were added to the cell, the additions being made with wet nitrogen flowing
through the cell. After each addition the solution was thoroughly mixed
and resistances were recorded when reproducible to :1: . 01%.

2. High Cell--The stock solution and appropriate weight dilutions
were measured directly in the high cell. In each case the cell was rinsed
with several portions of solution before a resistance measurement was
made. The cell was then emptied, re-rinsed, and a second check
determination made.

3. Cell Constants--The cell constants were determined using
potassium chloride solutions in a manner identical to that used for the
sample solutions. The stock solution was prepared from conductivity
water and salt which had been recrystallized twice from boiling con-
ductivity water and then fused in platinum under nitrogen.

4. Density Measurements--Densities of several solutions of barium
ra-benzenedisulfonate were measured to be used in converting molality
data to molarity. They were determined at 250C. using a fifty milliliter
pycnometer which was previously calibrated with water. The densities

are expressed by the equation
p = 0.9971 + 0.252 m

where m is the molality.

E. Reagents

The following is a list of the reagents used in this work:

Barium hydroxide, Ba(OH)2
"Baker's Analyzed" Reagent
Fischer Scientific, C’. P.. Reagent

Metabenzenedisulfonic acid, C6H6SZO6, Technical,
Eastman Organic Chemicals
Matheson, Coleman and Bell

Potassium chloride, KCL,
Baker's Analyzed" Reagent

Ethanol, C. P.

RESULTS AND DISCUSSION

The following relationships were used to calculate the equivalent

conductances of the solutions from the measured quantities:

in which

5:11:ch It" I: )3 12 [5?” (5m Is '0

2‘3

{.13
c:(w——f—-————m00

+ W) <1+mM7103> (Z4)

L=k(%-g:-—L&—) (25)
A . ____L103 (26)

C

is the normality of the solution;

is the sum of the weight increments of stock solution added;
is the density of the solution;

is the weight of water per gram of stock solution;

is the number of formula weights of solute per gram of stock
solution;

is the weight of "good" conductivity water;
is the molality of the solution;

is the formula weight of the solute;

is the Specific conductance of the solute;
is the cell constant;

is the resistance of the solution;

gis the resistance of the "good" water;

is the weight fraction of "good" water;

Xeis the weight fraction of equilibrium water;

Le is the specific conductance of the equilibrium water.

Some comment regarding the form of equation (25) is in order. The

total measured specific conductance (k. /R) is that due to the solute and

18

19

the solvent. The assumption was made that the solvent conductance is
just superimposed on that of the solute. The solute conductance is then
simply the total conductance minus the conductance of the water which
was measured previous to addition of solute. To take into account the
presence of two "kinds" of water, ”good" water and equilibrium water,
the assumption was, made that the two kinds of water contribute pr0por-
tionally as their weight fractions (mole fractions). The conductance of
the "good" water (0. 6 x 10"6 ohm"1 cm'l) was measured directly in the
conductance cell before commencing with stock solution additions. The
specific conductance of the equilibrium water (1. 2 x 10"6 ohm"1 cm‘l)
used in the preparation of the stock solution was calculated from a
resistance measurement made in a different cell. Using equation (25)
the solute specific conductance was then calculated.

. The advantage of the procedure used lies in the fact that even after
several stock solution additions have been made fig >> {(2, keeping the
solvent conductance essentially that of the ”good" water. In this way
the solvent correction to be applied to the total conductance is kept small.
Were equilibrium water to be used for dilution purposes, the solvent
correction would be an uncomfortably large percentage of the total con-
ductance. It would be impractical to prepare the stock solution with
better than equilibrium water in the interest of further minimizing the
solvent correction because elaborate precautions would be necessary to
avoid exposing it to the atmOSphere. For highly conducting solutions
the Specific conductance of the solute is sufficiently large that the solvent
effects are almost negligible and the use of equilibrium water for dilution
purposes is permissible.

To calculate the cell constants from resistance measurements of
standard potassium chloride solutions the equations given above were

used with the modification that equation (25) was used to evaluate k.

