ACTIVITY ME AS UREMEN TS IN WATER AND
CLAY-WATER SYSTEMS

By
G-oro Uehara

AN ABSTRACT
Submitted to the School of Graduate Studies of
Michigan State University of Agriculture and
Applied Science in partial fulfillment of
the requirements for the degree of
DOCTOR OF PHILOSOPHY
Department of Soil Science
1959

G-oro Uehara

ABSTRACT
Electrometric methods were utilized to measure plant
nutrient activities in water and clay-water systems on the
premise that activity is better than concentration as a
measure of nutrient availability.

A tertiary amalgam elect­

rode, silver-silver chloride electrode and a glass electrode
were used with each other or in conjunction with a reference
calomel electrode to measure ion and Ion pair activities.
The relationship between the activity and the chemi­
cal potential, as well as the significance of the electro­
chemical potential and the total activity in heterogeneous
systems, were discussed.
An experiment was devised to measure the relative
replacing power of several alkali and alkaline earth metals
for calcium in calcium saturated clay suspensions.
order of replacing power was found to be Rb

The

Mg> K > N a > L i .

Measurements of calcium ion, hydrogen ion, calcium
chloride and hydrochloric acid activities were carried out
in clay suspensions containing various ratios of bentonite
and kaolinite.

Similar measurements were made in suspen­

sions containing bentonite-vermiculite mixtures.
showed that:
kaolinite,

(l)

The data

bentonite formed a stronger acid than

(2) calcium and calcium chloride activities

were higher in kaolinite and vermlculite suspensions than

G-oro Uehara
in the corresponding bentonite suspensions,

(3) when

bentonite was mixed with kaolinite or vermiculite the Ion
activity values were not a purely additive function of the
two clays, but were greater than the sum of the activities
of the individual clays.

Interaction between exchange

sites of the different clays was cited as the cause for
the last observation.

ACTIVITY MEASUREMENTS IN WATER AND
CLAY-WATER SYSTEMS

By
G-oro Uehara

A THESIS
Submitted to the School of Graduate Studies of
Michigan State University of Agriculture and
Applied Science in partial fulfillment of
the requirements for the degree of

DOCTOR OF PHILOSOPHY

Department of Soil Science

1959

ProQuest Number: 10008621

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ACKNOWLEDGMENTS
This study was made possible through a Graduate
Research assistantship offered to the student by the
Soil Science Department of the Michigan State University
Agricultural Experiment Station.

The student is especi­

ally grateful for the freedom he was allowed in doing
research of his own choice.
Special thanks go to Dr. Max Mortland for his
help, suggestion and his encouragement to all his stu­
dents to conduct new and original research in the field
of Soil Science.

ii

TABLE OF CONTENTS
CHAPTER
I.

PAGE
INTRODUCTION................................

1

Generalizations Pertaining to Nutrient

II.
III.

Uptake...................................

1

Purpose of Study...........................

6

THE ACTIVITY CONCEPT.......................

8

THE ACTIVITY AND THE ELECTROMOTIVE FORCE
OF CELLS.........................

19

IV.

ELECTRODE THEORY............................

22

V.

PREPARATION OF E L E C T R O D E S .................

27

VI.

CLAYS AND CLAY P R E P A R A T I O N S ...............

36

ACTIVITY MEASUREMENTS IN WATER SYSTEMS.

47

VII.

VIII.

. .

Measurement of Mean Activities...........

47

Approximation of Individual IonActivities .

51

THE ELECTROCHEMICAL POTENTIAL AND THE
TOTAL ACTIVITY............................

IX.

59

CALCIUM CHLORIDE ACTIVITY MEASUREMENTS IN
CLAY-WATER SYSTEMS........................

63

Ion Competition in C l a y s . ...............

64

Calcium Chloride Activity Measurements
in Clay Suspensions Containing Mixtures

X.

of C l a y ................................

66

DISCUSSION..................................

74

LITERATURE

C I T E D ..................................

83

A P P E N D I X ...........................................

85

iii

LIST OF FIGURES
FIGURE
1.

PAGE
Cell for measuring CaClg activity; A tertiary amalgam electrode, B - silver-silver
chloride electrode.......... ........... .

28

Cell arrangement for amalgam preparation; A platinum anode, B - IN nitric acid, C- plati­
num contact, D - inlet for nitrogen gas, E .........
0.5N lead nitrate, F - Mercury. .

29

3.

Silver-silver chloride electrode.............

34

4.

X-ray diffraction patterns for the less than
two micron fraction of bentonite from Upton,
W y o m i n g .......................................

40

X-ray diffraction patterns for the less than
five micron fraction of ksoLInite from Bath,
North Carolina................................

41

X-ray diffraction patterns of vermiculite
(Zonolite).....................................

42

Differential thermal analysis curves of
bentonite and kaolinite ......................

43

2.

5.

6.
7.
8.

9.

10.

11.

Dependence of calcium and calcium chloride
activities in bentonite suspensions on the
addition of symmetry concentrations of
chloride salts................................

67

Dependence of calcium and calcium chloride
activities in kaolinite suspensions on the
addition of symmetry concentrations of
chloride salts................................

68

Dependence of calcium, calcium chloride,
hydrogen and hydrochloric acid activities
on the clay composition of calcium saturated
bentonite-kaolinlte suspensions containing
one symmetry concentration of hydrochloric
acid.
.......................................

71

Dependence of calcium and calcium chloride
activities on the clay composition of calcium
saturated bentonite-kaolinite suspensions
containing one symmetry concentration of
potassium chloride............................

72

iv

LIST OF FIGURES (continued)
FIGURE

PAGE

12.

Dependence of calcium and calcium chloride
activities on the clay composition of
calcium saturated bentonite-vermiculite
suspensions containing one symmetry concentra­
tion of potassium chloride..................... 73

13.

Dependence of the ratio of the hydrogen to
the square root of the calcium ion activity
on the clay composition of calcium saturated
bentonite-kaolinite suspensions containing
one symmetry concentration of hydrochloric
acid......................................

v

80

LIST OF TABLES
PAGE

TABLE
I.

II.

Activity Coefficients f, at 25° on the
Molarity Scale of Some Calcium Chloride
Solutions...................................

50

Individual Ion Activity Coefficients . . .

57

CHAPTER I
INTRODUCTION
Generalizations Pertaining to Nutrient Uptake
The agronomist is constantly faced with two funda­
mental problems:

(a)

Increasing crop yields per unit

area of cultivated land and (b) predicting magnitudes of
yields for a given set of field conditions.

Before he can

begin to solve these problems he must understand the vari­
ables which control crop yield.

First of all the agrono­

mist must consider all the factors that affect yield; he
can do this symbolically as a functional relationship thus:
y = f(a, b, c, • • ., a ^ , b , c , • , #)
(a’

b* ’, c* * , . . . )

(1)

where y represents yield; a, b, c t , , • are such nutrients
as nitrogen, phosphorous, potassium, etc.; a 1, b 1, c', • . .
the soil physical factors such as temperature, moisture,
soil structure, etc.,; and a 1 1, b* ' , 0 ' 1 , . . . repre­
sent such factors as the genetic make-up of the plant,
plant population, method of cultivation and planting, etc.
Having listed the factors which control yield, the
agronomist then attempts to show the exact functional re­
lationship between yield and a given variable.

1

Any change

2
in yield as a result of a change In this variable is ex­
pressed as:
dy = (dy/da)da
b,c...,a*,bf,c' ...,a'1,b*1,c*1...(2)
where a is the variable under investigation.

The evalua­

tion of similar equations is in fact the whole essence of
agronomic science.

There is, however, one very important

difference in the above equation as compared to other ex­
pressions of this type.

It is not enough in equation 2 to

maintain constancy of the other variables; It is equally
Important that these variables be kept at an optimum level.
This point cannot be overemphasized in agronomic work.
Let us take a case In point to clarify this state­
ment.

Consider the case of an agronomist trying to show

the essentiality of a minor element.

He takes great pains

to keep all other yield factors constant and demonstrates
to his satisfaction that application of Increasing incre­
ments of the element in question has no effect on yield.
Evaluation of this kind of data might lead one to believe
that the element was not essential for plant growth, or
was at least present in sufficient concentration in the
growing medium.

The conclusions drawn from this seemingly

simple experiment may prove to be wrong.
Liebig, long ago realized that crop yields were con­
trolled by the nutrient that was most deficient.

He be­

lieved that increasing application of one nutrient could
not increase yield if another essential element was deficient

to a greater degree.

More recently Baule (31) and Bray

(6) have made modifications to Liebig’s concept, but the
fundamental generalization proposed by Liebig is essenti­
ally correct.

The importance of maintaining the constant

variables at an optimum level now becomes apparent.
If the function y = f(a) is to attain a maximum,
none of the constant variables should be deficient, and
finally, the true functional relationship between #y*
and ’a ’ can be obtained only when this condition is main­
tained.

We can further extend Liebig’s argument to include

physical properties of the growing medium as well.
In brief, we should not be expected to demonstrate
true functional relationships between yield and the inde­
pendent variables if a single nutrient or physical growth
factor deviates even slightly from their optimum levels.
As far as the plant is concerned, the expression (dy/da)
= 0, for all values of fa ’, has no significance unless
’a ’ is the only limiting growth factor.
Having at last established the functional relation­
ship between yield and growth factors, the agronomist is
now in a position to predict crop yields - if he can
quantitatively measure the magnitudes of the growth factors
this is a difficult task indeed.

The degree with which he

measures and controls these growth factors represents in
part his success as an agronomist.
A soil physicist may spend a life time developing
methods for measuring the moisture content in the soil.

4
He learns early in his training that the total moisture
content is not a very useful measurement.

He turns his

attention to measuring the “available" water in the soil.
Similarly, the soil chemist attempts to measure the nutri­
ent content in the soil; he too learns that total elemental
analysis is not the best measure of nutrient availability.
The agronomist who spends his time correlating
yield data to soil chemical tests often finds his results
disheartening.

Examination of equation 2 reveals, in part,

reasons for this kind of results.
be kept under rigid control.

Too many variables must

Costly green houses and com­

plex experimental field designs can be used to overcome
some of these difficulties.

Another source of error in the

data is Inherent in chemical tests themselves.

A chemical

test showing acceptable correlation for a given nutrient,
a particular soil and requiring edisonian trial and error
method for its development may ultimately fail when applied
to another soil.

The weakness of soil tests may lie in

their use of concentration as a measure of nutrient avail­
ability.
If we consider the plant root and the mechanism of
nutrient uptake, we might obtain an insight to why use of
concentration might fail as a measure of nutrient avail­
ability.

Take for example a plant root penetrating the

soil medium; each root has many microscopic root hairs
which actively absorb plant nutrients from the soil solu­
tion.

There is reason to believe that nutrient uptake

5
Involves two steps, first a reversible, physical movement
of nutrient from the soil solution into the lfapparent free
space” (18) located somewhere in the plant body, and second,
an active Irreversible absorption, involving biological
carriers (7) from the "free space” Into the plant tissue.
We might look upon the surface of the root hair as
a membrane separating the soil solution from the "free
space” .

