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AN EXPERIMENTAL TEST OF THE
DEBYE-HUCKEL THEORY

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AN EXPERIMENTAL TEST OF THE
DEBYE-HÜCKEL THEORY

THESIS

PRESENTED TO THE FACULTY OF THE
STATE UNIVERSITY OF UTRECHT. THE
NETHERLANDS
BY

WOUTER BOSCH

IN PARTIAL FULFILMENT OF THE
REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY.

UTRECHT. JULY 9 193L

DRUK UTR. TYPOGRAFEN-ASSCXIATIE, KEIZERSTRAAT 5. UTRECHT

BIBLIOTHEEK DER
RIJKSUNIVERSITEIT
UTRECHT.

Dedicated to my Parents,
and to my Wife.

m

At the finish of my university education, I want to thank every
body who has contributed to my scientific development and to the
completion of my thesis.

In the very first place I would like to thank Professor I. M.
Kolthoff of the University of Minnesota, not only for his thorough
interest and help in our research, but also for the splendid oppor-
tunity, that he has given me to get acquainted with America and its
friendly population.

Further I wish to take the opportunity of thanking Professor
H. R. Kruyt of the University of Utrecht for having taken so much
interest in the work. His extraordinarily stimulating personality was
at all times a source of inspiration, especially when I started
teaching in the United States.

I wish to thank Professor Ernst Cohen, Director of the van
\'t Hoff Laboratory, for his fine lectures and for his unfailing kind-
ness and courtesy.

I also wish to thank Professor N. Schoorl and Professor W. C.
de Graaff of the University of Utrecht, whose ways of education in
many scientific fields will be among my most pleasant memories.

I particularly feel greatly indebted to the Authorities of the
University of Minnesota, Minneapolis and of the Oklahoma Agri-
cultural and Mechancal College, Stillwater, especially to Dean
O. M. Leland, Dean C. H. McElroy, Professor S. C. Lind and
Professor O. M. Smith. I want to thank them for the splendid
opportunities that they have given me to perform this work and for
their trouble in helping me to obtain several facilities.

My thanks are also due to Professor H. M. Trimble of the
Oklahoma A. and M. College for his kindness in helping me to
correct the English of this Thesis.

Finally I wish to take the opportunity of thanking the Holland—
America Foundation for its stipendium.

.m

Jr

«Wir

TABLE OF CONTENTS.

Page

I. Introduction...............11

II. Outline of the work............19

III.nbsp;Materials used..............22

IV.nbsp;Description of experiments:.........32

a.nbsp;Solubility Measurements

b.nbsp;paH Measurements

c.nbsp;P^Ag Measurements

V. Solubility of benzoic acid and activity coefficient of

the undissociated acid in aqueous salt solutions ... 43

V.nbsp;Hydrogen ion activity in benzoic acid — benzoate
solutions in the presence of neutral salts.....53

The activity coefficient of the benzoate ion.

VII. Solubility of silver benzoate in water and in aqueous

salt solutions..............63

The mean activity coefficient of the silver and
benzoate ions.

VIII. Silver ion activity and benzoate ion activity .... 67
IX. Discussion of the results. Summary.......74

rm

gt;

V

AN EXPERIMENTAL TEST OF THE
DEBYE-HUCKEL THEORY, i)

CHAPTER I.

Introduction.

The Theory of Electrolytic Dissociation of Svante Arrhenius
does not give a true picture of the behaviour of strong electrolytes
in solution. The crystals of strong electrolytes, to which class most
salts belong, are built up from ions and it is improbable, that these
ions would combine to undissociated molecules, when the salts
are brought into solution (See Kolthoff\'s article about activity
products and activity constants 2).

In addition to this there are other objections against the Theory
of Arrhenius. When NaCl dissolves in water the ionization is not
complete. If we assume that there exists the equihbrium NaCl
Na CP we can apply the Mass Action Law which gives us
the following equation.

^ [NayjCn

[NaCl]

This K ought to be a constant, but it has been found for strong
electrolytes to vary with the electrolyte concentration.

Another great objection against the theory is the fact, that the
degree of dissociation quot;aquot; gives different values in the same
solutions, when calculated from measurements a of the conductivity,
b of the lowering of the freezing point (or the osmotic pressure)
or c of the E.M.F. of concentration cells, as can be seen from the
following table taken from the publication of Kolthoff. 2)

concentrationnbsp;anbsp;anbsp;a

of KC!nbsp;(conduct,)nbsp;(E.M.F.)nbsp;(freezing point)

.001 molarnbsp;.979nbsp;\' .943nbsp;.985

.01 ..nbsp;.941nbsp;.882nbsp;.969

.1 „nbsp;.861nbsp;.762nbsp;.932

1 ,.nbsp;. 755nbsp;.558nbsp;.854

Several empirical equations have been advanced, which express

For a therraodynamical discussion of the Debye—Hückel theory we
want to refer to the papers of van Veldhuizen in the Chemisch Weekblad.
2) I. M. Kolthoff Chem. Weekbl. 27 250 (1930).

more or less satisfactorily the change of a with the concentration,
but none of these provide a clue as to which of the assumptions
the Arrhenius\' theory need modification.

Besides these there are other points, which cannot be explained
by this theory e.g. the influence of strong electrolytes upon the
solubility of difficultly soluble substances or the fact that a solu-
tion of IN HCl (containing 1.5% undissociated HCT) does not
have any appreciable vapor pressure of HCl.

Many authors have held the view, that some fundamental
modification of the theory was needed. J. J. van Laar 3) and
O. Jahn4) have attacked the assumption, the the mobilities of the
ions are independent of the concentration, their view being, that
the enormous electrostatic charges on the ions must alter the
properties of the solvent and influence the ionic speeds. Van Laar
expressed as early as 1900 the opinion, that in rather dilute
solutions of all strong electrolytes the degree of dissociation
becomes unity.

A. A, Noyes and Coolidge^) had the idea, that the decrease
of conductivity and of the calculated dissociation is due to a
physical cause (probably related in some way to the electrical
charges of the ions) and not to the specific chemical affinity.
Noyes lt;gt;) also brought forward evidence of a change in mobili-
ties with concentration, when he showed, that the transport
numbers of the ions of HCl and HNO3 alter with concentration.

Sutherland\'7) held the opinion, that the aqueous solutions of
strong electrolytes are completely ionized. Later on Milner^) and
BjerrumO) have also used the same hypothesis as a basis for
their discussion of the behaviour of salt solutions.

3)nbsp;J. J. van Laarnbsp;Z. physik. Chem. 15 457 (1894), 17 245 (1895),

Arch. Teyler 7 1 (1900), Z. anorg. allgem. Chem.
139 108 (1924).

4)nbsp;O. Jahnnbsp;ibid. 27 354 (1898), 33 345 (1900), 35 1 (1900),

36 443 (1901), 37 490 (1901).

5)nbsp;Noyes and Coolidge J. Am. Chem. Soc. 26 167 (1904).
«) Noyes and Sammetnbsp;ibid.nbsp;24 944 (1902).

Noyes and Katznbsp;ibid.nbsp;30 318 (1908).

7)nbsp;Sutherlandnbsp;Phil. Mag. 3 161 (1902), 7 1 (1906), 14 1 (1907).

8)nbsp;Milnernbsp;ibid. 23 551 (1912), 25 743 (1913).

quot;) N. Bjerrumnbsp;7e Intern. Congres voor toegep. chem. deel 10 59

1909). Z. Elektrochem. 24 321 (1918) Z. anorg.
Chem. 10 275 (1920).

As a mathematical interpretation of the interionic actions was
very difficult, N. Bjerrum») introduced quot;deviation coefficientsquot;
that were determined empirically and expressed the effects of the
electrostatic action of the ions upon the various properties of
electrolyte solutions. These coefficients give the proportion between
the observed value and those, that could be expected, if no inter-
ionic forces were active. He distinguished:
fg*. the osmotic coefficient
f^: the conductivity coefficient and

fa: the activity coefficient (The latter is of special interest in

our investigation).
Bjerrum\'s activity coefficient gives the proportion of the active
mass or the activity of the ions to the total concentration or the
ratio between the chemical or electrochemical activity and the total
ionic concentration.

As has been pointed out above Sutherland 7), Milner«) and
Bjerrumquot;) have put forward the view, that strong electrolytes are
completely ionized. However the theory of incomplete ionization
of Arrhenius is based upon facts which demand adequate explana-
tion. For instance the equivalent conductivity of a strong electrolyte
decreases as we pass from extremely dilute solutions to more
concentrated ones and so docs the activity coefficient. An answer
to the above question is found in the electrostatic forces, which
exist between the ions. If we consider any one positively charged
ion, its motion through the liquid will cause it to approach nega-
tively charged ions and also positively charged; in the first case
the attractive force between the two tend to bring them into closer
proximity, and in the second case the two will repel each other.
The net result will be to alter the average distribution of the ions.
Each positive ion will at any moment be surrounded by more
negative ions than positive ions, and visa versa. Debye and
Hxickel have found, that this state of affairs is capable of account-
ing for the decrease in the activity coefficient.

In 1923 they have published an articlc lo), in which they have
derived thermodynamically the relationship between the several
coefficients on the one hand and the concentration, valence and
specific nature of the ions on the other hand.

P. Dcbye and E. Huckcl Physik. Z. 24 185 (1923). 26 93 (1925).

Debye and Hückel\'s equation for the activity coefficient of an

ion IS

^ Z

In f _ ^

a - 2DhT ï\'i

where

f^ = activity coefficient of the ion
D = dielectric constant of the solvent
h = 1.37 X 10-16
T = absolute temperature

charge of a univalent ion

number of ions of kind i, formed by the dissociation of
the molecule

number of such ions in 1 cc

Zj = valency of the ions.