20

Values ofA (13) used to evaluate I: were calculated from .the

KCl
empiric a1 equation

1
AKCl : 149.87 - 93.985 c /2+ 31.8clogc+ 144C . .(27)

Since the second correction term in equation (25) involves the unknown
cell constant, a preliminary conductance L' is calculated assuming

_)_(_g = 1, then I___. is recomputed from the equation

1 Le

L=L'+Xe<—fi-g— - T (28)

21

The conductance results are given in Table II and are divided into
two series, fl and g In both series the measurements up to 4 x 10"3
normal were made using the same low cell of constant about one. In
series {3: the higher concentrations were measured using a "type B”
cell of constant about 30 while in series I”: a cell of constant about 10
was employed. In the low concentration region, the data of series é
were obtained in two runs and those of series E were obtained in one.
Both series have good internal precision but the conductances for the E
series are about two parts per thousand lower than those for series é
and is the reason for the division of the results into two series. The
reason for this discrepancy is not known. The internal consistency of
the high and low ends of each series which were obtained from measure-
ments with different stock solutions rules out mistakes in the preparation
of the stock solution as a cause. The cell constants were determined
for each series so that discrepancies cannot be attributed to an un-
detected change in the cell constant. The most significant fact is that
the stock solution for the two series were prepared from different
batches of salt. Perhaps impurities such as barium benzenesulfonate
in one or both caused the observed discrepancy. The measurements
of series E were used for the comparison of experiment and theory and
are shown in Figure I. ‘It is to be noted that the small discrepancy will

affect the value of A0, but not the theoretical interpretation of the

 

conductance. Included in Figure I is the Onsager limiting law slope,

aAo + {3, calculated using values of a and _[3_ taken from Harned

 

o
and Owen (14). The limiting equivalent conductance A was obtained

 

from the data using the extended theory. The phoreogram is slightly

catabatic. Besides the limiting law, several other theoretical

22

TABLE II. Conductance Results

 

 

 

 

Equivalent Conductance Normality x 104
Series.A
117.44 2.6586
116.43 3.6537
115.72 4.4667
115.05 4.7605
114.47 5.5919
114.10 6.3245
113.69 6.9629
113.32 7.6821
112.91 8.3110
112.51 9.0241
111.91 9.2072
111.04 10.5902
94.62 82.545
93.84 89.225
88.53 145.80
85.30 207.56
80.12 346.31
76.68 431.35
76.49 503.68
Series B

115.67 3.9055
113. 09 6. 9297
112.23 8.1790
110.98 9.9556
110.00 11.699
108.39 14.940
106.39 19.694
104.61 25.122
101.29 37.535
93.73 78.541
90.65 112.32
87.66 152.82
86.94 165.79

82.43 250.51

 

.opmco.:...._mflpoCoNconum»! Eamon. wo Empwoouoflm .H 0.2.3th

NE saunafiuoi
u

 

23

Nofl
./\

I: bod

I «la

 

I1 wHH

.l NNH

 

 

 

24

conductance equations are available with which to compare the experi-
mental data. The possible combinations are the Fuoss-Onsager theory,
the Fuoss-Onsager theory including higher order electrophoretic terms,
and either of these two including the Einstein viscosity correction for
one or both ions; also, ionic association might be considered.

Fitting the theory with the inclusion of ion-pairing involves four

adjustable parameters:

0

, the equivalent conductance at infinite dilution;

the distance of closest approach to the ions;

I’Ulm")

the ionic hydrodynamic radius; and

KA an association constant.

 

In all attempts to fit the data the assumption of ionic association was
excluded. Without KA , the number of adjustable parameters drOps to
three. While Ea; and—1;. are independent of £0, I: ought to be of “reason-
able" size, comparable in magnitude to}. . The model of Fuoss (6) makes
the assumption Bié' Using this assumption the number of adjustable
parameters reduces to only two. Although a reliable value of x°Ba++ is
available, none is available for the metabenzenedisulfonate ion. If it

0
were, A for barium metabenzenedisulfonate could be computed and

 

o
the only adjustable parameter would be _a_._ .
Several attempts to fit data were made in the following manner:
0
A preliminary value of A = 123. 20 ohm"1 cm2 equivTIWas obtained by

a graphical extrapolation of the phoreogram to zero concentration.

Using the program of Karl (9), values of [ l + 95-25 + —A§E] and AAE

(the electrophoretic correction including higher order terms) were then

0
computed for several concentrations and values of a andZXo. From
these quantities[ 3 's were calculated using equation (21) with the modifi-

1
cation that AAE replaced (3 c /2/1 + Ka when the higher order

 

electrophoretic terms were included. AD’ the conductance corrected

25

for the viscosity effect of the metabenzenedisulfonate ion, was computed

from the relation

An=A/(1+-Z-CP) (27)

where 4
— 1T R3 N c/Z

(P = 3 (28)
1000

 

Since the differences between the experimental data and the theo-
retical expressions are almost invisible on a direct graph of A versus
1 2 . . . .
c / , a more sen51t1ve plot was made as shown in Figure 11 to demonstrate

I
. . . . 0 O
the fit of the theory to experiment. The function shown is A -[ S where

A0 =A (experimental or theoretical)

+(0._N+B) cl/Z

which is the difference between [3 and the values predicted by the

 

limiting law. The data is best fit using .A.° = 123.30 ohm'lcmz
equivalent-1, andja = 6. 5 1g. . This combination fits up to l. 8 x 10'3
normal, after which systematic deviations occur.