If we assume the movement of nutrients across the

membrane to be a purely physical process, then when the
system is in equilibrium, i.e. when the phases on either
side of the membrane are in equilibrium with each other,
the chemical potential u, for a particular nutrient must
be the same on both sides of the membrane.

Symbolically

this same idea can be expressed as
u0 = U jl
where the subscripts o and 1 represent the soil solution
and the "free space” respectively.
Of course this system never attains equilibrium;
the plant continuously depletes the solution in the "free
space” of Its nutrients and the chemical potentials of the
components will he higher in the soil solution than in
the "free space” .

There will then be a tendency for the

nutrients to pass spontaneously from the soil solution
into the "free space".
The chemical potential is related to the activity a,
of the nutrient by the expression
u = u° + RTln(a)

6
where the constant u° is a function of the temperature T
alone and is the chemical potential of the nutrient In
its standard state of unit activity.
gas constant.

R is the universal

If we look upon the chemical potential,

defined In terms of activities as a tendency of the nutri­
ents to pass into the plant, then activities should be a
somewhat better measure of nutrient availability than con­
centration.
Up to this point nothing has been said about the
nature of the plant nutrient.

Most plant nutrients are

absorbed into the plant tissue as ions so that the signifi­
cance of the chemical potential as described earlier is
true only if the electrical potential

is the same In

both the soil solution and the plant tissue.

Since the

inequality of the electrical potential between these phases
is probably the rule rather than the exception, a special
chapter has been devoted to this subject.
Purpose of Study
It is not the purpose of this work to correlate
nutrient uptake with nutrient activity In soil systems.
Soil systems are too complex and Interpretation of activity
data would be at best difficult.

Instead activity measure­

ments were conducted in systems of known composition in
the hopes that generalizations from such measurements
could be extended to more complex soil systems.

7
Activity measurements were made electrometrically,
utilizing reversible electrodes.

Measurement of approxi­

mate single ion activities was also attempted.

CHAPTER II
THE ACTIVITY CONCEPT
In measuring the colllgative property of an Ionic
solution It Is evident that the measured property, for
example the depression of freezing point, does not in­
crease linearly with the number of dissolved particles
contained in the system.

According to early proponents

of the classical theory, this behavior was considered to
be associated with the degree of dissociation of the
solute.
It is well accepted today that partial dissociation
of strong electrolytes is not the cause for this anomalous
behavior of electrolytic solutions.

If we apply the laws

of chemical equilibrium to the dissociation of a unl-univa«
lent salt MA, which Ionized into a cation M+ , and an anion
A", It necessarily follows that the quantity
(M+) (A")
(m a )
calculated by means of the Arrhenius theory, must be a
constant.

We know, as a matter of fact, that when con­

centration Is used in equilibrium studies the quantity is
found to vary markedly with concentration.
X-ray diffraction studies on the crystal structure
of salts Indicate that many salts exist in the ionized

8

9
form even in the solid state.

Consequently, when such a

salt is dissolved in water, the particles going into solu­
tion do so as ions and not as molecules.

With this newer

concept in mind the physical chemist was forced to look
for a new approach to the problem of accounting for the
departure of electrolytic solutions from ideal behavior.
The early workers logically assumed that if electro­
lytes in solutions existed as charged ions then at least
part of the anomalous behavior could be attributed to lnterionic attraction and repulsion between charged particles.
This idea has helped to clarify many of the inconsistencies
observed in experimental work resulting from the use of
the Arrhenius theory.

Although the newer concept has

wider theoretical significance and predicts various proper­
ties of electrolytic solutions, it has by no means solved
all problems pertaining to solutions and particularly to
heterogeneous colloidal systems.
In the following paragraphs the theoretical aspects
of the Interionic attraction theory will be discussed.
The material covered In this section are for the most part
summarized from several textbooks of physical chemistry
(8), (12),

(21),

(29).

The activity concept is described

here in the hopes that it will aid In the understanding of
this study*
The basis for the theory of interionic attraction
depends on the assumption that strong electrolytes are
completely Ionized, and that the anomalous effects observed

10
are due to the unequal distribution of Ions resulting
from Interionic attraction*

Consider the case of a

strong uni-"univalent electrolyte in solution.

There

will be electrostatic forces of repulsion and of attrac­
tion between ions of opposite charge.

We can therefore

expect the probability of locating ions of opposite charge
around a central ion to decrease as the distance from the
central ion is increased.

Pictorially we might think

of an ion swarm around a central ion of opposite charge.
If we can measure or assume some functional relation
describing the distribution of the ions with respect to
one another and similarly, assume a relationship of the
forces acting on the ions due to the ions themselves in
the absence of external forces, we have a starting point
for the development of this theory.
Debye and Huckel who popularized this concept
selected the Piosson equation
JTC’*

dy'u

0

to describe the electrostatic potential Ijj , due to an
ion and its atmosphere, where/0 is the net charge per cm^
at any point (x,y,z) and D is the dielectric constant of
the solvent.

In the absence of external fields the ionic

swarm or atmosphere Is radially symmetrical with respect
to the central ion.
nate iS

Equation 3 expressed in polar coordi­

. y
j_ </_/-».*
r*- j - r V

/ I / . ,

yj. \
J =

_
0

where r Is the radial distance from the central ion.

11
The second fundamental assumption considered In
the development of this concept is the selection of some
distribution furmula which will describe the average charge
density P at the point where the potential is Ip .

Assum­

ing the Boltzmann distribution formula which states that
if n^ is the average number of i-ions in the differential
volume dV, the number of n^' whose potential energy is
above the average is
-

-- n L e
where

*T

(5)

and kT are the charge and kinetic energy of the

i-ion and 'Xfj is the potential onorgy of the 1-ion in the
vicinity of the central J-ion.

The charge density /° in

this volume is then the sum of the product n Z c e and may
be expressed as

fO

2-.

r

21

' B 'e

€ S

(6)

C-(

The exponential Q
for values of

converges rapidly when expanded

kT

much less than one.

This condi-

tion is true for'very dilute solutions where the interionic
potential energy is much less than the kinetic energy.
dilute solutions then

_ ±tSJPi
€

_

kT

kT

(7)

for a good approximation and
=

4->

*r

(8)

Electrical neutrality for the system as a whole requires
that

For

12
1 ftc'a o

O

^

(9)

so that equation (8) reduces to

P-

-

Z

<1 0 >

£Af

Combining equations (4) and (10) we finally arrive at
\ . A A r

j-

T 'dri

^ a , - ^ . = ** y .

d-r ) ' O k T

J

where for convenience we define K
v

K

T

\

(11)

3

as

1 /2 • -1*£ V

5^ 7 = 2_>

** *

£=>

(12)

The quantity K, called the Debye has the dimensions of
reciprocal length and varies with the number of ions,
ionic charge, temperature and dielectric constant of the
solvent.

It can be shown that the general solution of

equation (ll) is
- jK>\b

=

j A e

l.J L

y

T

y

Kr
<?

(13)

From this equation It is obvious t h a t b e c o m e s very large
as r approaches infinity; this difficulty is solved by
setting B=0 and the solution reduces to

\fi. =
3

or

.

A

V

e

_A ^ /— I<-v^

V

(14)

for small values of kr.
If we make the assumption that ions can be treated as
point charges, the constant can be determined by choosing

13
an Infinity dilute solution so that&£ approaches zero and
simply becomes A/r.

On the other hand if we consider

a point charge z^e in a medium of dielectric constant D,
the potential yf) at a distance r due to this charge alone
is z^e/Dr.

Since in the limit as-K" becomes zero
\b

JA_
Iry~

-

47

^
*

JZ
4j j4* -

(1 5 )

Dr

we arrive at a point where A is evaluated to be
A

t
rT~
~D

•

(16)

and equation (14) becomes

V,

- -fr

■ -

(17)

Equation (14) informs us that the potential ^ . i s the algebraic
sum of two potentials, the last
potential of the central
atmosphere.

term on

the

ion in the absence

right

being the

of an

ionic

The first term must then be the potential due

to the ionic atmosphere; it is this part that is of interest
in this discussion and shall be denoted by the experssion
Wj
)
q

.

_

_ _

JK

(i8)

However, it is not quite correct to treat ions as point
charges.

If we consider

we can write

Gauss' theorem

of electrostatics

^
-ft 7T

4/7*

~

e

(19)
where the lower limit a, represents the effective diameter
of the central j-lon.

The theorem in words is that the

14
total electric flux over any closed surface equals 4 pi
times the total charge inside the surface.

The integral

can be evaluated if p is expressed as some function of r.
The charge density

p and

-

was shown to be

<20)

Z
c»t

be

1

<2 1 >

'r"

Combining (20) and (21) we have
_

*.-*/,■*-

A

(2 2 )

C
whereiC has the same meaning as before.
this expression for
~co
a

K O

P

Substituting

in equation (19) we have
(2 3 )

(re'1
u.

which when integrated between the expressed limits becomes

A D (I
i

(24)

If equation (24) is solved for A and this value substituted
in equation (21) we have an expression for
_ K<*.

K a

§ --- • ? —

D

0 +

V^'

/<*)

—

(25)

r

which does not make the assumption of treating Ions as point
charges.

This potential

however, Includes the potential

that Is due to the charge on the central Ion along with
that part due to the ionic atmosphere.

If we subtract

15
that part due to the central ion, namely z^e/Dr from
equation (2 5 ) we have
0 .
W

,

-

(26)

^ S J L
D(t+K*)

which is again that part of the potential of the ion of
charge z^e which is due to the surrounding ions.
single ion the extra free energy />/

For a

. is equal to the

work that must he expended to charge the ion reversibly
to the required potential IP which is -zieK/D(l+Ka).
'V
, 7
ri>D C

-e X
'
ilp(i-tKa)
If the supposition is made that the deviation of
-

ionic solution from ideal behavior is entirely due to the
existence of electric charges on the solute particles, it
follows that the expression for the total free energy of
this system will differ from that of an ideal one by an
additional term due to the electrical energy of the solu­
tion.

Thus the free energy F of an ionic solution may be

expressed by the equation
F
where F ^

= Fu

(2 8 )

-+

and Fel are the free energies due

solution and electrical energy respectively.

to theideal
Furthermore,

for an ideal solution of concentration c, the chemical
potential u id per molecule is defined as
uid = constant + kTlnC
Ifthe solution is not ideal the chemical potential

(29)
u

16
per molecule Is
u = constant + kTlna^
= constant + kTlnC^ + kTlnf^

(30)

- u Id + M l n f ^
where

Is the activity and f^ the activity coefficient

of the solute

quation 30 expresses the actual chemical

potential u, in terms of the ideal chemical potential u ^
and the activity coefficient f^.

The Importance of this

expression Is that kTlnf^ Is the extra electric free energy
per ion and is equal to the work expended to charge the ion
reversibly to the potential

which is -z^e K/D(l + Ka) so

that
(31)
It follows from the above expression that the activity co­
efficient of the ion of valence z± Is given by the equation
(32)
It is frequently convenient to speak of the mean activity
coefficient of the electrolyte because the Individual Ion
activity coefficient is experimentally not measurable.