In this derivation several simplifying assumptions are made and
the equation can only be applied to very dilute solutions.

A less complicated formula, that can be derived from the
preceeding one by substituting in the different values is given

-log fa = Azi\' VTi

A = constant and is a function of the dielectric constant,
having a value of .5 at roomtemperature in aqueous
medium.

Zj — valency of the ion.

fx = ionic strength, defined by Lewis u) as half the sum of
the molar concentrations of each ion present, multiplied
by its valency squared. For example the ionic strength
of .01 molar bariumchloride solution is:

.01 X 22 .02 ^

, =-^- .03

It is evident from equation (2), that the activity coefficient in
very dilute solutions is dependent only upon the concentration and

quot;) G. N. Lewis and M. Randall Thermodynamics and the free energy of
chemical substances. McGraw Hill Co. New York 1923.

the valency of the ions and not upon their specific character.

If the solution is not very dilute the ionic size has to be taken
in account and equation (2) goes over in Debye-Huckel\'s
formula to

-log .5z . 2-^^^---(3)

1 .329 X 10 X b ]\'n

b = ionic diameter and has the value for KCl of 3.76 X 10 ^

and for K2SO4 of 2.69 X 10~8 etc.

The ionic size varies with the concentration as the ions exert
forces upon each other, as discussed before.

Also A in equation (2) is a function of the dielectric constant
and there is practically nothing known in the field of the dielectric
constants of electrolyte solutions.

Bronsted has drawn our attention to the fact, that we have to
deal with a „salting outquot; effect in concentrated electrolytes solu-
tions. The activity coefficient of a non-electrolyte is dependent
upon the ionic strength of the solution:

log f = B/t

in which B is a constant, which is different for a special substance
for different electrolytes.

If we assume, that the same kind of ..salting outquot; effect is
exerted upon ions equation (3) goes over into formula (4).

■log . 5z. 2---^ _B

1 .329 X 10 X b innbsp;(4)

Finally we want to mention, that we have to take into account
the so-called ion-association, that is a function of the ionic size
and ionic strength: Bjerrumi2).

Gronwall, La Mer and Sandved have published a study on
various terms of the Debye — Huckel equation 13).

When we give our attention to all the above mentioned facts,
it becomes quite doubtful, whether the formula No. 3 is valuable,
even in dilute solutions. The question arises, whether it would not
be better to find an empirical relationship between the activity
coefficient and the ionic strength as Bjerrum 12) has done.

N. Bjerrum Ergebn. dcr cxakten Naturwiss. 5 125 (1926).

quot;) Gronwall, La Mer and Sandved, Physik. Z. 29 358 (1928).

He finds, that the following equation reproduces quite well the
changes of the activity coefficient with the ionic strengths:

3_

-log f^ = A\'j/ fi-W fx

A\' and B\' are constants, that can be derived from experimental
data.

At smaller ionic strengths, the following formula gives suffi-
ciently good results:

-log f = . 5 [/ - B

In 1927 we started our research on the influence of neutral salts
on acid-salt, acid-base equilibria respectively and seven publica-
tions have been the result of a number of investigations in this
field. 14)

We will give here a brief summery of the conclusions, that we
have drawn from our experiments so far.

From measurements of the activity of the hydrogen ions in a
dilute solution of hydrochloric acid with uni-univalent salts in our
first investigation, we found in agreement with other investiga-
tors that small quantities of salts cause a decrease of the
activity coefficient, whilst with higher concentrations the coeffi-
cient tends to increase, reaching in the case of a .5 N solution of
Lithium chloride a value greater than 1.

It was also shown, that there is a distinct cation effect in the
order of the so-called lyotropic series and that the different anions
used had all the same influence. It was further concluded in agree-
ment with Scatchard 10) and Giintelberg 17), that the activity
coefficients of two individual ions are not equal to the mean of
their coefficients.

We found the same pronounced cation effect in our second
investigation in which we studied different equilibria in citric acid

quot;) I. M. Kolthoff and Wouter Bosch Rcc. Trav. Chim. 46 430 (1927), 47
558 (1928), 47 819 (1928), 47 826 (1928), 47 861
(1928), 47 873 (1928), 48 37 (1929),
IS) H. S. Harned J. Am. Chem. Soc. 38 1986 (1916), 42 1808 (1920), 48
326 (1926).

quot;) G. Scatchard J. Am. Chem. Soc. 47 641, 648, 696 (1925).
E. Giintelberg Z. physik. Chem. 123 199 (1926).

solutions. An application of the Debye-Hiickel equation (3) for
the calculation of the Ph in mixtures of citric acid and monovalent
citrate was not very succesful. It was found, that the activity
coefficient of the undissociated acid becomes much larger than I
with increasing concentration of the neutral salt; therefore we
concluded, that electrolytes apparently increase the first dissocia-
tion constant of citric acid.

Only in the case of potassium chloride the influence of the
salt upon the ppj of different mixtures could be approximately
calculated by means of the Debye-Hiickel equation. In using
sodium or hthiumchloride other factors seemed to complicate the
problem.

Neither was it possible to calculate quantitatively the influence
of neutral salts upon the pH of a dilute bicarbonate-carbonate
mixture on the basis of the Debye-Hückel theory, as was found
in the third part of our research.

The influence of neutral salts on the ppj of a very dilute mixture
of ter- and quadrivalent pyrophosphate is much larger than that
calculated according to the equation of Debye and Hückel. The
salt effect on a dilute mixture of di- and tervalent pyrophosphate
could be calculated by means of this equation accepting an average
ionic size of the ions of potassium chloride equal of 3.7 X I0~8
cm. and of sodium chloride of 2.3 X 10~8 cm.

In the summary of our fifth publication about the first and
second dissociationconstant of succinic acid, tartaric acid and
adipinic acid and the influence of neutral salts on different equili-
bria we stated, that the effect of these salts upon the p^ of a
weak acid and its monovalent salt is partly explained by the fact,
that the salts increase the activity coefficient of the undissociated
acid. There was no reason to assume, that neutral salts increase
the dissociation constant of the weak acids, that were investigated.

The influence of neutral salts upon the ratio of the activity
coefficients of the anions in a mixture of a mono- and divalent
anion of a weak acid could not be calculated on the basis of the
Debye—Hückel equation only. There seemed to be some specific
interaction between the cations of the salt added and the anions of
the weak acid.

The; assumption, stated above has been strengthened by our
sixth investigation in which we studied the dissociationconstant
of acetic acid, capronic acid and benzoic acid and the influence of

neutral salts upon the dissociationconstant of weak acids. We
found here again, that neutral salts do not increase these con-
stants and it also was stated in the summary, that the influence of
neutral salts on the pj^ of a dilute mixture of a weak acid and
its salts may be calculated by using the equation of Debye and
Hiickel, if the influence of the salts on the activity coefficient of
the undissociated acid is taken into account.

The last part of our previous research was carried out in the
field of weak bases with an investigation which had to do with
the apparently anomalous behaviour of a mixture of a weak base
and its salt on dilution and on the addition of a salt. We came
here to the same conclusion as before, e.g. that there is no special
anion effect, but that there is a pronounced cation influence in
the order K, Na, Li, which is just the reverse of that observed in
the case of an acid system. An explanation was given by the
assumption, that sodium- and lithium chloride increase the ionic
product of water.

Finally summarizing our research, that was carried out before
we started on the present problem we came to the conclusions:

a.nbsp;That there is a special cation effect in the order Ligt;Nafgt;K
for the influence of neutral salts upon the pn of different
mixtures of weak acids and their salts.

b.nbsp;That there has not been observed any special anion effect
upon these equilibria.

c.nbsp;That the influence of neutral salts upon the ppj of a weak
acid and its monovalent salt is partly explained by the fact,
that salts increase the activity coefficient of the undissociated
acid. If we assume this, this influence may probably be calcu-
lated by using equation Nr. 3 of Debye and Huckel.

d.nbsp;That there is no evidence, that neutral salts increase the
dissociation constant of weak acids.

To support and strenghten the statements, made above, and to
bring more light into this important field of the behaviour of strong
electrolyte solutions, we have carried out the research work that
will be outlined in the following chapter.

CHAPTER II.

OUTLINE OF THE WORK.

In the present work a study has been made of the activity
coefficient of the beilzoate ion and of the system benzoic acid —
benzoate in the presence of various neutral salts.

The advantage of this investigation over the work that has been
carried out previously is, that the activity of the undissociated
benzoic acid has been kept constant by working with saturated
solutions.

The dissociation constant of benzoic acid was calculated from
PH measurements in solutions of benzoic acid — sodium benzoate
1 : 1 and 2 : 1 and the dilutions thereof. As the hydrogen ion
concentration in the mixtures was rather high, the p^ values
measured in all dilutions had to be corrected for the dissociation
of the acid.

The activity coefficient f^, of the undissociated benzoic acid in
solutions of various salts was calculated from the values of the
solubility of the acid in water and in the salt solutions. These
activity coefficients were compared with those obtained by diffe-
rent authors.

Along with the solubility measurements p^j determinations

were carried out both with the hydrogen electrode and with the

quinhydrone electrode. In a previous investigation is) of the

system benzoic acid — benzoate we had found already, that these

measurements were very troublesome. We noticed that there was

a certain drift in the value of the dissociation constant; with

increasing ionic strength a higher value of the constant was found.

Jn this research we met with the same difficulties which we could

quot;ot explain. Especially in the dilute solutions it was quite impossible

to obtain constant E. M. F. values. However, the quinhydrone

electrode proved not very satisfactorily either as will be mentioned
later.

Kolthoff and Bosch Rec. Trav. Chim. 47 876 (1928).