Two of the less successful attempts at fitting, curves 1?: and E,
illustrate the effect of changes in% on the predicted conductance. All the

0
curves in Figure 11 were made assuming A. = 123. 30. The major

 

effect of changing A) is a slight displacement of the conductance

curve rather than a change in its shape. The Einstein viscosity effect

is not very large, for this case, decreasing the equivalent conductance

at 10"4 normal by only about one part in ten thousand and at 5 x 10"3
normal by four parts in one thousand. All the curves in Figure 11

include the viscosity correction, which is made only for the metabenzene-

. . o
disulfonate ion, and assumes R = a.

 

Curve A shows that the Fuoss-Onsager theory without ion-pairing

0
predicts conductances which are too high for any reasonable value of a.

26

om

{swim mcflfihwd ofi Eoum
mcofimmoumxo adoflouoofi Hano>om was some Hmucocfiuomxo 9.3 m0 mcofimgofl

so we finsfisoz

ON OH

.n sssmE

 

 

_ ‘

m6

 

 

 

oo.mu

 

27

Only by using an unlikely; of less than 33: could this conductance
equation be made to come close to fitting the experimental data.

While curve D fits the data very well it is probably not unique; the
data could no doubt have been fit as well without the viscosity term by
using a lowerfa or by including the viscosity correction for both ions
and using a slightly larger 2a. All this means is that the presence of the
viscosity effect is not proven by these data, but, on the other hand this
theoretically predicted effect is certainly compatible with the data.

The concentration at which the theory breaks down seems reasonable,
as one would expect systematic deviations to begin to occur at about

2. 5 x 10'3 normal, or onewfourth the concentration at which the theory
breaks down for 1—1 electrolytes.

The value of A 0 obtained in this research combined with the

 

value of )‘OBa++ given in Robinson and Stokes (15‘; yields 59. 67 ohm'lcmz

equivalent"1 for the metabenzenedisulfonate ion.

The results of this work show that the 2-2 electrolyte barium meta-
benzenedisulfonate gave the expected strong electrolyte behavior and that
the extended theory can successfully analyze the data to a reasonably
high concentration without assuming ionic association. Only after this
and other 2-2 electrolytes have been studied in water and mixtures
such as dioxane-water, can the general applicability of the extended

theory to 2-2 electrolytes be determined.

U'IFPUON

10.
11.

12.

l3.

14.

15.

LITERATURE CITED

. Arrhenius, 8., Z. physik. Chem., 1, 631 (1887).

 

Debye, 13., and Hiickel, B., Physik 2. gig, 185, 305 (1923).

. Onsager, L. Physik Z. 28, 277 (1927).

 

..Fuoss, R. M., and Onsager, L., J. Phys. Chem., 61, 668 (1957)..

 

Fuoss, R. M., and Onsager, L., Proc..Nat. Acad. Sci., 4_:_1_,
274, 1010 (1955).

 

. Fuoss, R..M., and Accascina, F. , ”Electrolytic Conductance, "

Interscience Publishers, Inc. , New York (1959).

. Dye, J. L., Faber, P. M., and Karl, D..J., J. Am. Chem. Soc.

 

333, 314 (1960).

. Dye,.J..L., and Spedding, F. H., J. Am. Chem. Soc., 7_6_, 888

 

(1954).

. Karl, D.. J. , "I. The Electrophoretic Contribution to Equivalent

Conductance Using the Complete Exponential Distribution Function:
l-l Salts in Dioxane-Water Mixtures, " Ph. D. Thesis, East Lansing,
Michigan, Michigan State University Library. 1960. '

Fuoss, R. M., and Onsager, L., J. Phys. Chem. 62, 1339 (1958).

 

Thompson, H. B., and Rogers, M. T., Rev. Sci. Instruments, 3.1,
1079 (1956).

Daggett, H. M., Bair, E. J., and Kraus, C. A., J. Am. Chem. Soc.

 

 

12, 799 (1951).
Owen, B. B., J.1Am. Chem. Soc., 61, 1393 (1939).

 

Harned, H. S., and Owen, B. B. , "The Physical Chemistry of
Electrolytic Solutions, " 3rd Edition, Reinhold Publishing Co. ,
New York, (1958).

Robinson, R. A. , and Stokes, R. H. , "Electrolytic Solutions, "
Butterworth Scientific Publications, London, (1955).

28

 

 

CHEMISTRY I YRR A RY