The

mean activity coefficient f+ of the electrolyte Is defined
by the equation

17
for an electrolyte molecule which ionizes in solution to
yield v number of ions of which v+ are positive and v- are
negative.

The individual ionic activity coefficients are

represented by f+ and f- for the positive and negative
ions respectively.
Before equation 32 is substituted into equation
33 a to obtain an expression which is experimentally measur­

able, it is convenient to introduce practical units such as
concentration

£*' -

7 T

(34)

1000

and the ionic strength I

I - Z

<35)

i

as well as to combine constants such as
A

8

^ ----------S' 2- 7T A'1 \ /o
Z 2>o$(DkT^/L
I& Q O

(

-

8 rr N c
I
V iooo O k T

\ 4

so that equation 32 becomes

"
/ +B*i f l
Finally substituting the expression for the activity
coefficient of the positive and negative ions into equation
33 a we have

X. i

( ^

/

for the mean activity coefficient.
—

f - f

Sa.i'ff

(3 *

Since *£2^-^2-- the quantity
"2:f ?■-

18
and equation 36 reduces to
Z-rZ-

(37)

-t-

/ -f d a -- f j T
which is the expression for the mean activity coefficient
of strong electrolytes as developed by Debye and Huckel.
The constants A and B vary with the temperature and the
dielectric constant of the solvent so that for a given
solvent and temperature the mean activity coefficient
depends upon the ionic strength I of the solution and the
average effective ionic diameter aj,.

The mean activity a+

of an electrolyte is related to the mean molarity 0 + and
the mean activity coefficient f+ by the identity
a+ = f+ C+
The mean ionic quantities are in turn related to the in­
dividual ionic quantities, indicated by the subscripts
plus and minus, in the following manner.

Equation 37 fails for concentrated solutions because
in the expansion of the exponential in the Boltzmann equa­
tion only the first two terms were considered.

Other

factors such as the effect of the solute on the solvent
molecules were not considered.

Extension of the Debye-

Huckel theory to more concentrated solutions can be found
in advanced textbooks of physical chemistry and will not
be discussed here.

CHAPTER III
THE ACTIVITY AND THE ELECTROMOTIVE FORCE OF CELLS
The emf of a cell depends upon the activities of
the constituents of the solution.

For any reaction such

as

(38)
if the activities of A and B at the start are a^ and aB ,
while the activities of C and D at the end of the reaction
are a^ and a^ respectively, then the free energies of each
of these substances per mole at a temperature T are given
by the expressions

(39a)
(39b)
(39c)
(39d)
where the F0,s represent the free energies at unit activity
of the respective species and R is the universal gas con­
stant.

By definition the free energy change of the re­

action is

Substituting equation 39&> 39b, 39c and 39d into

19

20
equation 40 we have

^

^

where £

/

f

) - fa (l
A+

(41)

represents the free

j]

energy change of the reaction in the standard state.
This expression is usually written a s ^ F°, and equation
\

41 becomes

^

^

■

^

V

/

r

r

Z

<2* die

'

( « >

Any work performed by a cell can be accomplished
only at the expense of a decrease in free energy taking
place in the cell.

When the cell operates reverslbly, the

electrical work is a maximum and the decrease in free energy
must equal the electrical work done.

The above statement

describes the fundamental relation between emf and A F
which is
A ^

=

rjc r+*—F

^

(4 3 )

where z represents

the number of electrons involved, cf~ the

faraday unit and E

the emf of the cell.

Dividing equation 42 by - ^ y " w e have
£- = - A E . ° ^
^

(44)

A
a ^ a b

■

When the activities of

all the products and reactants
^ 6
^ p 0
are unity, the value of the emf is A * --- ^ . The E° is
called the standard emf of the cell.

E° f o r

7^
^ i

If we now substitute

in equation 44, we have the important relation

describing the dependence of cell emf to temperature and
activities of the reactants and products, which is
r

~

c

°

F T

/

a $ .■ ■

CHAPTER IV
ELECTRODE THEORY
In electrochemical work it is often possible to use
a pure metal in equilibrium with a solution of its ions as
one of the electrodes in the cell*

The general reaction

of these metal-metal ion electrode Is

M

* M

”

-the'

(46)

and for which the electrode potential Is expressed by

(47)
The pure metal in contact with a solution is reversible
to Its own ions and the measured potential E^ is deter­
mined by the activity of its own ion a ^ n and the standard
electrode potential E^ of the pure metal*
In many Instances, however, the metal reacts vio­
lently with aqueous solutions and provisions must be em­
ployed to reduce the activity of the metal.

This can often

be accomplished by substituting an amalgam of the metal for
the pure metal.
Amalgams of metals more active than mercury behave
essentially as do the pure metals, the only difference
being that the activity of the metal is lowered somewhat
22

23

by dilution In the mercury.

Electrodes of these amalgams

are preferred frequently because equilibrium can be estab­
lished much more rapidly than with the pure metal, and
because they are more readily reversible.
The successful use of amalgam electrodes In homo­
geneous systems is evident from the large number of pub­
lished data obtained from use of such electrodes, but
measurements of ion activity in heterogeneous systems
present certain difflculties.

Extraneous ions may react

with the amalgam and render the electrode ineffective un­
less some protective measure is undertaken.

Joseph (15)

using a cell Involving a calcium amalgam and a silversilver chloride electrode obtained activity coefficients
of various calcium chloride solutions which compared
favorably with data obtained by other workers.

He was less

successful when similar measurements were made In hetero­
geneous biological systems containing diffusible amines
and ammonium ions.

In a later paper (l6 ), Joseph prepared

an amalgam electrode suitable for use in heterogeneous
systems.

It is on the strength of Joseph's work that a

similar electrode Is prepared for activity measurements in
colloidal silicate systems.

The theory of this particular

electrode is described in the following paragraphs.
In a saturated solution containing lead and calcium
oxalate the activity of each cation depends on that of the
other.

The solubility product of each electrolyte Is ex­

pressed as

24

C C * ' ] L U 0

[n*y{c,

- J

'J

0

k,Z

■

where the bracketed quantities represent activities of
the ions.

Since the oxalate ion is common to both cations

it follows that

k~

/ / / 7
L f? j [P H

-

-TT

--

(48)

and from the above equation we see that the activity of
each cation Is proportional to the other; the proportional­
ity constant being determined by the solubility products
of both oxalates.
An electrode described by the chain

P L ( ttg ) j

P L C x f) ^ j C

a

C j-D *

j

^

In which calcium ions made contact with lead amalgam through
lead oxalate reacts according to the equation

PL + C<3l C%0 +

=

P L C iO if^ C a .

J le "

(50)

If a silver-silver chloride electrode is Immersed in a
calcium chloride solution along with the amalgam electrode
to form a cell, the amalgam electrode is negative and under­
goes an oxidation.

For the oxidation the electrode reaction

is given by the preceeding equation with an electrode poten­
tial given by
F

E cF

‘

-

£Z-

s f

JL

(51)

25
The significance of this equation lies in its similarity
to equation 47*

Although the standard electrode potential

in equation 51 is characteristic of the amalgam elect­
rode and not that of the calcium metal, the important fea­
ture of the amalgam electrode is the dependence of the
single electrode potential E^a on the activity of the cal­
cium ion aQa++.
The silver-silver chloride electrode will undergo
reduction for which the reaction is

ZAgC/

+

(52)

and the single electrode potential is

E ct

• E<*

-

4$. ^_

-

a Ce.-

(53)

On adding equation 50 and 52 we find the cell reaction to
he

+-tC & . (54j

ph + C^Ci.09 + 3A$CI r 7 Ay +

and similarly on adding equations 51 and 53 the cell emf
becomes
j-

E

rr*

'

£

3 # r

0

„

- ygT ^

^

(55)

where &+cacl2 is the mean activity of the electrolyte and
is defined in terms of the individual ionic activities a+
and a- as

a% = (a?aY~)

**

for an electrolyte whose molecule ionizes into v number
of ions of which v+ are positive and v- are negative.

26
This amalgam electrode behaves as a reversible
calcium electrode only if other cations capable of forming
Insoluble oxalates and anions which form insoluble lead
salts are absent or are present in sufficiently low con­
centration.

CHAPTER V
PREPARATION OF ELECTRODES
The cell employed in the experiment is illustrated
in figure 1.

A silver-silver chloride and an amalgam

electrode reversible to calcium ions are suspended in the
arms of an H-shaped tube.
In order to prevent oxidation of the amalgam by
atmospheric oxygen the amalgam was sealed in a calcium
chloride drying tube as shown in figure 1.

A platinum

wire was sealed in a capillary tube and welded to one end
of the calcium chloride drying tube.

Contact with the

amalgam was made by placing an exposed section of the
platinum wire approximately 0.5 cm from the mouth of the
tube.
Lead amalgam was prepared by using triple distilled
mercury as a cathode in a 0 .5 N solution of recrystallized
lead nitrate.

The anode was a perforated platinum foil

in a solution of IN nitric acid; the two solutions being
connected by means of an inverted glass U-tube filled with
IN nitric acid.

Nitrogen gas was bubbled through the

cathode compartment throughout the electrolytic process.
Figure 2 illustrates the arrangement employed for prepara­
tion of the amalgam.

This arrangement was necessary

27

28

Pig hi*© 1 * Cell for measuring CaClg activity >
A - tertiary amalgam electrode, B - silver-silver chloride
electrode.

29

TW

Figure 2. Cell arrangement for amalgam preparation;
A - platinum anode, B - IN nitric acid, C - platinum
contact, D - inlet for nitrogen gas, E - 0.5N lead nitrate,
F - Mercury.

30
because amorphous lead peroxide formed on the anode during
electrolysis.
A rectifier provided with a powerstat was used as
a direct current power source.

A rnilliameter connected

in series with the cell was employed to measure the current.
Approximately 0.2 amperes of current was passed until the
lead concentration in the mercury reached a value in the
neighborhood of five percent.

Fay and North (9) report

that all amalgams between the limits two and fifty five
percent of lead form a two phase system at 25°C, consist­
ing of a granular phase of constant composition represented
by Pb 2 Hg, and a liquid phase which also has a definite
composition when equilibrium is reached.

Henderson and

Stegman (14) studying lead standard cells, found that
amalgams having a percentage of lead between 2,5%° and 6,0%
possessed a constant and reproducible electromotive force.
When the electrolysis was complete, the cathode
compartment was detached from the cell and used as the
container for washing the amalgam.

Conductance water

freed of oxygen by heating and saturated with nitrogen
was used for washing the amalgam.

The amalgam was subjected

to at least ten washings, with the water being removed by
siphoning.

In the final washing the last traces of water

were removed by blotting with the tip of a clean filter
paper.

During the whole washing process, a stream of

nitrogen gas was constantly passed into the mouth of the
flask containing the amalgam.

31
The cathode compartment still holding the amalgam
and filled with nitrogen gas was suspended into a tall
half liter beaker half filled with distilled water and
heated.

A five percent lead amalgam has two phases at

25 °G as described earlier, but becomes completely liquid

when heated to 100 °C*

This hot melt was poured into the

calcium chloride tube which had just been flushed with a
stream of nitrogen.

A moist cellophane membrane was

blotted between filter papers and immediately stretched
over the mouth of the tube and held in place with a rubber
band.