The activity coefficient f^ of the benzoate ion can be calculated
in the following way:

[aH ] [abenzoate~] _ Uh I [c benzoatequot;] ^ ^^

K =

[aHbenzoate]nbsp;[^Hbenzoate]

— log fi = — log K [aHbenzoatel — PaH — pcbenzoatequot;

p^ll is the experimental value

[cbenzoate~] i® ^^^ concentration of the benzoate ions, corrected
for the dissociation of the acid.

[aHbenzoatequot;quot;quot;! ^^ ^^^ constant value of the activity of the
undissociated benzoic acid and can be extra-
polated from measurements of the solubility
of the acid in solutions of sodium benzoate
of decreasing concentrations and paH deter-
minations.

An objection against this type of work is that the measurement
of a single activity coefficient involves an uncertainty on account
of the liquid junction potential. It is possible to decrease the value
of this junction potential by the use of a saturated potassium
chloride solution, but this measure is not satisfactory. We also
can calculate the potential, but this involves considerable un-
certainty.

Therefore it is impossible to determine exactly single activity
coefficients. Guggenheim i») even states: quot;The electric potential
difference between two points in different media can never be
measured and has not yet been defined in terms of physical
realities; it is therefore a conception which has no physicaf
significancequot;. It is believed that the uncertainty, involved in using
saturated potassium chloride as bridge solution is one of the
smaller errors in this work.

It was further decided to determine the activity coefficient of
the benzoate ion in quite a different way. Pure silver benzoate
was prepared and its solubility in water and in various salt
solutions was determined. From these values the mean activity
coefficient fo of the silver and benzoate ions can be calculated.

Assuming that in saturated solutions in pure water f Ag =
fbenzoate then

10) E. A. Guggenheim J. Phys. Chem. 33 842 (1929).

quot; = ■• = /Vx\'benzoaeequot; = f^g l \'

Pbenzoate 1 = K = / true solubility product
2

f -= A . ^

benzoate 2 \' f

So = solubility at ionic strength = 0
s = solubility at ionic strength given.

However since we were interested to know the activity

coefficient of the benzoate ion, we had to know the activity

coefficient of the silver\' ion fAg is evident from the above

equations. This silver ion activity coefficient was determined in

the saturated solutions of silver benzoate potentiometrically by

means of the silver electrode. Since f. , X f,nbsp;— was

• Ag\'Tquot; benzoate

found from the solubility measurements andf, . is determined,

Ag

f,nbsp;— could be calculated,

benzoate

Incidentally it may be mentioned that the determination of the
f^^^ involved an exact study of the silver electrode.

By working with silver benzoate solutions with the same salt
and same ionic strength as in the system benzoic acid — benzoate
the values of the activity coefficient of the benzoate ion found by
two entirely different methods could be compared.

CHAPTER IIL

MATERIALS USED.

Certain reagents were prepared or especially purified for this
research.

1.nbsp;Pure water.

The quot;pure waterquot; was obtained from ordinary distilled water
by a redistillation over Ba(OH)2 and KMn04 in an all tin
apparatus. Before use the excess carbon dioxide was removed by
drawing through CO2 free air for two hours.

2.nbsp;Benzoic acid.

The benzoic acid was a U.S.P. product from the Research
Laboratory of the Eastman Kodak Company, Rochester, N.Y.

A preliminary test showed, that the product was not very
pure, so we recrystallized the acid. 200 grams of the impure
material were dissolved in as little boiling 95% alcohol as possible
and the solution was filtered through a Büchner funnel. Then two
liters of hot distilled water were added, and after cooling the
crystals were separated as thoroughly as possible from the deep
yellow colored mother liquid,

A second purification was performed in a similar way with the
exception, that in stead of distilled water, quot;purequot; water was
used. The upper part of the crystallized acid in the Büchner funnel
was scraped off and used in the experiments, so it could not be
contaminated with filter paper fibres.

After being dried to constant weight over sulphuric acid, the
benzoic acid was tested for purity. 0.5 gram, dissolved in 100 cc
of quot;purequot; water used more than 10 cc. IN KMn04 solution after
boiling for five minutes and a pungent odor was evident. According
to this test the purified product was no better than the original
material. However we had the same experience with a U.S.P.
product from Merck (recrystallized from toluene) and even with a
sample of pure benzoic acid from quot;Kahlbaum, für kalorimetrische
Bestimmungen, geprüft von Prof. Dr. P. E. Verkade, Verbren-
nungswärme pro Gramm in luft gewogen 6324 Kai. 15°. Asche-

gehalt ca. .005%.quot; So we drew the conclusion, that there is
probably a destruction of the benzoic acid, when boiled in neutral
medium with permanganate solution and that the latter is not
an adequate test for its purity.

Our recrystallized product did not change color in strong
sulphuric acid and 1 gram of acid, dissolved in 30 cc of hot „purequot;
water did not use more than 1 drop of . 1N permanganate solution
after the addition of some sulphuric acid.

Finally we made a chlorine test as described in the Pharmaco-
poeia of The United States of America 1926. 0.5 gram of benzoic
acid was* mixed with . 7 gram of pure Calciumcarbonate and a
little distilled water in a crucible, the mixture dried and incinerated
at a low red heat. The residue was dissolved in 20 cc of dilute
nitric acid, the solution filtered and the insoluble residue and
filter washed with 15 cc of distilled water. To the filtrate . 5 cc of
. IN AgNOa was added and the solution diluted with distilled
water to 50 cc. The liquid showed a slight turbidity of about the
same degree as in the blank test, so we concluded, that chlorine
was absent.

Further purity tests were made by comparison of our product
with the benzoic acid quot;Kahlbaumquot; as described below under
quot;standardization of NaOH, approximately .05 Nquot; and under
quot;solubility measurementsquot; and as a result of chese tests we
concluded, that our recrystallized product was as good as the
Kahlbaum preparation.

3. Sodium benzoate.

U.S.P. Sodium benzoate by Merck was used after recrystallizing
from water. The solubility of this salt in water is large at room
temperature and the temperature coefficient of the solubility is
small. However, from data, available in the literature, it seemed
to be the only possible method of purification.

Sodium benzoate was dissolved in water and a saturated solution
made at boiling temperature. The foiling liquid was filtered
through a Büchner funnel and the solution cooled in ice. The white
voluminous mass was separated from the liquid, washed twice
with small amounts of cold distilled water and once with a small
volume of cold absolute ethyl alcohol. The product was dried to
constant... weight at 150° C.

A chlorine test was performed as described in the Pharmac-

opoeia of the U.S.A. 1926. 1 gram of sodium benzoate was
dissolved in 10 cc of water in a separatory funnel, 10 cc of dilute
sulphuric acid added and the benzoic acid shaken out with 2
successive 20 cc portions of ether. After evaporation of the solvent
a test for chlorinated compounds was made as described under
benzoic acid. The test was negative.

The test for alkalinity was also negative, as 2 grams of sodium
benzoate, dissolved in 20 cc of distilled water did not produce a
red color with Phenolphthalein.

A further test for purity of our product is described under
quot;solubility measurements of benzoic acidquot;. We determined the
solubility of benzoic acid in sodium benzoate solutions of different
strengths. We made these solutions by weighing out our product
or by preparing the solution by neutralization of benzoic acid with
sodium hydroxide. As will be seen the checks were very satis-
factory.

4. Sodium Hydroxide, Approximately .05N.

The sodium hydroxide solution was made by proper dilution
with quot;purequot; water of a stock solution of NaOH quot;Kahlbaum,
precipitated by alcoholquot;, according to the method of Sörensen. The
concentrated base was filtered through a Jena filter crucible with
a fritted glass bottom.

The standardization was done with two samples of benzoic
acid, that by Kahlbaum and our own preparation (see under
benzoic acid) using Phenolphthalein as an indicator and neutral
alcohol for solution of the acid.

To check the water content, both preparations were also used
for the standardization after they had been melted for one half
hour at 130° C. in a paraffin bath. From the following table it may
be seen, that the material was dry.

Standardization of sodium hydroxide with benzoic acid.

quot;KAHLBAUMquot;

quot;OUR PREPARATIONquot;

5.nbsp;Chloroplatinic acid.

The chloroplatinic acid, used for the coating of the hydrogen
electrodes was prepared according to a procedure of Wichers. 20)

Approximately 1 gram of platinum foil was dissolved in pure
aqua regia and the solution three times evaporated to dryness
with pure HCl to remove the HNO3. The residue was dissolved
in 50 cc of distilled water and the chloroplatinic acid precipitated
with a 15% pure ammonium chloride solution. The precipitate was
washed by décantation with a large volume of the 15% NH4CI
solution and finally separated from the liquid in a small Büchner
funnel.

The ammonium chloroplatinate was decomposed to platinum
sponge in a silica crucible at 1000° C. in an electrically heated
muffle furnace.

The pure platinum was then dissolved in aqua regia, the nitric
acid removed as before and finally the HCl by a last evaporation
to dryness. The hloroplatinic acid was dissolved in 100 cc of
quot;purequot; water and this solution, containing 1% of platinum, used
for platinizing.

6.nbsp;Silver benzoate.

The silver benzoate was prepared as follows: 40 grams of
sodium benzoate Merck U.S.P. Quality were dissolved in 500 ml
of distilled water, the solution boiled and added to a boiling
solution of 45 grams of silver nitrate (Mallinckrodt C. P. Quality,
Maximum impurities less than .13%) in 500 ml of distilled water.
After standing over night the precipitate, which had a slight brown
color was separated as thoroughly as possible from the mother
liquid in a Büchner funnel and washed five times by décantation
by rubbing in a mortar with distilled water. Finally the Ag-
benzoate was washed with absolute ethyl alcohol and dried to
constant weight at 120° C.