Lead oxalate freshly precipitated from lead acetate

and excess oxalic acid was evenly spread over the cello­
phane membrane and covered with a second membrane.
membranes.were cemented in place with collodion.

The
When the

collodion hardened, the tube was inverted and inserted into
the H-cell.

In each case enough amalgam was prepared to

construct two electrodes.

These two electrodes were placed

In a 0 .05 K CaClg solution, short circuited and allowed to
reach equilibrium.

When no potential difference between

the two electrodes could be measured, the electrodes were
considered ready for use.
There are three general types of the silver-silver
chloride electrodes in common use today.

Smith and Taylor

(3 2 ), (3 3 ) have made a thorough study on the reproducibil­
ity of these three types.

They classified these electrodes

Into the electrolytic, thermal electrotytic and thermal
type.

The electrolytic type (2), (23) is prepared by

32
electroplating a platinum gauze, foil or wire with silver
and then converting part of this silver to silver chloride
by using It as an anode in a chloride solution.

Alterna­

tively, the thermal-electrolytic type is made by coating
a spiral of platinum wire with freshly percipitated silver
oxide and heating this in an electric furnace to 400°C.
This heating reduces the oxide of silver to porous, finely
divided silver which in turn Is coated with silver chloride
by electrolysis in a chloride solution.

Preparation of the

thermal type electrode involves the thermal decomposition
of a paste mixture of silver chlorate, silver oxide and
water.

This last method avoids the step of electrolyti-

cally coating silver chloride on the electrode surface by
automatically forming a silver and silver chloride mixture
in the process of heating the paste.
Initial activity measurements were made with the
thermal type electrode as described by Noyes and Ellis
(26 ) and modified by Harned (11).

Harned omits the step

of electrolytlcally depositing a film of silver on the
platinum spiral before placing the silver oxide paste on
the wire.

Electrodes prepared in this manner gave favor­

able results in aqueous systems but failed In clay-water
systems.

This failure was attributed to Infiltration of

fine clay particles into the pores of the electrode.
Preparation and use of the thermal type electrode was
not attempted since similar difficulties were anticipated.
There remained the last choice of using the

33
electrolytic type silver-silver chloride electrode.

The

method of preparation suggested by Brown (2) was used.
Electrodes were prepared by electroplating silver on a
platinum wire and then partly converting the silver to
silver chloride by electrolysis in a hydrochloric acid
solution.

A serious weakness was observed in the use of

this electrode.

When the potential of the cell was measured,

the balance point was reached very slowly.

This character­

istic of the electrode was probably due to a polarization
effect resulting from a small electrode surface.

Con­

struction of an electrode with a larger surface to reduce
both the polarization effect and the electrical resistance
of the solid-liquid Interface was considered necessary.
The most consistent results were obtained by using
an electrode prepared by a method described in a text,
Experimental Physical Chemistry, by W. Gr. Palmer (28).
Figure (3) shows the general features of this electrode.
A strip of pure, untarnished silver, one cm by five cm,
was washed in acetone.

This rectangular piece was rolled

into a spiral and suspended by means of two platinum wires
from a silver wire sealed In a glass tube.

The clean sil­

ver metal was coated with silver chloride by electrolysis
In normal hydrochloric acid solution with a current of
six milli-amperes for about an hour.

Two or more electrodes

were prepared at any given time and they were short cir­
cuited and allowed to stand overnight in tenth normal

34

Figure 3.

Silver-silver chloride electrode.

35
calcium chloride solution.

Electrodes prepared in this

manner gave potentials which agreed within 0,1 millivolts.

CHAPTER VI
CLAYS AND CLAY PREPARATION
Clays selected for this study were bentonite from
Upton, Wyoming and kaolinite from Bath, North Carolina.
These two clays were selected as representative members
of the two major clays types occuring in soils.

The

montmorillonite group minerals, of which bentonite is a
member, are characterized by their high cation exchange
capacity and their plastic and swelling properties associ­
ated with their high capacity for adsorbing water.

Kaoli­

nite, which is a member of the kaolin group minerals, is
contrasted from montmorillonite by its low exchange capa­
city and non-swelling property.

Chemical analysis, cation

exchange capacity, X-ray and differential thermal data of
both clays are given below.
Chemical Analysis
Kaolinite
Bath, South Carolina

Mon tmo rillonite
Upton, Wyoming
SiOo -.....
KLoO-z
Fe2o|
FeO
KfeO
CaO
NapO
K 2°
h 2 o+
h So ............

S10 2
A1 2 0 3
Fe 2 0 3
FeO
MgO
CaO
Ha 20
K 20
H 20+
H 20 T10 2

51^9%
20.27

2.92
0.19
3.18
0.23

1.32
0.28
6.85

7.63

0.12
ufop -----------Total
100.48*

---------*5.58*
---------37.62
---------1.00
---------0.13
— — -— — .
0.03
— 1——■—— “—■
0.82
-----------0.42

Total
36

0.49
13.42
0.63
1.42

100.06*

37
The total chemical analysis data were extracted from
Reference Clay Minerals, American Petroleum Institute Pro­
ject 4-9*

The symbols HgO" and H 20 + represents water loss

below 105 degree centigrade and above 105 degrees respec­
tively.

The formula proposed for this'bentonite is
^A 1 .08si3.92^°lP

( ° H )2 (N a . i 7 —

;03>*

111118

formula was calculated after allocating appropriate amounts
of the oxides to impurities in the sample.

It is evident

from the proposed formula that the exchange sites, satis­
fied by sodium and calcium ions, arise from substitution
of magnesium for aluminum in the octahedral positions.
In the case of kaolinite most mineralogists agree
to the formula Alij.SI^O^o(^H )8 *

oxides other than silica,

alumina and water were attributed to Impurities in the sam­
ple.

Cation exchange capacities In kaolinite is believed

to arise from broken bonds around the edges of the silicaalumina units.
It must be realized that chemical analyses of clays
will vary even among samples taken from the same deposit.
Different leaching rates and composition of percolating
water, minor variations in the mineralogy of the parent
rock, degree of weathering and additions of impurities all
contribute to variations in chemical data.

Optical studies

on the Upton deposit show impurities in the form of quartz,
feldspars and traces of limonite.

Impurities expressed on

a weight basis ranged from six to twelve percent in the
Upton deposit.

Similar studies on the Bath, South Carolina

kaolinite deposit show impurities of sericite, quartz,
feldspar and limonite.

The percent impurity was deter­

mined to be in the neighborhood of six percent.
Cation exchange capacities of the clays were deter­
mined conductometrically as outlined by Mortland (25).
The cation exchange capacity of the clays were 72.5 and
3.00 milliequivalents per 100 grams of oven dried (100°C)
clay respectively for bentonite and kaolinite.

Briefly,

the method involves saturating a clay with barium Ions
and titrating the clay In an alcohol-water system with
standard magnesium sulfate.
X-ray data were obtained by depositing a thin
layer of the calcium saturated, glycerol-solvated clay on
a porous ceramic plate and rotating the sample with respect
to a beam of monochromatic X-ray with a scanning goniometer.
The Instrument used was a Norelco X-Ray Diffractometer
(Philips Electronic, Ina), equipped with a Geiger-Miller
counter and a scaler-rate meter with an automatic stripchart recorder, utilizing a copper tube and nickel filters.
Identification of bentonite and kaolinite by X-ray dif­
fraction methods is relatively simple for-pure clays.

When

the clays are deposited on the ceramic plate, each particle
preferentially orients with its ab plane parallel to the
surface of the ceramic plate.

This condition Is favored

because the clay particles themselves are platy in struc­
ture.

Mineralogists have been quick to put this property

to good use; clays oriented thus give d-spacings of the

39
unit cell thickness In the c- crystallographic direction.
Fortunately, the common clay minerals have d-spacings along
this axis which are characteristic for each group.

For

example, the 17.7 angstrom spacing of the glycerol solvated
bentonite (see figure 4) represents an alumina layer sand­
wiched between two silica layers plus two layers of glycerol
molecules; this arrangement being repeated many times along
the c axis.

In the case of kablinite the 7.2 angstrom peak

corresponds to the unit cell thickness in the direction of
the c-crystallographic axis (see figure 5).

The 17.7 and

7.2 angstrom lines of bentonite and kaolinite are used as
identifying features for these two minerals.
Thermal analyses were run on a hand-made differen­
tial thermal apparatus constructed by Dr. R. L. Stone of
the University of Texas.

The analyses were obtained by

using platinum-rhodium thermocouples with anhydrous alumi­
num oxide as a reference material.

A temperature range

from room temperature to 1000°C at a rate of 15° per minute
was utilized.

The high water adsorptive capacity of bento­

nite is reflected in the first endothermic peak at 150°C
(see figure 7).

This endothermic reaction corresponds to

the release of adsorbed water from the interlayer spacings
of the bentonite clay.

The magnitude of this peak varies

considerably with the amount of adsorbed water on the clay.
The second endothermic peak beginning at about 600° is
analytically more useful and corresponds to the destruction
of the crystal lattice with release of hydroxyl water.

The

Potassium

S a tu ra te d , H e a te d

Potassium

S a tu rate d ,

H eated

Calcium S a tu ra te d , G lycerol

at

at

550°

105°

C

C

S olvated

I__________l_______
30

25

15

20

D e g re e s

2

10

6

Figure 4. X-ray diffraction patterns for the less than
two micron fraction of bentonite from Upton, Wyoming.

41

Potassium

Saturated,

H eated

to 5 5 0 *

Potassium S a tu rate d ,

H eated

to 1 0 5 *

Calcium

30

25

S a tu ra te d , G lycerol

D EG R EES

C

Solvated

10

15

20

C

2

0

Figure 5. X-ray diffraction patterns for the less than
five aileron fraction of kaolin!te from Bath, North Carolina.

42

1 0 .0 2

1 4 .9 A

Varmiculita (Zonolita), Light Fraction

12.$ A

Varm iculit* (Zonolita), Haavy Fraction

I------------1------------1----------- 1----------- 1----------30

23

20

15

DEGREES

Figure 6.
(Zonolite).

2

10

L

5

.

J
2

6

X-ray diffraction patterns of vermiculite

4-3

Wyoming

Bontonito

Koolnito

J
100

i

I

i

i

i

500

i

i

i
1 ,0 0 0

Dogroos Configrodo

Figure 7. Differential thermal analysis curves of
bentonite and haolinite.

44
third endothermic peak is caused by further thermal de­
struction of the lattice and is followed by an exothermic
reaction probably resulting from recrystallization of the
thermal decomposition products.
Kaolinite gives a characteristic endothermic re­
action which starts at about 500° and reaches a maximum
at 6l0°C.

This reaction is associated with the thermal

decomposition of the lattice and the resultant release of
water.

Recrystallization of amorphous alumina is believed

to be the cause of the charp exothermic peak occuring at
980-1000°C.
Both X-ray and thermal data indicate high purity
of the samples.

No thermally identifiable impurity is

discernable in the differential thermal curves (see figure
l) and only a small trace of quartz is evident in the X-ray
curves.
Vermiculite, another common soil mineral was pre­
pared for use in this study.

The chemical composition

and structure of vermiculite is probably related to the
mineral biotite, K(Mg,Fe)^Si^A101 0 (OH)2 .

In vermiculite

much of the potassium has been weathered out so that the
interlayer spaces are accessible to water and exchange­
able ions.

Zonolite, a vermiculite commerically used as

an insulator was selected.
water and allowed to settle.

The mineral was stirred In
The lighter fraction which

remained afloat was removed and saved for this study.
Figure 6 shows the X-ray patterns of the light and heavy

45
fractions.

The heavy fraction is mainly interstratifled

mica and vermiculite with some discrete mica and vermicu­
lite.

Mica Is indicated In the X-ray patterns by the ten

angstrom line, interstratified mica-vermiculite by the
broad peak at 12.6 angstrom and vermiculite by the 14.9
ang&trom line.
with some mica.

The light fraction was mainly vermiculite
Cation exchange capacity was determined

to be 63.1 milliequivalents per 100 grams of the clay.
Before Ion activity measurements can be made in
clay-water systems it is necessary to saturate the clay
with the ion whose activity is to be measured.

Soil scien­

tists have in the past saturated clays with the desired
ions by neutralizing the hydrogen saturated clay with the
appropriate hydroxides.
couraged.

This method should best be dis­

It is well accepted today that hydrogen satur­

ated clays remain so only for a short time; acid clays are
unstable and become aluminum saturated as a result of
lattice decomposition and release of aluminum Ions into
the clay solution.
Bentonite Is for the most part sodium saturated in
its natural state and kaolinite is probably saturated with
aluminum and hydrogen ions.

Both clays were electrodialyzed

to a pH of about 5.0 and dLspersed Immediately with addition
of 0.1N sodium hydroxide to a pH of about 8.0.

This dis­

persed clay suspension was stirred and allowed to settle.
Using Stokes law for the determination of the sedimentation
rate, the less than two and five micron fractions of bentonite

46
and kaolinlte respectively were siphoned off for use in
this study.

The larger size fraction which included un-

dlspersed clay aggregates, quartz and feldspar was dis­
carded.

Selection of the five micron size for kaolinlte

was based on the observation that kaolinlte generally
occurs In the larger size clay fraction In soils.

The

sodium saturated clay was flocculated with a large excess
of calcium chloride and filtered.

Several washings of

the clay with increments of calcium chloride solution
assured complete saturation with calcium ions.

The clay

was washed with conductance water until test with silver
nitrate solution showed no trace of chloride Ions in the
filtrate.

Lastly, the clays were air dried and stored in

bottles for use at a later time.

CHAPTER VII
ACTIVITY MEASUREMENTS IN WATER
Measurement of Mean Activities
Before activity measurements were initiated in
clay-water systems it was thought advisable to test the
electrodes In water systems.

Calcium chloride solutions

ranging in concentrations from 0.001 to 0.1 molar were
prepared by dilution of a standard molar solution of the
electrolyte.

Standardization of the molar calcium chloride

solution was carried out gravimetrically by precipitation
of the chloride

ion as the silver

salt.

About 75

ml. of the dilute

calcium chloride solu­

tion were poured into the H-shaped container and the amalgam
and silver-silver chloride electrodes suspended Into the
solution as illustrated in figure 1.

A slow stream of

nitrogen gas was bubbled through the solution via the stop­
cock located at

thebottom of each arm of the container.

This step was necessary to create
throughout the clay water system.

uniform conditions
Bubbling nitrogen gas

had the added advantage of reducing the oxygen content of
the solution thereby increasing the longevity of the amal­
gam electrode, and also eliminated the question of the
effect of oxygen on the properties of the silver-silver
47

chloride electrode.

Dissolution of carbon dioxide gas

was also kept at a minimum and thus the effect of the car­
bonate ion on the activity of calcium chloride was reduced.
All activity measurements were carried out at 25°*
0.5°C by employing a constant temperature bath.

The elect­

rodes were allowed to equilibrate for an hour at which time
the amalgam electrode was removed and inverted to allow a
fresh amalgam surface to make contact with the lead oxalate.
The amalgam electrode was then placed In its former position.
Approximately ten to fifteen minutes were required after the
last step for the cell to reach a constant emf reading.
Cell emffs were measured on a Sargent Recorder, an
automatic self-balancing, variable range, potentiometer
having an accuracy of 0.1^ or 20 micro volts whichever is
greater.

There are certain difficulties encountered

the emf of a single cell is measured.

when

For example, the

accuracy of the cell emf reading of a 0.002 molar calcium
chloride solution is 5171' 1.0 mv.

An accuracy of at

least a tenth of a millivolt is required for good results.
This cannot be attained in the higher ranges of this in­
strument.

This problem can be readily remedied by using

cells of the type
Ag; AgCl/CaCl2 (m^)/CaOx/PbOx/Pb(Hg)-(Hg)Pb/
PbOx/CaOx/CaC^CmgJ/AgGl; Hg
For such an arrangement the emf of the cell is

49
Since the quantity (E^ - E|) is equal to zero, the poten­
tial measured from such a combination of cells is propor­
tional only to the ratios of the activities of each cell.
It now becomes possible to read the potential of the cell
on a lower range of the potentiometer, thus making possi­
ble readings of greater accuracy.

E* is the emf of the cell

containing the reference solution; the activity coefficient
for this solution is extracted from the literature (30),
thereby giving a basis of reference for the activity co­
efficient of all the other calcium chloride solutions.

In

Column 6 and 7 of Table I are listed the measured activity
coefficients obtained experimentally as compared to values
calculated from an equation derived by Shedlovsky and
Maclnnes (30).

The equation

-

where f and C are the mean activity coefficient and the
molar concentration respectively, has been shown to give
accurate values of activity coefficients from C = 0.002
to 0.10.
The experimentally determined activity coefficient
f(Qb S ) was calculated from the relation -logf/f* = 11.27
(E - E*) + logc/c*, where f*, E# and C# represent the mean
activity coefficient, the measured emf and the concentra­
tion respectively of the reference 0.002 molar solution.
The constant 11.27 is equal to the reciprocal of the ratio
3x2.303RT/2F at 25°C.

50

iH
cti

LA
CVJ
LA
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51
Approximation of Individual Ion Activity
There is presently no known method for measuring In
a strictly thermodynanflLc sense the activity of a single ion
species.

It is possible to predict the activity coefficient

of an ion species from the Debye-Huekel formula, but this
formula holds only for very dilute solutions.

Kielland

(17) has tabulated Individual activity coefficients for
various inorganic and organic ions.

His calculations were

based on the utilization of the diameter of the hydrated
ion as the effective ion diameter.
Although a strictly thermodynamic method for deter­
mining the activity of a given Ion species is still non­
existent, it is sometimes convenient to speak of the activ­
ity of ions.
cept.

A classical example is the use of the pH con­

Even though pH is often defined as "the logarithm

of the reciprocal of the hydrogen ion activity*, there is
no way of knowing whether such a quantity is actually being
measured.

The ambiguity arises In part from an uncertain

liquid junction potential developing from the use of the
reference calomel electrode.

This has not discouraged the

use of the pH concept among research workers; in fact pH
has been widely used in the biological and agricultural
sciences with great benefit to both.
When an electrode reversible to calcium ions and
another reversible to chloride ions are Inserted into a
solution containing both Ions, the emf of this cell mea­
sures the mean ionic activity of the two ions.

Unfortunately,

52
the mean activity tells nothing about the activity of the
individual ions.
If one wishes to estimate the activity of each ion
he can do so by making certain assumptions.

Maclnness (22)

was one of the earliest investigators to propose generali­
zations concerning the possible determination of individual
ion activities.

He is credited with suggesting the equality

of the activity coefficient of both ions in a potassium
chloride solution.

Harned (13) employing the assumptions

suggested by Kaclnnes proceeded to determine individual ion
activity coefficients potentiometrically using cells having
liquid junctions.

He assumed the liquid junction potential

to be negligible.

Lewis and Randall (19) described a

method for calculating individual ion activities based on
non-thermodynamic methods.

Two assumptions are inherent in

their method, first that the mean activity coefficient of
the potassium chloride.salt is the same as the individual
ion activity coefficients of the potassium and chloride
ions, and secondly that for solutions of equal ionic
strengths the activity coefficient of the chloride ion is
the same whether the solution be a calcium chloride or
potassium chloride solution, or for that matter any solu­
tion containing chloride ions.

This method implies that

if some value of activity coefficient is assigned to an
ion in a solution of ionic strength I, one can then pro­
ceed to determine the activity coefficient of any other
Ion.

53
For example, a 0.01 molar calcium chloride solution
has the same ionic strength as a 0.03 molar potassium
chloride solution.

If the activity coefficient of the

chloride ion is assumed in the manner just described and
the mean activity coefficient of the 0.01 molar calcium
chloride Is known, the activity coefficient of the calcium
ion can be calculated from the relationship
fC a =

( f C ia O lg P

(5 6 )

(fdi)2
where fQa and f ^

represent the individual activity coeffi­

cients of the calcium and chloride Ions and ^ c a C ^ ’

mean

activity coefficient of calcium chloride.
The calcium ion activity coefficient for several con­
centrations of calcium chloride solutions as calculated by
the method suggested by Lewis and Randall is listed in
Column 8 of Table II.
The method just described is quite satisfactory for
solutions of known ionic strength.

In clay water-systems

containing mixtures of electrolytes the ionic strength is
not always known or can be measured only with great diffi­
culty.

Some other method must be developed for approxi­

mating individual Ion activities in solution of unknown
ionic strength.

In the following paragraphs such a method

will be described.
If the emf of the cell
Ag; AgCl/KCl(m)/KCl(sat)/HgCl; Hg

54
is measured, the cell emf will be
E = E ‘ - RT In aCl
F
where

(57)

represents the algebraic sum of the standard

electrode potential of the silver-silver chloride elect­
rode, the potential of the reference calomel electrode and
the liquid junction potential.

The assumption is made here

that Ej is a true constant and does not vary with the com­
position of the solution.

This same electrode combination

can be employed to measure the chloride ion activity in a
calcium chloride solution.

If a solution of calcium chlo­

ride of concentration A gives an identical emf reading
with a potassium chloride solution of concentration B,
then the previously made assumption leads to a useful con­
clusion, namely, that both solutions have the same chloride
ion activity.

If now the mean activity of the potassium

chloride solution is known, we can obtain the chloride ion
activity from the assumption made earlier that
(aKCl)2 = (aCl)2 = (aK)2

(58)

and finally the calcium ion activity can be calculated
from the relationship
(aCaCl2 )3 = (aCa) x (aCl)2

(59)

The activity coefficient of the calcium ion fCa
can be determined if the concentration of the calcium Ion
Gftp is known from the relation

55
fCa = f^Ca
160)
^Ca
Briefly this method involves measuring the emf of
the cell for various standard calcium and potassium chloride
solutions.

Concentrations of both chloride solutions are

plotted against cell emf on semi-log paper so that for a
given emf a calcium chloride solution of say concentration
A, one can easily pick off the potassium chloride concentra­
tion having the same chloride activity.