Tests: Inorganic substances: 5 grams of silver benzoate were
dissolved in boiling distilled water, the silver precipetated with
hydrochloric acid and the AgCl filtered from the solution. The
filtrate was evaporated to dryness in a weighed evaporating dish
and finally heated to remove all benzoic acid. As there was no

20) Edw. Wichers, J. Am. Chem. Soc. 43 1268 (1921).

residue present, we concluded that inorganic matter was absent.
Silver determination:

A further purity test was made by a gravimetric determination
of the silver content:

. 4013 grams of silver benzoate yielded . 2500 grams of silver chlo-
ride = 46.89% of Ag. (Gooch crucible method).
. 3737 grams of silver benzoate yielded . 2336 grams of silver chlo-
ride = 47.05% of Ag. (Filter paper method).

The theoretical value of Ag/Ag-benzoate = 47.13%.

7.nbsp;Silver nitrate.

General Chemical Company, C. P. Quality quot;Maximum impuri-
ties less than .022%quot;.

Preliminary tests showed that this chemical was not as pure as
was mentioned on the label. Therefore we purified it by melting in
a silica dish, keeping it at the melting point for about 15 minutes,
(most of the nitrates decompose at this temperature, except silver
nitrate). The melt was then poured upon a porcelain plate and
after cooling the crust was powdered and brought into solution
with distilled water. The liquid, that showed a black precipitate of
probable lead and bismuth oxides was filtered and evaporated to
dryness on a water bath. The crystals were then heated until they
just melted in order to remove the water.

A purity test was made by an electrometric titration with a
solution of potassium chloride quot;Kahlbaumquot;:
. 5006 grams of silver nitrate used 29.50 ml of . 1 N KCl solution =
63.75% of Ag.

. 5002 grams of silver nitrate required 29.48 ml of . 1 N KCl solu-
tion, = 63.58% of Ag.

The theoretical value of Ag/AgNOs -- 63.50%.

Certain commercial reagents were used in this work. Their
quality is set forth below.

8.nbsp;Barium nitrate.

Central Scientific Company, C. P. Quality, quot;Maximum impuri-
ties less than .04^quot;.

Tests: Neutrality: 5 grams, dissolved in 25 cc of water reacted
neutral to phenolphtalein.

Chlorine : negative

Water : negative; 2.0082 grams did not lose any
water, when left for 3 months over sul-
phuric acid.

9.nbsp;Barium chloride.

Baker\'s Analyzed, C. P. Quality, quot;Maximum impurities less
than .011%quot;.

Tests: Neutrality: 5 grams, dissolved in 25 cc of water react ed
neutral to phenolphtalein.

Water : direct determination: 2.0167 grams lost
. 2945 g of water, when heated to constant
weight at 200° C 14.60% water
indirect determination (barium determina-
tion)

. 2889 gram of salt gave . 2759 g of barium

sulphate 14.92% water

. 4503 gram of salt gave . 4297 g of barium

sulphate 14.88% water.

Theoretical value for BaCl2.2HoO 14.74%.

10.nbsp;Calcium nitrate.

Riedel-de Haen, quot;chemically pure crystalsquot;.

Tests: Neutrahty: 5 grams, dissolved in 25 cc of water used
1 drop of HCl .05N to methyl orange to
neutralize.

Chlorine : negative

Water : direct determination: 2.2815 grams lost. 6650
g of water, when heated to constant weight
at 240° C. 29.15% water
indirect determination: (calcium determina-
tion) 1.1025 g of salt gave . 2717 g of CaO

29.56% water
1.1580 g of salt gave . 2785 g of CaO 29.65%
water.

Theoretical value for Ca(N03)o.4Hgt;0
30.51%.

11.nbsp;Calcium chloride.

Riedel-de Häen, quot;chemically pure crystalsquot;.

Tests: Neutrality: 5 grams, dissolved in 25 cc of water reacted
neutral to phenolphtalein.

Water : direct determination: 2.4738 grams lost
1.2057 g of water, when heated to constant
weight at 200° C. 48.74% water
indirect determination (chlorine determina-
tion)

. 3057 g of salt used 28.05 ml . 1007N silver
nitrate solution for the Mohr\'s chloride
titration: 48.74% water
. 3674 g of salt used 33.66 ml . 1007N silver
nitrate solution for the Mohr\'s titration:
48.80% water.

Theoretical value for CaCl2.6H20 49.34%,

12.nbsp;Lithium nitrate.

Baker\'s Analyzed. C. P. Quality, quot;Maximum impurities less
than .054%quot;.

Tests: Neutrality: 5 g dissolved in 25 cc water reacted neutral
to phenolphtalein.

Chlorine : negative

Water : 1.0954 g of salt lost .0522 g of water, when
heated to constant weight at 105° C.: 4.77%
1.1117 g of salt lost. 0543 g of water, when
heated to constant weight at 105° C.: 4.88%.

13.nbsp;Lithium chloride.

Power\'s Weightmann Rosengarten, quot;Maximum impurities less
than .08%quot;.

Tests: Neutrality: 5 g dissolved in 25 cc of water used 1 drop
HCl .05N to phenolphtalein.

Water : 1.0318 g of salt lost .0395 g of water, when
heated to constant weight at 105° C.: 3.83%
1.0159 g of salt lost. 0392 g of water, when
heated to constant weight at 105° C.: 3.86%.

14.nbsp;Magnesium nitrate.

Riedel-de Haen, quot;chemically pure crystalsquot;.

Tests: Neutrality: 5 g dissolved in 25 cc of water reacted neu-
tral to phenolphtalein.

Chlorine : negative

Water : a direct water determination seemed to be
impossible, as magnesium nitrate decompo-
sed already at 130° C.

indirect water determination (magnesium
determ.) . 7202 g of salt gave .3114 g of
MgoPoOr : 42.42% of water.
Theoretical value: 42.14% for Mg(N03)2.
6H2O.

15.nbsp;Potassium nitrate.

Baker\'s Analyzed, C. P. Quality, quot;Maximum impurities less
than .004%quot;.

Tests: Neutrality: 5 g dissolved in 25 cc of water reacted neu-
tral to phenolphtalein.

Chlorine : negative

Water : 2.0356 g of salt did not change in weight,
when left for 3 months over sulphuric acid.

16.nbsp;Potassium chloride.

Sterhng, C. P. Quality, quot;Analysis certified for maximum impu-
rities, less than .036%quot;.

Tests: Neutrality: 5 g dissolved in 25 cc of water reacted
neutral to phenolphtalein.

Water : 3.5486 g of salt did not lose in weight, when
left for 3 months over sulphuric acid.

17.nbsp;Potassium bromide.

Mallinckrodt, C. P. Quality, quot;Maximum impurities less than I %quot;.

Tests: Neutrality: 5 g dissolved in 25 cc of water used less than
1 drop of .05N HCl to phenolphtalein.

18. Potassium sulphate.

Central Scientific Company, C. P. Quality. quot;Maximum impuri-

ties less than .04%quot;.

Tests: Neutrality: 5 g of the salt, dissolved in 25 cc of water
reacted neutral to phenolphtalein.

19» Sodium nitrate.

Bakers Analyzed, C. P. Quality. quot;Maximum impurities less

than . 006%quot;.

Tests: Neutrality: 5 g of the salt, dissolved in 25 cc of water
reacted neutral to phenolphtalein.

Chlorine : negative

Water : 2.0254 g of the salt lost .0008 g of water.

by drying for 3 months over sulphuric acid!

20.nbsp;Sodium chloride.

Central Scientific Company. C. P. Quality. quot;Maximum impuri-
ties less than . 033%quot;.

Tests: Neutrality: 5 g of the salt, dissolved in 25 cc of water
reacted neutral to phenolphtalein

Water : 2.874 g of the salt did not loose any water.

when left for 3 months over sulphuric acid.\'

21.nbsp;Strontium nitrate.

Powers Weightmann Rosengarten, Maximum impurities less
than .11%.

Tests: Neutrality: 5 g of the salt, dissolved in 25 cc of water
used less than 2 drops of . 05N NaOH to
phenolphtalein.

Chlorine : negative

Water : 2.0016 g of the salt lost .0053 g of water,
when left for 3 months over sulphuric acid\'
.25% water.

3.5297 g of the salt lost .0104 g of water,
when heated to constant weight at 130° C.
.30% water.

22.nbsp;Strontium chloride.

Baker\'s Analyzed, C. P. Quahty, Maximum impurities less
than .022%.

Tests: Neutrality: 5 g of the salt, dissolved in 25 cc of water
reacted neutral to phenolphtalein.

Water : direct determination: 2.0330 g of the salt
lost. 8067 g of water, during a drying period
of 3 months over sulphuric acid. 39.68%
water

indirect determination (chlorine det.) . 4074g
salt used 30.88 ml AgNOs sol. .1007N
39.50% water

.4004 g salt used 30.36 ml AgNOg sol.
. 1007N 39.49% water.

23.nbsp;Potassium thiocyanate.

Baker\'s Analyzed, C. P. Quality, quot;Maximum impurities less
than .022%.

In this investigation three solutions of KCNS approximately .01,
.03 and .1 N respectively were used. The first two were made by a
proper dilution of the strongest and all solutions were standardized
potentiometrically against the purified silver nitrate.

CHAPTER IV.
DESCRIPTION OF EXPERIMENTS.

a. Solubility measurements,

1. Benzoic acid.

All the solubihty measurements were carried out in an electri-
cally heated water thermostat made by the quot;Central Scientific
Companyquot;, Chicago. Since the temperature fluctuations, using the
mercury thermoregulator, furnished with the thermostat, were too
large, it was replaced by a toluene-mercury regulator of 300 cc
volume. The heating capacity of the two electrical knife type
heaters was reduced by a set of light bulbs, connected in series
with the heaters, thus securing a better distribution of the heat.
A two blade brass stirrer, driven by an electrical stirring motor
gave the necessary movement of the water. With these impro-
vements the temperature of the bath was kept constant at 25° C
±.01°.