As an example, a

0.00500 molar calcium chloride solution gives the same emf
reading as a 0.00955 molar potassium chloride solution.
The activity coefficient of potassium chloride solution of
this concentration is 0.9046 and the activity of the chloridd
ion is 0.08639 = 0.0955x0.9046.

The activity coefficient

of the chloride .ion in the calcium chloride solution is
0.8639 = 0.08639/2x0.00500.

Since the mean activity of

calcium chloride is 0.7905> the activity coefficient of the
calcium ion f^a is calculated to be
fCa = °*7905^/0.8639s = 0.6620
The activity coefficient of calcium ion as calcu­
lated by this method is given in Column 7 of Table II.
It Is evident from the data in Table II that the activity
coefficient of the calcium ion as determined potentiometrically is slightly larger than the values obtained by
the method described by Lewis and Randall.

The values

deviate considerably at the higher concentrations.

This

56
deviation may be the result of the fallacy of assuming con­
stancy of the liquid junction potential.

There are two

possible sources of error in the method of Levels and Ran­
dall:

first, the assumption of equal activity coefficients

for potassium and chloride ions may not hold for high con­
centrations of potassium chloride solutions and second,
the equality of single ion activity coefficients in solu­
tion of constant ionic strength fails at higher concentra­
tion unless the effective diameters of the various ions
are considered.
If the error lies in the potentiometric method,
it might be said in defense of the data that the error is
by a constant factor in the lower concentrations, a fortuit­
ous situation because this Is the range utilized in most of
the experimental work with clay-water systems.

Further­

more, although the true calcium Ion activity is of real
Interest to us, the ability to demonstrate relative dif­
ference between systems is of greater significance.

57
TABLE II
INDIVIDUAL ION ACTIVITY COEFFICIENTS

Cone, in moles/1 of CaCl2 and KOI
Activity
having equivalent activities of
Coefficients
chloride ions
for KC1
CaClg
KC1
solution

Activities
of chloride
Ions In CaClp
and KC1 so In.

0.100

0.171

0.7346

0.1256

0.0800

0.138

0.7490

0.1034

0.0600

0.105

O.768 O

0.08064

0.0400

0.0710

0.7950

0.05645

0.0200

0.0366

0.8375

0.03065

0.0100

0.0188

0.8740

0.01643

0.00900

0.0171

0.8788

0.01503

0.00800

0.0153

0.8840

0.01353

0.00700

0.0134

0.8900

0.01193

0.00600

0.0115

0.8964

0.01031

0.00500

0.00955

0.9046

0.008639

0.00400

0.00771

0.9132

0.007041

0.00300

0.00580

0.9228

0.005352

0.00200

0.00390

0.9343

0.003644

0.00100

0.00195

0.9523

0.001856

58

Activity Coeff.
of chloride
ions In CaClg
solutions

Mean Activity
Coefficients
of CaCl 2
solutions

Ca ion activity
coefficients
Lewis &
Experimental
Randall

0.6280

0.5269

0.377

0.307

0.6463

0.5444

.386

.323

0.6720

0.5688

.407

.346

0.7056

0.6050

.445

.385

0.7663

0.6695

.511

.461

0.8175

0.7326

•589

.545

0.8350

0.7413

.584

.557

0.8456

0.7519

.595

.574

0.8521

0.7628

.611

.589

0.8592

0.7752

.631

.607

0.8639

0.7905

.662

.631

0.8801

0.8052

.674

.653

0.8920

0.8265

.710

.686

0.9110

0.8525

.746

.729

O. 928 O

0.888

.813

..790

CHAPTER VXII
THE ELECTROCHEMICAL. POTENTIAL AND THE TOTAL ACTIVITY
In speaking of equilibrium conditions in a system
containing two or more phases the equality of the chemical
potential u, of the soluble constituents in all phases was
cited.

However, when electrically charged particles are

considered, the chemical potential must be replaced by
the electrochemical potential u, a term first suggested by
Guggenheim (10), which contains the additional energy term
ze ijt , where z is the valency of the ion, e is the elect­
ronic charge, and

the electrical potential.

The quantity

ze IjJ is the potential energy of a body with an electric
charge ze at a point where the electric potential is

.

If the particle under investigation is an ion, the potential
energy per mole becomes zF
electricity.

, where F is a farady of

For charged particles in equilibrium between

two phases of different electric potential

(61 )
If a suspension of a hydrogen-clay is allowed to
equilibrate in a beaker for several days, two distinct
phases will develop.

The clay particles will settle to

the bottom leaving a clear supernatant portion near the

59

60
surface; "the boundary between phases may be sharp.

Measure­

ment of pH will disclose a difference of 2 - 3 pH units
between phases, the pH being higher in the supernatant por­
tion,

In making these measurements two assumptions are

made, first that the system is in equilibrium and second,
that the liquid Junction potential arising from the use of
the calomel reference electrode is negligible.

If the

assumptions are correct, then it can be said that the hydro­
gen ion activity and therefore the chemical potential of
the ion is greater in the sediment than in the supernatant
liquid.

If the position of the calomel electrode is held

constant and that of the reversible glass electrode is
varied, no change in pH value is discernable.

This is

equivalent to observing a zero emf between two reversible
electrodes placed in each of the two phases.

The zero emf

between the two reversible electrodes signifies that the
electrochemical potential u, is the same in both phases
and that the system is in a state of equilibrium.

In other

words a system in equilibrium can do no work and a zero
potential is to be expected.

If instead of two reversible

electrodes, calomel reference electrodes are used, a poten­
tial difference will be observed.

If we examine equation

61, we see the reason for this phenomenon.

Equation 61

can be re-written in the form

V,

(62)

61
Presumably the calomel electrodes measures the Quantity
problem of the liquid Junction potential
again lends ambiguity to the measured quantity.
Adair and Adair (l), however, used this quantity
to calculate the charge on protein particles, and also the
relationship between
tions.

and the pH of protein solu­

Low (20) using a method similar to Adairs*

relationship between

showed

and the ionic strength, clay

concentration and zeta potential In heterogenous clay-water
systems.

He strongly suggests the greater significance of

the electrochemical potential u, and the total activity
over the chemical potential and the corresponding individual
ion activity.

His argument is based on the premise that

the total activity a, defined in terms of the electrochemi­
cal potential u by the relationship
u = u° + RTlna

(6 3 )

is the true measure of the escaping tendency of an ion.
The significance of the total activity In soils
has yet to be determined.

Overstreet (21) postulated

that owing to the higher chemical potential of cations
in soil sediments than in the equilibrium soil solution,
It would be expected that cations would be more readily
absorbed from the sediment than from the corresponding
supernatant liquid.
support this theory.
this respect.

No experimental data were given to
Overstreet probably is In error in

Thermodynamics predict that a plant sending

roots into a soil sediment as well as the equilibrium soil

62
solution will absorb ions equally well at both points.
This is assuming, of course, that the electrical potential
of the root Is the same at both points.

Since the soil

and soil solution are in equilibrium the escaping tendency
of the cation Into the root must be the same at all points
In the system.
The agronomist making activity measurements in soils
must be aware of the difference between the chemical poten­
tial and the electrochemical potential if he is to inter­
pret his data correctly.

CHAPTER I X

C A L C IU M C H L O R ID E A C T I V I T Y

MEASUREMENTS I N

C LA Y -W A T E R SYSTEMS

Cell emf measurements were carried out In claywater systems in very much the same manner as was described
earlier for the water systems.

In the double cell arrange­

ment one cell contained a standard 0.002000 molar calcium
chloride solution while the other held the variable claywater system of unknown calcium chloride activity.

A zero

emf reading for such an arrangement indicated equal calcium
chloride activity in both cells.

A concentration of 0.002000

molar was selected for the reference solution because this
was the lowest concentration giving a steady emf reading
over a long period of time.
After each measurement involving a clay-water system,
the cells were washed and tested in aqueous calcium chloride
solution.

The cells were considered operative when equal

concentration of calcium chloride in both cells gave a
zero emf reading.
Two sets of activity measurements were carried out;
the first involving measurement of calcium ion and calcium
chloride activities in clay-water systems to which free
chloride salts had been added.
63

This particular experiment

64
was made to measure the relative replacing power by various
cations for calcium adsorbed on clays.
The second series of activity measurements were
made to show the variation of ion and salt activity as a
function of the clay type and the clay composition of the
systems.
In the following paragraphs the results of these
measurements will be discussed in detail.
Ion Competition in Clays
Different cations have different affinities for Ion
exchange sites in clay minerals.

For example, If an equiva­

lent concentration of cation A and the same concentration
of cation B Is added to a clay, both Ions will not be
equally adsorbed.

This is analougous to the differential

adsorption of ions observed In synthetic ion exchangers.
This experiment was set up to study the relative
affinities of various cations for clays.

Since an electrode

reversible to calcium ion was the only one available, it
was necessary to devise some method for utilizing the
change In calcium or calcium chloride activity as a measure
of relative cation affinities.
the following manner:

This problem was solved in

four grams of calcium saturated

bentonite were placed in each of five 250 cc Erlenmyer
flasks.

One hundred ml of solution containing thirty eight

m.e. of lithium chloride equivalent to a symmetry concentra­
tion of the four grams of clay, were poured into one of the

65
flasks.

In the same manner equivalent concentrations of

sodium, potassium, rubidium and magnesium chloride were
added to the remaining flasks.

The flasks were stoppered

and allowed to sit for two weeks with intermittent shak­
ing.
The principle underlying this experiment is that
the added cation will replace a portion of calcium from
the clay into the solution phase, thereby making possible
measurement of calcium chloride activity.

The cation hav­

ing the greatest affinity for the clay necessarily replaces
the largest fraction of the calcium and thus gives the
highest activity value.
This experiment was repeated with kaolin!te clay.
Fourty five grams of clay having an exchange capacity of
3*30 m.e. per 100 grams of clay was used.

The larger

sample size was necessary to maintain a sufficient con­
centration of calcium ions in the solution phase in order
for the amalgam electrode to function as an electrode re­
versible to calcium ions.

One hundred ml of solution

containing 14.85 milliequivalents of the cation were added
to each of five flasks holding the clay.
In each of the above systems only one symmetry con­
centration of salt was added.

These systems were also

studied for calcium chloride and calcium ion activities
in which two and three symmetries of the salts were added.
This particular phase of this experiment was carried out
to determine the effect of increasing salt concentration
on the activity values.

66
Figures 3 and 9 show the dependence of calcium ion
and calcium chloride activities on the kind and amount of
chloride salt added to the clay suspensions.

The data show

that the relative affinities of the cation for the exchange
site follow the sequence L i < Na< K < M g ^ Kb.
Calcium Chloride Activity Measurements in Clay
Suspensions Containing Mixtures of Clay
The variability in physico-chemical properties among
the various soil clays has immense practical significance
in the field.

As an example, 100 grams of calcium satu«

rated bentonite have approximately 100 milliequivalents of
adsorbed calcium; on the other hand an equal weight of
calcium saturated kaolinite has only three to ten mlllidquivalents of this ion.