The different saturated solutions were made in 250 cc Pyrex
glass bottles, closed with cork stoppers (impregnated with paraf-
fin in a vacuum dessicator) and wired in with copper wire.

As a shaking device the apparatus was used illustrated in fig.
No. 1. It is similar to that in use at the van \'t Hoff laboratory of
the State University at Utrecht. The great advantage of this shaker
is, that it can be immersed under water without the trouble of
making^ connections through the walls of the thermostat. The
bottles are fastened to the rod ab by means of the clamps c, d, e
and f and are rotated in this way end over end producing a very
thorough mixing.

After saturation had been obtained the solution was drawn out
into a (25 of 50 ml) pipett by means of a suction pump. The tip of
the pipett was closed with a piece of glass tubing, that was drawn
out in the middle and filled with a piece of absorbent cotton in
order to filter the solution. The pipett was then delivered into
10 ml of distilled water as to prevent crystallization of the acid
from the saturated solution.

ShdbinJ Appdrdlus Tor
Immersion In Thermostats,

e

Fig. 1

It may be added here, that the temperature in the laboratory
was regulated between 24° and 26° C.

The benzoic acid in solution was finally titrated with sodium
hydroxide as described on page 24,

2, Silver benzoate.

Silver benzoate was brought to saturation in the various solu-
tions in the manner described under benzoic acid.

The saturated solutions were drawn into a calibrated 25 ml
pipett provided with the same filtering device. The silver content
was determined by a potentiometric titration with an approxima-
tely . 01 N potassium thiocyanate solution. A normal calomel elec-
trode was used as reference electrode and an agar-agar siphon,
saturated with potassium sulphate as connecting bridge.

b. paH measurements.

The paH measurements were carried out in a second thermostat,
similar to the first one, with the exception, that the original thermo--
regulator was used as a temperature control, accurate to ± . 1° is
sufficient for E.M.F. measurements for paH or paAg determina-
tions.

The hydrogen electrode used by us for the determination of the
hydrogenion concentration was the same as used in all our pre-
vious experiments 21) and depicted in fig. No, 2.

Hijdro^erv ^c
Electrode

The glass bottom of the vessel is perforated so that the hydro-
gen, entering through the bent tube a is devided into small bubbles
in order to saturate rapidly the platinized platinum spiral. The
upper part of the vessel has two holes, one for the hydrogen elec-
trode and the other for a siphon to make the electrolytic contact
between the hydrogen and reference electrodes.

This type of electrode has several distinct advantages:

a.nbsp;The potential soon becomes constant.

b.nbsp;The electrode requires but little hydrogen.

c.nbsp;It may be used in a thermostat at all temperatures.

d.nbsp;Even if the electrolyte is as dilute as . 001 N the readings
are sharp.

e.nbsp;The amount of solution is very small (about 5 cc).

f.nbsp;The electrode is inexpensive and not easily broken.

We have used in this investigation a quinhydrone electrode in
the standard acid mixture (.OlN HCl and . 09N KCl) as refe-
rence electrode. The quinhydrone was washed several times with
the standard solution and the platinum electrode heated to red heat
each time before using. The liquid was renewed twice a day. Wor-
king in this way the electrode is reproducible within . 1 millivolt
even in dilute solutions. 22)

A „Leeds and Northrupquot; potentiometer, the readings of which
could be made within ♦ 1 millivolt was used as a compensation appa-
ratus. The potentiometer was checked against a calibrated „type
Kquot; potentiometer and found te be accurate within the experimental
errors (. 1 millivolt).

c. paAg determinations.

The paAg determinations proved very troublesome, as we
expected. There are several procedures given in the literature, but
none of them gave the desired results in our experiments.

Randall and Young 23) have compared the different types, used
by many authors.

Jahn24) and Halla25) used platinum foil electrodes of about 1
square centimeter area, upon which silver was deposited electro-
lytically in a rather thick layer from a potassium silvercyanide

22)nbsp;I. M. Kolthoff und Wouter Bosch, Bioch. Zeitschrift 183 441 (1927).

23)nbsp;Randall and Young J. Am. Chem. Soc. 50 990 (1928).

24)nbsp;Jahnnbsp;Z. phys. Chem. 33 545 (1900).

25)nbsp;Hallanbsp;Z. Elektrochem. 17 179 (1911).

solution. After washing for a couple of days the electrodes were
coated with AgCl by electrolysis, making them anodes in a 25%
HCl solution, using a current of small amperage. The current was
reversed after two hours, until a weak hydrogen evolution took
place at the cathode. After washing for some days with a dilute
NaCl solution, the electrodes showed a potential difference of . 1
to 2 millivolt.

Lewis, Brighton and Sebastians?) and Giintelberg 28) prepared
several electrodes in this manner, which showed a maximum dif-
ference between themselves of ♦ 9 millivolt.

Also Bronsted\'s 28) silver plated platinum foil electrodes gave
poor results, that were usually too high.

Since this type of electrode has proved too inaccurate we
decided not to use it.

Randall and Young also studied the various forms of silver
crystals, made by electrolysis. Large crystals produced by elec-
trolysis with a low current density from silver\'nitrate solutions are
far from reproducible.

Crystals deposited electrolytically from a molar solution of sil-
ver nitrate by the method of Linhart29) proved more satisfactory.
The deposition was carried out at 90—100° C. using a point elec-
trode of platinum wire with a current of about 6 amperes (Ran-
dall and Young 23), More finely divided crystals were made in the
same manner from a , 1 molar AgNOa solution. This form of silver
was readily reproduced and electrodes made from it never varied
by more than . 4 mV, when checked against each other.

Although this type of electrodes seemed to be satisfactory, we
did not use this method as we wished to use the same set of elec-
trodes in all our experiments and we were afraid, that the elec-
trodes made from these crystals could not be used for different
determinations with varying concentrations because of the diffi-
culty of washing them. Another disadvantage was, that equilibrium
was reached only after 3-4 days.

Another type of electrode was that used by Brester30). Xhe
first part of the method, which he used in preparing them was the

20) Lewis, Brighton andnbsp;Sebastian J. Am. Chem. Soc. 39 2245 (1917).

Güntelbergnbsp;Z. phys. Chem. 123 199 (1926).

28) Brönstednbsp;ibid. 50 481 (1904).

20) Linhartnbsp;Z. phys. Chem. 41 1175 (1919).

30) Bresternbsp;Ree. Trav. Chim. 46 328 (1927).

same as used by Noyes and Ellis 3i). The spiral electrodes, made
from . 6 mm. platinum wire were silverplated, properly washed and
then coated with a paste of pure silver oxide (prepared from a
silver nitrate solution by the addition of sodium hydroxide) and
then heated during a period of 4-6 hours at a temperature of
400—500° C. to decompose the oxide to metallic silver. As Brester
found, his deviations in E.M.F. were not larger than . 3 mV.
However our results with this type of electrode were very poor
as the following figures, taken from a large number will show:

a.nbsp;E.M.F. of silver electrode in . 1 N silver nitrate solution,
measured against quinhydrone electrode in Sorensen stan-
dard mixture after hour........ 1603 Volt

b.nbsp;electrode refilled with same solution..... 1632 „

c........... ..... 1647

d. electrode washed with boihng distilled water and heated at
500° for 3 hours (cleaning method, as prescribed by Bres-
ter) in same solution as under c

E. M. F. after 5 hours........1617 Volt

Better results were obtained by us, using the method of Walter

R. Carmody 32).

This author notes, that the following factors influence the
potential of the silver electrode:

a.nbsp;cyanide ion, absorbed in the silver plated electrode

b.nbsp;light

c.nbsp;time of electrolyzing

d.nbsp;concentration of the chloride solution

We want to add to this as fifth very important factor

e.nbsp;influence of air

as will be discussed later.
As we got fair results with Carmody\'s procedure, we have
adopted his method of preparing the electrodes, which will now
be described.

d. Preparation of silver electrodes and their use in silver nitrate
and silver benzoate solutions.

The platinum gauze electrodes were of cylindrical shape with
a diameter of . 5 cm. and a height of 1 cm. and the mesh was 52

31)nbsp;Noyes and Ellis J. Am. Chem. Soc. 39 2533 (1917).

32)nbsp;Carmodynbsp;J. Am. Chem. Soc. 51 2901 (1929).

to the inch. The wire had a diameter of .01 mm. They were
cleaned with boiling nitric acid and after washing and heating
to red heat plated with silver from an approximately IN solution
of potassium silver cyanide. This solution was prepared by the
addition of 13 grams of KCN, dissolved in 100 cc of distilled
water to a solution of 18 grams of silver nitrate in 100 cc of water.

The electroplating was carried out in a H-shaped, black painted
vessel with a current of 1 milli ampere during 18 hours, using a
strip of pure silver as anode. After boiling with distilled water,
that was changed three times, the electrodes were covered with a
thin layer of silver chloride by using them as anodes during
20 minutes in IN hydrochloric acid with a current strength of
3.5 milli amperes.

Finally the electrodes were washed with a very dilute NaCl
solution. They were kept in the dark at all times during prepara-
tion and during the measurements.

Although this method of preparation gave by far better results
than any of our previous measurements, the checks were not good
enough, especially not in the more dilute solutions.

As already mentioned we had noticed in our experiments the
great influence of air upon the electrodes. Some values, that will
illustrate this point, are given below.

One electrode vessel was filled with • IN AgNOs solution and
the E.M.F. measured against the quinhydrone electrode in the
Sorensen standard mixture:

E.M.F. after hournbsp;. 1542 Volt

after passing air for 1 hournbsp;. 1542 „

......2 hoursnbsp;. 1549 „

......3 „nbsp;.1551

........12 „nbsp;.1571

This change in voltage was not due to an increase of concen-
tration, as evaporation was prevented by passing the air through
water before sending it through the cells.