It is not surprising then that

for equal weights of the clays a bentonite suspension would
have a higher calcium activity.
Will a mass of calcium saturated bentonite having
ten milliequivalents of calcium release calcium ions more
readily than a larger weight of kaolinite also having ten
milliequivalents of adsorbed calcium?

Furthermore, if

five milliequivalents of calcium bentonite were mixed with
five milliequivalents of calcium kaolinite, would the cal­
cium released into the solution phase simply be an addi*tive property of the two clays?

The following experiment

was designed to answer these two questions.
One gram of calcium bentonite having 0.950

67

CaClg activity
++

ro
I
O

CM

I
O
X
'5
o
o
^1
o
o
O

X

Na

o
o

+
4-

O
o

Na

Symmetry Concentration
Figure 8 , Dependence of calcium and calcium chloride
activities in bentonite suspensions on the addition of
symmetry concentrations of chloride salts.

CaCI2 activity
Ca + + activity

Rb
Ca^"^ activitv x I0~

Co Cl2 activity x 10 ~

14

12

Rb

Na

8
Na

2
Symmetry Concentration

Figure 9. Dependence of calcium and calcium chloride
activities in kaolinite suspensions on the addition of
symmetry concentrations of chloride salts.

69
milliequivalent of adsorbed calcium was placed in a 250
ml Erlenmyer flask and similarly 28*787 grams of calcium
kaolinite having an equal amount of adsorbed calcium ions
were placed in another flask*

Systems containing bentonlte-

k a o U n i t e mixtures were also prepared*

In each case the

sum of the concentration of the adsorbed calcium ions
from both clays was 0*950 milliequivalents.
rated clays were used in all cases.

Calcium satu­

To each of these flasks

100 ml of solution containing 0.950 milliequivalents of
hydrochloric acid was added.
for two reasons;

Hydrochloric acid was added

(l) to add chloride ions into the system

and (2) to release part of the calcium ions Into the solu­
tion phase by exchange with hydrogen ions so that the activ­
ity of calcium chloride in the suspension could be measured.
The flasks were allowed to equilibrate for two weeks
with Intermittent shaking.

The data in figure 10 illustrate

the variation of calcium chloride, hydrochloric acid, hydro­
gen and

calcium ion activities with change in the composi­

tion of

the system.

There was some doubt as to the validity

of the data, owing to the low pH values of the suspensions.
There Is reason to believe that at low pH aluminum from the
crystal lattice Is released into the solution rendering the
activity values more a function of the aluminum content than
that of the clay composition.

In order to avoid this pro­

blem activity measurements were made in systems
neutral

to which

potassium chloride was added Instead of hydrochloric

70
acid (see figure 11).

Similarly, calcium chloride activity

was measured In a series of systems containing bentonitevermicullte mixtures.

Figure 13 summarizes the data ob­

tained for measurements in the bentonite-vermlcullte mix­
tures.

71

C a++ activity
CaCI2 activity
H + activity
HCI activity

+
a:

O
Cj
16
o
o
o

*
1
o

70

14

17

12

16

10

15

8

14

6

13

4
100

12

5 5

X

s

t%.
VJ

6 0

4 5

o

5 0

7!

3 5

/ /
4 0

3 0

2 5

15

0

20

4 0

6 0

Bentonite

% Kaolinite

8 0

Kaolinite

Figure 10. Dependence of calcium, calcium chloride,
hydrogen and hydrochloric acid activities on the clay
composition of calcium saturated bentonite-kaolinite
suspensions containing one symmetry concentration of
hydrochloric acid.

activity x I0~

HCI

6 5

72

24

—

CoCI

—

Ca + + activity

2

activity

22

20
Ca++ activity x I0~

•O
I
o

x

£* 6 .5
o
o
O

5 6.0

5 .5

5 .0

20

40

60

Bentonite

80

100

Kaolinite
% Kaolinite

Figure 11. Dependence of calcium and calcium chloride
activities on the clay composition of calcium saturated
bentonite-kaolinite suspensions containing one symmetry
concentration of potassium chloride.

73

— Ca Cl2 activity
— Ca + + activity

100

Bentonite
% Vermiculite

Vermiculite

Figure 12. Dependence of calcium and calcium chloride
activities on the clay composition of calcium saturated
bentonite-vermieulite suspensions containing one sysr-etr'"concentration of potassium chloride.

CHAPTER X
DISCUSSION
Validity of the data obtained in tiiis work depends
on several factors.

All data depend on the truly reversi­

ble character of the amalgam and silver-silver chloride
electrodes.

For the single ion activity measurements, not

only is the reversibility of the amalgam and the silversilver chloride electrode essential, but the liquid junc­
tion potential arising from the use of the reference calomel
electrode must be negligible.

Finally, the data must be of

systems in equilibrium if they are to have any significance.
It is evident from the comparison of mean activity
coefficients in Table I that the amalgam and the silversilver chloride electrodes are reversible to calcium and
chloride ions.
limitations.

The tertiary amalgam electrode has certain
The amalgam electrode cannot be used to measure

calcium activity for calcium ion concentrations much less
than 0.001 moles per liter, and any cation other than calcium
forming insoluble oxalates interferes with the proper func­
tioning of the electrode.
There are certain barriers to demonstrating the
significance of the single ion activity data.

In the first

place liquid junction potentials cannot be measured and
74

75
secondly, the assumption of the equality of the potassium
and chloride activities in potassium chloride solutions
may not hold for concentrated solutions.

An excellent

discussion on the problem of the liquid Junction potential
arising from use of the calomel reference electrode in soil
suspensions can be found in a paper by Coleman, et.al.

(4),

with a lengthy comment by Marshall at the end of the arti­
cle.

Coleman and his coworkers hold the view that the

liquid Junction potential may be as large as 300 milli­
volts in clay suspensions while Marshall favors the idea
that for calomel electrodes, making contact with the suspen­
sion through a saturated potassium chloride salt bridge, the
potential is negligible.

The argument continues for obvious

reasons; there is no proven method for measuring liquid
Junction potentials, and much of the argument is based on
conjecture rather than experimental data.

Unless a sound

experimental method is devised for measuring the liquid
Junction potential this question will have to be left ionanswered.
To assure activity measurements in equilibrated
systems the clay suspensions were allowed to sit on the
shelf for two weeks or more with intermittent shaking.
Direct evidence for equilibrium in these systems was ob­
tained by inserting a silver-silver chloride electrode in
the sediment and another in the supernatant portion of a
clay suspension that had been allowed to settle, and ob­
serving a zero emf between the two electrodes.

76
The experiment for measuring the relative affinities
of the various cations for exchange sites needs little ex­
planation.

The wide differences in the replacing power of

the various cations for calcium ions are obvious from the
data.

There is some uncertainty in all measurements carried

out in systems containing magnesium ions.

If the concentra­

tion of magnesium ions is too high, precipitation of mag­
nesium oxalate is possible so that the activity values re­
flect not only calcium but also magnesium ions.

Joseph (16)

has shown that addition of as high as 0.024 moles of mag­
nesium chloride per liter of solvent has no effect on the
activity values of calcium chloride with the exception of
course of the effect due to the ionic strength.
Davis (5), in a study very similar to the one pre­
sented here, added to a monoionic bentonite suspension in­
crements of the corresponding chlorides and measured ion
pair activities.

By plotting the mean activity against

the molality of the added chloride, he was able to show
the relative affinities of several metals for the exchange
sites on bentonite clays.
In one variety of bentonite the order was Rb> Cs>
K>Na>Li,

while for another bentonite, no definite trend

could be observed.

In the present study the relative

affinities of cations for exchange site, measured by their
ability to replace calcium, was found to be Rb>v Mg > K > N a > L i .
This was true for both clays.

This order is in accord with

general observations on the relative adsorbabillty of the
various ions.

77
The activity values measured In the suspensions
containing lithium ions may he in error.

It was stated

earlier that the amalgam electrode was Incapable of measur­
ing calcium ion activity In solutions of concentrations
much less than 0.001 moles per liter.

The activity values

for the lithium systems indicate that the calcium Ion con­
centration may have been below the critical level.

If the

values are in error then they are values which are probably
too high, for values much higher than those observed would
indicate that calcium ion concentrations were sufficiently
high to allow proper functioning of the electrode..
Another point which may warrant examination Is the
relative difference of the replacing powers for calcium
of the various cations between the two clays.

The general

trend is similar in both clays but potassium appears to
have a replacing power for calcium more like rubidium and
magnesium in bentonite than in the corresponding kaolinite
suspensions.
Two features of the activity measurements in mixed
clay systems are significant.

First, the activity of

calcium ions and calcium chloride are higher in pure kaoli­
nite than in bentonite, while an opposite effect is noted
for hydrogen and hydrochloric acid.

Secondly, calcium and

calcium chloride activities are not additive functions of
the two clays in systems containing mixtures of clays.
The fipst phenomenon has been observed in the green
house.

Chu and Turk (3) showed that plants absorbed more

78
calcium from kaolinite than bentonite when equivalent con­
centrations of the calcium clays were added to sand cul­
tures.

Here is an example of the failure of concentra­

tions to give a true picture of nutrient availability.
The acidic properties of hydrogen bentonite and kaolinite
have been known for some time.

Marshall (24) explains

this difference on the basis of the nature of exchange
sites on each of the two clay types.

Exchange sites on

kaolinite arise from broken bonds having weak acidic propert­
ies, whereas, montmorillonlte (bentonite) particles possess
negative charges arising from substitution In the lattice
which when balanced by hydrogen Ions dissociate to a greater
degree.

The salts of bentonite are less dissociated than

kaolinite because the cations penetrate far into the lattice.
This explanation fails when applied to the bentonite-vermi­
culite mixtures.

Both bentonite and vermiculite are structur­

ally alike and both derive their charges from lattice sub­
stitutions.
these clays.

The origin of the charges are different In
For bentonite the charge originates from sub­

stitution In the octahedral layer while vermiculite has most
of its charge from substitution In the tetrahedral layers.
The origin of charge site may be an explanation for the wide
difference in the measured

activities between these two

clays.
Comparison of figures 9 and 11 indicates that the
exaltation of the calcium and calcium chloride activities
Is not due to aluminum.

It is unlikely that free aluminum

79
Ions can be in the KOI system since the pH was near seven.
The fact that the exaltation effect remains even in neu­
tral suspensions suggests an Interaction of the clay min­
erals.

The difference in the hydrogen and calcium ion

activities as shown In figure 13 has practical significance
to the agronomist.

It is the general recommendation to

farmers In the Michigan area to maintain Inorganic soils
at approximately 70$ calcium, 15$ hydrogen, 10-15$ magnesium
and 1-2$ potassium saturation, accompanied by trace amounts
of the minor elements.

On the basis of figure 11 It is

evident that the ratio of the activities of the hydrogen
to the square root of calcium ions varies with the kind of
clay present In the soil.

This is apparently one reason

why nutrient recommendations vary from soil to soil.
Several possible explanations for the exaltation of
the activities were considered.

Error In the calculation

of the cation exchange capacity, failure to use completely
saturated clays, and negative adsorption of anions were
considered as possible causes of this phenomenon.

These

factors may change the slope or the Intercept of the Ideal
curve, but will not account for the deviation from it.

It

appear inescapable that there is an interaction between the
two kinds of clays.