Then we tried to obtain better results by removing the air with
an indifferent gas e.g. nitrogen. However our trials failed also
here, as may be seen from the following figures:

E.M.F. of Ag-electrode in .IN AgNOs, measured against the

quinh. electrode in the standard solutionnbsp;. 1566 Volt
after passing nitrogen, washed

through water for one half hournbsp;♦ 1540 „

for one hournbsp;. 1542 „

for 12 hoursnbsp;, 1640 „

When we purified the nitrogen by passing it over glowing
copper and then through wash botdes, containing sulphuric acid,
sodium hydroxide and water the results did not improve, as shown
by the following results:

E.M.F, after 15 minutes . 1528 Volt
» 75 .. . 1520 „

The values using No purified by passing through alkaline pyro-
gallic acid, sulphuric acid, sodium hydroxide and water in turn
are the following:

E.M.F. after 5 minutes . 1567 Volt
10 „ . 1558 „
„ 15 „ . 1550

Also the checks of the different electrodes among each othei;
were terrible, as the following values measured with three different
electrodes in the same solution, will show:

E.M.F. electr. No. I after 5 minutes . 1568 Volt

...... 2 ....... 1567 „

...... 3 ....... 1554

E.M.F. electr. No. 1 after 10 minutes .1561 ,

...... 2 ....... 1558 ,

......3.......1541 ,

E.M.F. electr. No. 1 after 15 minutes .1560 ,

...... 2 ....... 1550 ,

......3 „ -.....1530

Since it seems from these experiments, that the influence of air,
and even of nitrogen, which is probably indifferent, is very large,
we thought it worthwhile to try the effect of removing all gases
as much as possible by evacuating the electrode vessel and the
liquid in the same way as Brester (I.e.) has done. This, as will

be seen, made it possible to get results, which were satisfactorily
constant and reproducible.

The final design of the apparatus, as we used it in all our
experiments, is pictured in fig. 3 and the method of using the
silver electrodes — prepared as given at page 38 — in these vessels
will be described.

The apparatus consists of a vessel d in which the silverplated
and silver coated platinum gauze electrode e is fixed by means of
an one hole rubber stopper. The long tube c sticks into the
distilling flask b. At the left side is a wide tube, which is fitted
with a glass stopcock f of 3 mm. bore, which in turn leads into
the vessel g.

This end was closed by means of a piece of rubber tubing with
a screw clamp, the distilling flask filled with a suitable amount
of the liquid to be measured and the apparatus put together as
shown in the illustration, with the exception of the vial g, which
was connected later.

After opening of the stopcock f a suction was applied at the
tube a by means of an oil vacuum pump. The air was then admitted
through he tube, filling the entire apparatus with liquid. This
operation was repeated three times, decreasing the pressure each
time until the liquid in the vessel started boiling. This was
necessary to remove air bubbles sticking to the electrode and to
the walls of the vessel as thoroughly as possible. The distilling
flask was then removed and the electrode vessel closed at both
sides c and g and immersed in the thermostat over night. The
next morning the tap f was closed and the tubes c and g opened.
The latter was then connected with the vial g which had been
filled with a concentrated potassium chloride solution, while the
other end c was attached to a Kipp apparatus, filled with air.

By the pressure it was possible to make fresh contact in the
tube g between the silver solution and chloride solution. There
was a small turbidity at the end of this tube, but as it was wide
(4 mm. inside diameter) there was no danger of stopping up. The
necessary contact with the reference electrode (quinhydrone in
standard mixture) was made with a 2% agar bridge, saturated
with KCl at 25° C. (approximately 3.5 N).

With this setup the E.M.F. readings checked readilly within . 1
millivolt, even in the most dilute solutions, e.g. .001 N and the
values were also reproducible.

B

The question arose, whether there was any danger of increasing
the concentration by evaporation, caused by decreasing the
pressure with the resulting boiling of the liquid. To determine the
amount of evaporated liquid we put a trap, immersed in ether and
solid carbon dioxide between the distilling flask and the oil pump.
After three successive evacuations the amount of condensed liquid
in the trap was about one drop, an absolutely negligable amount,
compared with the total quantity of 50 mis.

It may be pointed out here, that, in order to avoid any possible
error, that might occur in trying to get reproducible values,
three electrodes were used in all our experiments without any
replating. Shortly thereafter the electrodes were used again in
,01N silver nitrate solutions and the E.M.F. compared with values
that were obtained before. They were always found to check
satisfactorily.

The measurements of the paAg of silver benzoate in silver
nitrate and in sodium benzoate solutions had to be carried out
later in the Chemistry Department of the Oklahoma Agricultural
and Mechanical College, Stillwater, Oklahoma, U.S.A. with
entirely new and different material. However the values, measured
in . 1 and . 01 N AgNOs solutions and in a saturated solution of
silver benzoate in water were the same as those obtained in the
School of Chemistry at the University of Minnesota, Minneapolis,
Minnesota. U.S.A.

This fact certainly strenghtens our confidence in the reprodu-
cibility of this type of silver electrodes.

CHAPTER V.

SOLUBILITY OF BENZOIC ACID AND ACTIVITY
COEFFICIENT OF THE UNDISSOCIATED ACID
IN AQUEOUS SALT SOLUTIONS.

The activity coefficient f^^ of the undissociated benzoic acid in
solutions of various salts was calculated from the values of the
solubility of the acid in water and in the salt solution.

As has been mentioned in the outline (Chapter II) the activity
of the undissociated acid was kept constant by working with
saturated solutions.

All measurements of the solubility of benzoic acid have been
made in the presence of .01 N sodium benzoate. In this way
the dissociation of the acid into hydrogen ions and benzoate
ions can be neglected, as may be inferred from all pj^ measure-
ments, reported in Chapter VI, or a sligt correction could be
applied if the dissociation were not neglegibly small. The activity
of the benzoic acid is sligthly smaller in .01 N sodium benzoate
than in water (see page 57); however this small effect will be
the same in the presence of neutral salts .Therefore the activity
coefficient f^ of the undissociated acid could be calculated by the
simple equation

f. ^—

where s^ is the solubility of benzoic acid in . 01 N sodium benzoate
s „ „ .. Mnbsp;.. .. the salt solution.

In Table 1 we give the values of f^, in the different salt solutions.

44

TABLE L

Activity coefficient f^ of undissociated benzoic acid in salt
solutions

Salt added ionic strength normality normality benzoic f ^ —log- f^

The first column gives the kind of salt added, the second and third
columns the ionic strength (Chapter I note 11) and the norma-
lity respectively. The normality of the benzoic acid, found by
the titration with the standard alkali is given in the fourth, and
in the fifth and sixth column the values of f^^ and -log f^ are
recorded.

The results are further represented graphically in figures 4
and 5; the abcissae giving the ionic strength and the ordinates the
corresponding -log f^. These graphs in which the effects of the
monovalent and divalent salts have been plotted separately show
very nicely the salting-out effect, giving straight lines in every
case. A slight curvature of the lines is found in the case of the
nitrates.

.b

Fig. 4

.10

.75

Fijf. 5

It may be concluded that there is a pronounced specific cation
effect in the order Li4quot; ^nbsp;Kquot;^ and also a distinct anion

effect in the order Gl~gt; Br~gt; S04=gt; Iquot;quot; gt; NOaquot;quot;.

In the series of bivalent salts there is a small difference between
the action of the cations in changing f^^, but the same large
deviation Cl~gt; NOsquot;quot; as noted in the monovalent series.

We also have compared our values for f^^.with those obtained
by different authors. These results are set forth in Tables 2 and 3.

TABLE 2.

Comparison of (activity coefficient of undissociated benzoic
acid) determined by different Authors and calculated.

Larsson Larsson Rordam

det.
18° C.

det.
25° C

det.

25° C. Langebeck

Bosch
det
25° C.

49

TABLE 3.

Comparison of f^ determined and calculated by Larsson and
determined by Kolthoff and Bosch.

Salt added Ionic strength Larsson det. 18°C Kolthoff Larsson calculated

Larsson 33) 34) 35) who performed most of his experiments at
18° C. has also determined the temperature coefficient of the
activity coefficient in some cases 35) and found that this tempe-
rature coefficient is small in salt solutions, so that it is possible
to compare his values with ours.

The last column gives the values as calculated using his formula

lognbsp;= kc, in which for instance

nbenzoate

k = . 177 in NaCl solutions and

k = . 137 in KCl solutions.

Rordam and Hoffman and Langebeck\'s figures as they are
recorded in the fifth and sixth columns have been taken from a
review of Randall and Failey^c).

The values between parenthesis give the ionic strength in those
cases where this figure is different from that occurring in the
second column.

The agreement is in general satfsfactory and strengthens our
confidence in the accuracy of the measurements.

In a second series of measurements we have determined the f

33)nbsp;E. Larssonnbsp;Z. Physik. Chem. 148 A 307 (1930).

3-1)nbsp;E. Larssonnbsp;ibidnbsp;153 299 (1931).

35)nbsp;E. Larssonnbsp;ibidnbsp;153 466 (1931).

30)nbsp;M. Randall and C. F. Faileynbsp;Chem. Rev. 4 295 (1927).

values of benzoic acid in sodium benzoate solutions of various
concentrations. These determinations, together with p^^ measure-
ments were necessary in order to calculate the constant value of
the activity of the undissociated acid in water as will be described
in the following Chapter.

Many measurements have been made in order to check the four
following factors that influence the solubility:

a.nbsp;different preparations of benzoic acid

b.nbsp;size of acid crystals

c.nbsp;amount of benzoic acid

d.nbsp;time of shaking

a. and b.: As described in Chapter III 2 we have compared our
preparation of benzoic acid with a product quot;Kahlbaumquot; in two
ways, first by using them as standard substance in the titration of
NaOH and second by the determination of the solubility of both
products, the results of which are given in Table 4.