The most plausible explanation seems

to be the supposition that the total cation exchange capa­
city of the mixture is reduced when bentonite is mixed with
kaolinite.

Clays not only have cation exchange properties,

but also possess some anion exchange capacities as well,

80

28
Theoretical
Experimental

24

20
<NI
I
O
x
CM

N
I

+o
u

20
Bentonite

40

<
60

% Kaolinite

80

100
Kaolinite

Figure 13. Dependence of the ratio of the hydrogen
to the square root of the calcium ion activity on the
clay composition of calcium saturated bentonite-k&olinite
suspensions containing one symmetry concentration of
hydrochloric acid.

81

with the latter property being greater In kaolinite than
bentonite.

When these two clays are mixed, the cation

exchange sites of bentonite may be partially satisfied by
the positive exchange sites of kaolinite resulting in a
net decrease in the cation exchange capacity of the mix­
ture.

This same argument may be applied to the bentonite-

vermiculite systems.
Activity studies in heterogeneous soil systems are
hindered by the lack of suitable activity measuring devices.
It is hoped that in the future durable instruments similar
to the glass electrode will be developed so that activity
measurements can be made on a routine basis.

It is felt

that the successful measure of available nutrients lies
with the application of the activity concept to soil systems.
The understanding of the chemical potential, and for hetero­
geneous systems, the electrochemical potential and the
corresponding total activity is essential for intelligent
interpretation of chemical data pertaining to nutrient up­
take .

LITERATURE CITED
1.

Adair, G • S., and Adair, M. E. Membrane potentials,
valences and theoretical and observed mobilities of
haemoglobin and egg albumin.
Trans. Faraday Soc.
36:26-32.
1940.

2.

Brown, A. S. A type of silver-silver chloride elect­
rode suitable for use in dilute solutions. J. Am.
Chem. Soc. 56:646-647.
1934.

3.

Chu, T. S., and Turk, M. L. Growth and nutrition of
plants as affected by degree of base saturation of
different types of clay minerals.
Mich. St. College
Agr. Expt. Sta. Tech. Bull. 214. 1947.

4.

Coleman, N. T., Williams, D. E . , Nielsen, T. R . , and
Jenny, H. On validity of interpretations of potentiometrically measured soil pH.
Soil Sci. Soc. Amer.
Proc.
15:106-114.
1950.

5.

Davis, L. E.
Ion pair activities in Bentonite suspen­
sions.
Clays and Clay Minerals. National Academy of
Sciences-National Research Council. Publication 395.
1955.

6.

Diagnostic Techniques for Soils and Crops.
The American
Potash Institute. Washington, D. C. 1948.

7.

Epstein, E.
Mineral Nutrition of Plants: Mechanisms
of Uptake and Transport.
Ann. Rev. Plant Physiol.
7:1-24.
1956.

8.

Falkehhagen, H.
Oxford.
1934.

Electrolytes.

The Claredon Press,

9.

Fay, H . , and North, E. On the nature of lead amalgams.
Am. Chem. Journ.
25:216-231.
1901.

10.

Guggenheim, E. A. Conceptions of electrical potentials
difference between two phases and the Individual
activities of ions.
J. Phys. Chem.
33:842-849.
1929.

11.

Harned, H. S.
The electromotive force of uni-univalent
halide in concentrated aqueous solutions.
J. Am.
Chem. Soc. 51:416-427.
1929.
82

83
12.

Harried, H. S., and Owen, B. B.
The Physical Chemistry
of Electrolytic Solutions.
2nd ed., rev. and enl.
Reinhold Pub. Corp., New York.
1950.

13*

Harned, H. S.
The thermodynamic properties of the
ions of some strong electrolytes and of the hydrogen
ion in solutions of tenth molal hydrochloric acid
containing uni-univalent salts. J. Am. Chem. Soc.
42:1808-1832.
1920.

14.

Henderson, W. E., and Stegman, G-. A lead standard
cell and a determination of the potential of the
lead electrode.
J., Am. Chem. Soc. 40:84-89.
1918.

15.

Joseph, N. R. Heterogeneous equilibrium of protein
solutions.
II.
The interaction of calcium chloride
and other salts with proteins, as determined by a new
type of calcium amalgam electrode. Journ. Bio. Chem.
126:389-402.
1938.

16.

Joseph, N. R. Interaction of amino acids and salts.
III.
The determination of the activities of calcium,
barium, and strontium chloride in amino acid solutions
by means of electrodes of the third kind.
Journ. Bio.
Chem.
130:203-217.
1939.

17.

Kielland, J. Individual activity coefficients of
ions in aqueous solutions.
J. Am. Chem. Soc. 59s
1675-1678.
1937.

18.

Leggett, J. E . , and Epstein, E. Kinetics of sulfate
absorption by barley roots.
Plant Physiol.
31?222-

226. 1956.

19.

Lewis, G-. N. and Randall, M. Thermodynamics and the
Free Energy of Chemical Substances.
McG-raw-Hill Book
Co., Inc., New York. 1923.

20.

Low, P. F. Ionic activity measurements in heterogeneous
systems.
Soil Scl. 77?29-41.
1954.

21.

MacDougall, F. H. Thermodynamics and Chemistry.
ed.
J. Wiley & sons, Inc., New York.
1939.

22.

M.aclnnes, D. A. The activities of the ions of strong
electrolytes.
J. Am. Chem. Soc. 41:1086-1092.
1919.

23.

Maclnnes, D. A., and Parker, K. Potassium chloride
concentration cells. J. Am. Chem. Soc. 3 7 :1445-1461.
1915.

3d

84
24.

25.

26.

Marshall, C. E.
The use of membrane electrode In the
study of soils.
Soil Sci. Soc. Amer. Proc. 7:182186.
1947.
Mortland, M. M . , and Mellor, J. L. Conductometric
titration of soils for cation-exchange capacity.
Soil Sci. Soc. Amer. Proc.
18:363-364.
1954.
Noyes, A. A., and Ellis, J. H.
The free energy of
hydrochloric acid in aqueous solutions.
J. Am. Chem.
Soc.
39:2532-2544.
1917.

27.

Overstreet, R. Ionic reactions in soils and clay
suspensions.
The significance of soil filtrate.
Soil Sci. 59:265-270.
1945.

28.

Palmer, W. G-. Experimental Physical Chemistry. Bently
House,
Cambridge University Press, London.
1941.

29.

Robinson, R. A., and Stokes, R. H. Electrolyte Solu­
tions,
Butterworth Scientific Pub., London,
1955*

30.

Shedlovsky, T . , and Maclnnes, D. A. The determination
of activity coefficients from the potentials of con­
centration cells with transference.
III. Potassium
Chloride.
IV.
Calcium chloride.
J, Am. Chem. Soc.
59:503-506.
1937.

31.

Spillman, W. J., and Lang, E. The Law of Diminishing
Returns.
World Book Co., New York.
1924.

32.

Smith, E. R., and Taylor, J. K. Reproducibility of
the silver-silver chloride electrode.
U. S. National
Bureau of Standard Journ. of Research.
30:837-847.
1938.

33.

Taylor, J. K . , and Smith, E. R. Reproducibility of
silver-silver halide electrodes.
U. S. National
Bureau of Standards Journ. of Research.
22:307-314.
1939.

APPENDIX

86

TABLE III
DEPENDENCE OF MEAN ACTIVITY OF CALCIUM CHLORIDE ON emf
emf in
millivolts

conc.

mean ionic mean activity
conc.
coefficient

mean
activity

---

0.00100

0.00159

01888*

0.00141

0.00

0.00200

0.00318

0.8523

0.00271

24.00

0.00400

0.00635

0.795

0.00505

38.00

0.00600

0.00952

0.762

0.00726

55.8

0.0100

0.0159

0.725

0.0115

80.1

0.0200

0.0318

0.618

0.0216

102.1

0.0400

0.0635

0.617

0.0392

115.55

0.0600

0.0952

0.569

0.0542

132.5

0.1000

0.159

0.531

0.0845

*Mean activity coefficient on the molality scale ex­
tracted from Prutton and Maron, "Fundamental Principles of
Physical Chemistry," The MacMillan Company, New York, Re­
vised edition, 1951» p. 4-78.

87
TABLE IV
DEPENDENCE OF CALCIUM AND CALCIUM CHLORIDE ACTIVITIES
IN BENTONITE SUSPENSIONS ON THE ADDITION OF
SYMMETRY CONCENTRATIONS OF CHLORIDE SALTS

E - E

A+ CaClg A+3ca0l2 £ACe"

AC1“

A 2C1“

A+

Ll

45.8

.00889

7026

68.5

.0283

.008004

Na

52.2

.0105

1158

68.5

20283

.0008009 .00145

K

66.5

.0152

3512

68.5

.0283

.0008009 .00439

Rb

79.8

.0215

9938

68.7

.0281

.0007896 .0126

Mg

79.6

.0214

9800

68.9

.0279

.0007784 .0126

1

65.9

.0149

3308

51.8

.0550

.003025

.00109

Na

79.2

.0211

9394

51.8

.0550

.003025

.00311

K

87.2

.0261

1778

51.8

.0550

.003025

.00588

Rb

98.2

.0345

4106

51.8

.0550

.003025

.0136

Mg

97.9

.0342

4000

52.0

.0547

.002992

.0134

L1

79.3

.0212

9528

42.2

.0810

.OO656 I

.00145

Na

92.0

.0295

2567

42.2

.0810

.OO6561

.00391

K

98.7

.0350

4288

42.3

.0806

.006496

.00660

Rb

108.9

.0454

9358

42.4

.0803

.006448

.0145

Mg

108.7

.0452

9235

42.5

.0800

.006400

.0144

.000877

88

TABLE V
DEPENDENCE OF CALCIUM AND CALCIUM CHLORIDE ACTIVITIES IN
KAOLINITE SUSPENSIONS ON THE ADDITION OF SYMMETRY
CONCENTRATIONS OF CHLORIDE SALTS

E - E

Ai CaClg Ai^CaCXg

E aCl“

aCl"

aCi-2

aCa++

L1

15.9

.00410

6892

93.0

.0107

.0001145

.000602

Na

21*5

.00475

1072

93.0

.0107

1145

.000936

K

34.2

.00659

2862

93.0

.0107

1145

.00250

Rb

40.2

.00770

4565

93.2

.0106

1124

.00406

Mg

38.7

.00739

4036

93.8

.0103

1061

.00380

L1

34.2

.00660

2875

76.8

.0204

.0004162

Na

42.2

.00810

5314

76.9

.0203

4121

.00129

K

54.8

.0112

1405

76.9

.0203

4121

.00341

Rb

60.0

.0128

2097

76.9

.0203

4121

.00509

Mg

59.0

.0125

1953

77.1

.0200

4000

.00488

.OOO691

h.
Na

45.4

.00880

6815

67.3

.0297

.0008821

58.0

.0122

1816

67.3

.0297

8821

.00206

K

66.1

.0151

3443

67.2

.0298

8880

.00388

Rb

70.9

.017 0

4913

67.4

.0296

8762

.00561

1%

70.1

.0167

4657

67.8

.0292

8526

.00546

.000773

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