TABLE 4.

Solubility of benzoic acid in water.

amount per 200 cc time of shaking normality of satur-

quot;Kahlbaumquot; melted

quot;our preparationquot; melted

In the first column the kind of acid used is recorded: both prepa-
rations also have been used after they had been kept at the mel-
ting point for one half hour. The crust was then powdered, so that
there was a great difference in the size of the crystals before and
after melting.

c.:nbsp;Different amounts of benzoic acid from .8—3 grams were
shaked with 200 ml of water (Table 4 column 2)

d.:nbsp;The time of shaking varied from 5—22 hours: column 3. As we
found, saturation was obtained in the case benzoic acid — water
already after 5 hours; the figures for the solubility for a shaking
period of 22 hours do not differ from the ,,5 hourquot; values by
more than the experimental error, so that it was not necessary to
extend the shaking time for longer thans 22 hours.

Kilpatrick and Chase 37) have used a shaking time of even 217
hours and did not find any increase in solubility after 5 hours
of shaking.

The values of the benzoic acid normalities are set forth in the
fourth column; the agreement between the figures is very good
and we have taken therefore as an average normality of a satu-
rated aqueous solution of benzoic acid of . 02778 at 25° C. Table
5 gives the values obtained by other workers.

TABLE 5.

Some previous determinations of the solubility of benzoic acid
in water at 25° C.

Solubility
moles per liternbsp;Observer

.02808nbsp;Paulnbsp;Z. physik. Chem. 14 105 (1894)

.02793nbsp;Noyes and Chapin J. Am. Chem. Soc. 20 751 (1898)

.02796nbsp;Hoffmann and Langebeck\'Z. physik. Chem. 51 385 (1905)

.02799nbsp;FrcundUch and Seal Kolloid Z. 11 257 (1912)

.02791nbsp;Rordamnbsp;Thesis Copenhagen (1925)

02781nbsp;Larssonnbsp;Z. Anorg. Chem. 155 247 (1926).

.02781nbsp;Kilpatrick and Chase J. Am. Chem. Soc. 53 1734 (1931)

(25.15° C.)

quot;) Kilpatrick and Chase J. Am. Chem. Soc. 53 1734 (1931).

The solubihties and f^ values of benzoic acid in sodium benzoate
solutions of various concentrations are given in Table 6. The cal-
culation of fp lt;vas carried out in the same way as described before.
As will be seen from the figures in the fourth column the f^, values
are all smaller than 1 in contradiction with those obtained before
in the neutral salt solutions.

TABLE 6.

Also Larsson 35) has found that the activity coefficient of ben-
zoic acid in sodium benzoate solutions is smaller than 1 in concen-
trations from .01—1.0 N at 18° C.

In a 1 N solution Larssen\'s value for f ^^ at 18° C. is . 61, whereas
we have found .60 at 25° C. at this concentration. 38)

Larsson tries to explain this anomalous behaviour by the as-
sumption, that the benzoate ions have a special action (relative
to the dipole character of the ions) upon the activity of the ben-
zoic acid molecules, besides their free electric charge. He also
thinks it possible, that there exist acid benzoate ions, which are
in equilibrium with the benzoic acid molecules and benzoate ions.
The temperature may possibly have an influence upon this equili-
brium and this will account for the large temperature coefficient

of fo.

38) E. Larsson Z. physik. Chem. 148 A 148 (1930).

CHAPTER VL

Hydrogen ion activity in benzoic acid — benzoate solutions in
the presence of neutral salts.

The activity coefficient of the benzoate ion.

As mentioned in the outline (Chapter II) it was planned to
determine the activity coefficient f^ of the benzoate ion in the
presence of various neutral salts.

Application of the Mass Action Law for the ionization of benzoic
acid gives us the following equation:

^ _ [\'Hquot;^] X f benzoate-] _ pHquot;^] X fbenzoate quot;] X ^ ^^

----p-----—-Zj---— ---p-=- (Ij

L^Hbenzoate Jnbsp;L Hbenzoate J

From this we find for the activity coefficient f^ of the benzoate ion

—log fi = —logj K X [^Hbenzoate ] |-paH^-pcbenzoate-(2)
1. Determination of K.

For the calculation of the ionization constant of benzoic acid
we have carried out pH determinations in two series of solutions,
containing sodium benzoate : benzoic acid in ratio\'s of 1 : 1 and
2:1.

The dissociation of the acid is so large that a correction has
to be applied. For instance:

We measured in a solution, that was .005 N to benzoic acid and
.005 N to sodium benzoate a pH of 4.124. This is equal to a
hydrogen ion concentration of 7.516 X 10quot;quot;^ The corrected
benzoate ion concentration is then 507.5 X 10quot;\' and the corrected
concentration of the benzoic acid 492.5 X 10~~^
We calculate then for K\'

f Hbenzoate ]nbsp;492.5

7.745 X 10quot;^ or p/ = 4.111

The results of the dilution series 1 : 1 are reported in Table I.

54

TABLE 1.

By application of the simple Debye-Hiickel equation — log f^ =
.5nbsp;in the different solutions, we find at infinite dilution

PKO = PK\' • 5 y . 01 = 4-151

These values are set forth in the fourth column. If we correct for
the difference between p and PgH we find

p^H infinite = p^ = 4.177 — 4.188 or

K = (6.66 to 6.50) X 10quot;^ or an average of 6.60 X 10quot;\'.

The results of the second dilution series 2 : 1 are given in
Table 2.

TABLE 2.

PH and p^ values of .25 normal benzoic acid and .50 normal
sodium benzoate and its successive dilutions at 25° C.

average of 6.65 X 10 5.nbsp;^

In a previous investigation we found a value of 7.0 X 10quot;^
whereas Jones and collaborators 40) calculated from conductivity
measurements a value of 6.8 X 10~5 at 25° C.

38) Kolthoff and Bosch Ree. Trav. Chim. 47 876 (1928).
Jones Am. Chem. Joum. 44 159 (1910); 46 56 (1912).

The agreement is quite good, especially when we consider the
difficulties, that are connected with pj^ determinations in these
solutions.

When we started our p^ measurements in this investigation
it was quite impossible to get constant E.M.F. values; there was
a certain drift in the E.M.F. that could not be explained. The
following table, taken from a large number of experiments may
illustrate this:

Influence of time upon the E.M.F. between the hydrogen
electrode in a solution of .025 N sodium benzoate and .025 N
benzoic acid and the quinhydrone electrode in the Sorensen
standard solution.

Timenbsp;E.M.F.

These facts could not be explained by an oxygen content of
the hydrogen used; in a first series of measurements the gas was
passed through an alkaline pyrogallol solution and then through
washbottles containing sulphuric acid and water. In a second
series we passed the hydrogen over the above reagents and then
over red hot copper wire, but this did not give any better results.

An explanation of this irregular behavior was then sought in
the method of platinizing. It was found, that the rate of increase
of the E.M.F. was proportional to the thickness of the layer of
platinum black on the electrode.

Therelore we came to the conclusion, and the experiments
proved it, that it was advantageous to platinize the electrodes as
lightly as possible. For platinizing\'we used a currcnt of 20 milli
amperes during 5 minutes. After using the electrode as a cathode
in a 1 N sulphuric acid solution with a current of 20 milli amperes
for 5 minutes the spiral electrode had a slight grayish color.

Using this procedure in platinizing, the potentials usually became
constant after 10—15 minutes and stayed constant for several
hours. However it happened once in a while, that it still was

impossible to get constant values. Replating of the electrode helped
sometimes but because of the uncertainties the ppj values in sodium
benzoate solutions with concentrations larger then .25 N may be
considerably in error.

We have not been able to find any explanation for these irre-
gularities. When we measured p values in solutions that con-
tained nitrates a possible explanation could be found in the
formation of ammonia. In a solution, containing .002 N hydro-
chloric acid and .5N sodium nitrate the p pj measured with the
quinhydrone electrode was 2.698 and the value, determined with
the hydrogen electrode after one half hour of Ho passing through
was 3.015. When this latter solution was compared with the
original solution, the former showed a more alkaline reaction
(ppj of about 3) to thymolblue as an indicator. It was also pos-
sible to make a positive test for ammonia with Nessler\'s reagent.
We have not been able to find such a reduction in the case of
sodium benzoate.

2. Activity of undissociated benzoic acid: [^Hbenzoate]

The activity of undissociated benzoic acid is constant in
saturated solutions and its value, as it occurs in equation 2
Chapter VI was extrapolated from the values in sodium benzoate
solutions of various concentrations.

As it is not petmissable to consider benzoic acid as completely
undissociated we had to correct the normality values of benzoic
acid for this dissociation. For instance: we measured in a .01 N
sodium benzoate solution a solubility of benzoic acid of .02663
moles per liter and a p^ of 3.668 or a hydrogen ion concentration
of 2.148 X 10quot;~4. The corrected value for [cHbenzoatel is then
2.663 X 10quot;2. _ .021 X 10 2 ^ 2.642 X 10quot;2.

The different results are given in table 3. In columns 1 and 2
the sodium benzoate and benzoic acid normalities are given
respectively, whereas we have reported in the third and fourth
column the ppj and hydrogen ion concentration. The last column
gives the value of the concentration of undissociated benzoic acid,
corrected for dissociation.

In order to extrapolate we have plotted the results from Table
3 in figure 6, the abscissae giving the sodium benzoate concen-

trations and the ordinates the corresponding concentration values.
The graph shows a straight line relationship except in the most
dilute solution and we therefore felt confident in accepting an
extrapolated value of 2.635 X 10~2 for [aHbenzoate] in aqueous
solutions at 25° C.

58

TABLE 3.

[ \'^Hbenzoate] values in .25 N sodium benzoate and its successive

dilutions at 25° C.

3 and 4 : pafi and pcbenzoate ♦

The two remaining factors in equation 2 for ths calculation of
pfj^ are the paj^ — this is the experimental value — and
pcbenzoatequot;. cbenzoatequot; is equal to the normality of the added
sodium benzoate e.g. .01 N, corrected again for the dissociation
of the acid. All results have been reported in Table 4. The first
column gives the ionic strength and kind of salt added, the second
and third the pa^ values, determined with the hydrogen electrode
(the calculation based on a pa^ of 2.075 in the standard mixture)
and with the quinhydrone electrode respectively; the fourth column
gives the negative logarithm pcbenzoate— ^^^ corrected ben-
zoate ion concentration, and the fifth -log fi, the negative logarithm
of the activity coefficient of the benzoate ions, calculated with
equation .2. For example we calculate for -log fj in .5 N KCl
solution:

-log f = - log K - log pcbenzoate] quot; P^Hquot; P^enzoatequot; =

= -log K -log pcbenzoate] quot;P^H ^°9[%enzoate-

= 4.175 1.579 — 3.627 —log (.01 .0003) = .137

We also have applied the simple Debye—Hückel equation
—log f = .5 y^ the results of which are given in the next (sixth)

column. The last column gives the fj values, corresponding to
the -log fi values occurring in the fifth column.

TABLE 4.

Activity coefficient fi of the benzoate ion in salt solutions.

Comparing the —log fj values in the fifth and sixth columns
it is evident that the agreement between the values, calculated
from experimental data and calculated with the simple Debye-
Hiickel equation is very poor and that it is not permissible to use
this equation for the calculation of activity coefficients in more
than very dilute solutions.

Therefore we have also applied the more complicated Debye—
Huckel equation Chapter 1 equation 3

1nbsp;.5//U

.log f = --^-1=nbsp;(3)

1 .329 X a X 10 )//\'nbsp;^ ^

in which a is the ionic size of the ions and has an average value
of 3.76 Aquot;.U. for KCl and of 2.35 A quot; U. for NaCHi). If we
calculate —log fj with these values we find the figures given in
Table 5.

quot;) E. Huckel Physik. Z. 26 93 (1925).

Since the agreement is not good at all, we can not draw a con-
clusion from these values about the validity of the D. H. equation
as the —log fi values in the third column of Table 5 seem to be
irregular.

As these values seem to be normal in the cases of KNO3 and
NaNOg we have calculated an A value (= .329 X a X
using the —log fi value from the fifth coimn Table 4 for the .25 N
solutions.

TJiis A figure we have used in calculating —log f^ values in the
other concentrations of potassium and sodium nitrate as they occur
in the first column of Table 4.42)

The results are given in Table 6.

TABLE 6.

quot;2) F. H. Mc Dougall J. Am. Chem. Soc. 52 1392 (1930) calculated from
solubility measurements of silver acetate A values varying from 1.408—1.479 in
KNO3 solutions up to an ionic strength of 1.

From these figures we draw the conclusion that the more com-
plicated Debye—Hückel equation can not be applied successfully
for the calculation of activity coefficients in these solutions either.

Finally we have calculated the activity coefficient fi of benzoate
ion in solutions of sodium benzoate of different concentrations
saturated with benzoic acid. These results are reported in table 7.

The first column gives the normality of sodium benzoate. the
second the paH as determined experimentally, the third the
benzoate ion concentration, corrected for the dissociation of
benzoic acid, whereas we have reported in the fourth column the
—log fi values as calculated in a way similar to this calculation
in the case of the system benzoic acid - sodium benzoate and
salts (page 58).

We also have applied the simple D. H. equation in calculating
—log fi and these results occur in the fifth column. The fi values
as they belong to the —log fj values from the fourth column are
found in the last row of figures of Table 7. It seems, that this
equation holds approximately up to an ionic strength of .1 in these
solutions.

TABLE 7.

CHAPTER VIL

Solubility of silver benzoate in water and in aqueous salt solutions.
The mean activity coefficient of silver and benzoate ions.

The mean activity coefficient of the silver and benzoate ions f^
has been calculated from solubility measurements of silver ben-
zoate in water and in salt solutions. The relationship between
this activity coefficient and the solubility is given by the follo-
wing equation:

/f , V fnbsp;__s^nbsp;(1)

^Ag ^benzoate--g

in which s is the solubility of silver benzoate in the salt solution

and s„ is the solubility if L = f. i = f,nbsp;- = 1

°nbsp;° Ag benzoate

Assuming that in a saturated solution of silver benzoate in

water f , , = f,nbsp;— then s- at an ionic strength o =

Ag benzoate

water j/^Ag ^ ^benzoatenbsp;^ Vnzoatequot;

= y true solubihty productnbsp;(2)

The solubility of silver benzoate in water has been determined
several times and the influence of the shaking period has been
checked. As an average of 12 values we find a normality of a
saturated aqueous solution of silver benzoate of .01162. The largest
and smallest figures found are .01166 and .01156 respectively.

The solutions were saturated after 3 days of shaking. Acciden-
tally we were able to determine the solubility of a solution, that

Sn = s

had been rotating for 25 days continiously and we found a figure
of .01156.

Assuming that the simple Debye—Huckel equation —lof f =
holds in this dilute solution we find for —log f = .5 X
yrm^- -054 or f^ = .883.

When we insert this value in the equation for s we calculate
s^ = .01162 X .883 = .01026.

All results have been recorded in Table 1. The first column gives
the kind of salt added and its analytical strength, the second the
solubility of silver benzoate in moles per liter, the third the total
ionic strength, whereas we have given in the two last columns
the — log 4 and fo values respectively as calculated by means of
equation (1).

TABLE 1.

An application again has been made of the two Debye — Huckel
equations

.5 i\' /t

-loaf =-

— log f = .5 y At (1) and —log
and the results can be found in Table 2.

TABLE 2.

Application of the Debye — Huckel equations (1) and (2) for
the calculation of the mean activity coefficient f^ of the silver-

and benzoate ions in salt solutions.

Kind of salt Total ionic

-log fo calculated -logr fo calculated A

-log- fg calcu-

In the first and second column the kind of salt and the total
ionic strength respectively are given. The values of -log f^ in the
third row are those occurring in the fourth one of table 1. The
fourth column of Table 2 gives the —lof f^, figures calculated with
the D. H. equation (1).

The A value in the cases potassium and calcium nitrate has been
calculated in the .25 N solutions with the second D. H. equation,
taking the -log f^ values from column 3 table 2. This A value
finally has been used to calculate the figures of the negative loga-

^^^nbsp;coefficient in the remaining concentrations

of KNO3 and Ca(N03)2 and are reported in the last column of
this Table.

As can be seen is the agreement between the values of the
columns 3 and 4 very poor and is it not permissable to use this
simple equation in solutions of an ionic strength higher than .05
In contrast to this, the application of the second D. H. equation
m some cases is more fruitful, as can be seen from a comparison
of the figures for -lof from the third and sixth rows in Table 2

CHAPTER VIIL

Silver ion activity and benzoate ion activity.

As was mentioned in the Outline (Chapter II) it was our aim
to determine the activity coefficient f^ of the benzoate ion in
quite a different way, i.e. with the silver electrode.

In the preceding Chapter we have calculated from solubility
measurements the mean activity coefficient f^ of the silver and
benzoate ions. For the calculation of fi we had to know the
activity coefficient f^g of the silver ions. The difficulties which
we had to overcome in the measurements of the silver electrode
potentials have been fully discussed in Chapter IV, to which we
refer.

In order to calculate the normal potential of the silver electrode
we measured the potentials in .05 N silver nitrate and successive
dilutions.

For the calculation we applied the well known Nernst\'s equation
c c . RT , 1

Eo = E —In

nF quot;Ag

At 25° C. and using monovalent salts the above equation becomes

Eo = E f .0591 log.-^ = E K0591Iog ^^^^^

ThefAg values have been calculated by means of the simple
Debve—Huckel equation —log f = .5 . All results are repor-
ted in Table 1,

68

TABLE 1.

The normal potential of the silver electrode.

The first column gives the analytical concentration of the silver
nitrate solution, the second the —log f^g values as calculated
with the D. H. equation (1). the third the corresponding ffigu-
res, the fourth the activity of the silver ions and in the fifth column
the potentials (measured against the quinhydrone electrode in
the Sorensen standard mixture: .01 N HC1-.09 N KCl). Finally
the E^ values have been recorded in the last column.

For instance we calculate in the .0402 N silver nitrate solution
for —log fnbsp;X yTMoI = .1002, with a corresponding value

for fAg = -794. With c = .0402 the activity of the silver ions
aAg = -0^02 X .794 = .03192.

Inserting these values, together with the measured E.M.F. of
.1386 Volt, in the equation for E^ we calculate

E^ = .1386 .0591 log^^^ =.2270

The check between the Eq values is quite good and we therefy
ore feel condifent in taking an average of .2269 as the zero poten-
tial of the silver electrode.

Considering the good checks of the E^ numbers in Table 1 we
draw the conclusion that the D. H. equation (1) can be used satis-
factorily for the calculation of the activity coefficient of the
silver ion in silver nitrate solutions up to an ionic strength of .05.

In order to calculate the activity coefficient of the silver ions in
a saturated aqueous solution of silver benzoate we have deter-

mined the E.M.F. a large number of times. The measurements were
quite difficult and it was not easy to obtain a good check. The
values varied from .1068—.1081 Volt and as an average of seven
we find an E.M.F. of .1073 V, corresponding to a silver ion
activity of .009462. From Table 1 Chapter VII we take the solubil-
ity figure of silver benzoate in water of .01162. Then we calculate