UNIVERSITY OF CALIFORNIA
AT LOS ANGELES
GIFT OF
'ARNEGIE INSTITUTION
OF WASHINGTON
Electrochemical Investigation of Liquid
Amalgams of Thallium, Indium,
Tin, Zinc, Cadmium, Lead,
Copper, and Lithium.
THEODORE WILLIAM RICHARDS
WITH THE COLLABORATION OF
J. HUNT WILSON AND R. N. GARROD-THOMAS.
PIBLISHED BY THE
CARNEGIE INSTITUTION OF WASHINGTON
1909
7 43
Electrochemical Investigation of Liquid
Amalgams of Thallium, Indium,
Tin, Zinc, Cadmium, Lead,
Copper, and Lithium.
BY
THEODORE WILLIAM RICHARDS
WITH THE COLLABORATION OF
J. HUNT WILSON AND R. N. GARROD-THOMAS.
PUBLISHED BY THE
CARNEGIE INSTITUTION OF WASHINGTON
1909
CARNEGIE INSTITUTION OF WASHINGTON
PUBLICATION No. 118
CONTRIBUTIONS FROM THE CHEMICAL LABORATORY
OF HARVARD COLLEGE
ort (gafttmore (prcee
BALTIMORE, MD., U. S. A.
Library
CONTENTS.
ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS OF THALLIUM, INDIUM, AND
TIN. BY T. W. RICHARDS AND J. H. WILSON.
PAGE
Introduction I
Values of Constants 3
Preparation of the Amalgams 8
Densities of the Amalgams 12
The Cell IS
The Potentiometer 17
Electromotive Force between Thallium Amalgams 20
Electromotive Force between Indium Amalgams 25
Electromotive Force between Tin Amalgams 27
Temperature Coefficient of the Amalgam Cells 30
Application of the Equation of Cady 31
Application of the Equation of Helmholtz 33
Summary 37
II.
ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS OF ZINC, CADMIUM, LEAD,
COPPER, AND LITHIUM. BY T. W. RICHARDS AND R. N. GARROD-THOMAS.
Introduction 39
Zinc Amalgams 39
Electromotive Force between Zinc Amalgams 41
Determination of the Temperature Coefficients of Cells containing Zinc
Amalgams 43
Lead Amalgams 47
Copper Amalgam 50
Iron Amalgam 54
Lithium Amalgams 55
Application of the Equation of Cady 57
Equation of Helmholtz 64
Comparison of Deviations from Concentration Law 68
Summary 71
iii
209154
I.
Electrochemical Investigation of Liquid Amalgams of
Thallium, Indium, and Tin.
BY THEODORE W. RICHARDS AND J. HUNT WILSON.
INTRODUCTION.
The change in free energy during a chemical reaction may be regarded
as composed of at least two separate quantities, one which may be said to
be due to the affinities involved in the reaction, the other depending upon
the relative concentration of initial substances and products. The calcula-
tion of the magnitudes of these quantities is a matter of prime importance,
for free energy is the driving agency of all earthly things. Unfortunately
the actual determination of changes of free energy is only possible in the
case of easily reversible reactions, and these form a comparatively small
part of many examples of chemical change.
Of great theoretical importance in this connection are the reversible
galvanic cells, which involve in their action simply the dilution of liquid
amalgams, and consequently suffer no appreciable change of heat capacity.
The study of such cells can furnish much light upon the second of the two
independent quantities which together constitute the total free energy of
a reaction, namely, concentration effect. Von Turin pointed out the
analogy between such cells and the concentration elements first investi-
gated by Helmholtz and offered the first consistent theory of amalgam
cells. G. Meyer measured cells of this type, but much more accurate data
have been obtained at Harvard University. The object of this recent work,
which concerned itself with cells containing zinc and cadmium amalgams
over a considerable range of concentration, was to test the application of
the gas law to solutions of this type, as well as to apply the equations of
Helmholtz and of Cady to the data. Great accuracy was sought. Since
the two metals presented widely different phenomena, and since both of
these metals are bivalent, it seemed desirable to extend the work by meas-
uring similar cells, employing a wide variety of other metals with other
valencies. In this way a more complete survey of the possibilities would
certainly be obtained.
2 ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS
This monograph embodies the results of the further investigation of
amalgam cells, containing not only the two metals already mentioned, but
also thallium, indium, tin, lead, copper, and lithium. The first section of
the monograph deals with thallium, indium, and tin. These metals are
especially interesting because they are respectively univalent, trivalent,
and (under some conditions) quadrivalent. Thallium is, moreover, inter-
esting in its chemical behavior, having in common with the alkali-metals
a soluble hydroxide, carbonate, and sulphate, while on the other hand
resembling lead in the possession of an insoluble chromate and sulphide,
and a slightly soluble chloride. Indium is the only trivalent metal that
forms satisfactory amalgams for the present purpose. 1
The effort was made to attain precision sufficient to afford an adequate
basis for the desired theoretical considerations. No attempt was made to
attain the greatest conceivable precision, because such an attempt would
have defeated the object of the investigation, by so limiting the variety
of results obtainable in the limited time as to have restricted their gen-
eralization.
1 An almost complete historical review may be found in the monograph of Rich-
ards and Forbes (Publication of Carnegie Institution of Washington, No. 56;
Zeitschrift fur phys. Chem., 58, 683 [1907]). A paper by J. Regnauld (Compt.
Rend., 53, 533 [1861]) on the heat of amalgamation of the metals was overlooked
in this review, and the date of Helrnholtz's publication (Monatsbericht d. kgl. pr.
Akad., Berlin, 1877, p. 713) was accidentally given as 1882 instead of 1877. The
reference to Lindeck's work is Wied. Ann., 35, 311, 1888. Mention should be made
of a mathematical paper by Trevor on the " Electromotive Force of Concentration
Cells" (Zeitschr. Elektrochem., 11, 681 [1905]). While this paper contains inter-
esting features, experimental verification of the equation deduced therein is not
possible at present. In a recent paper published after most of the work embodied
in this monograph had been completed, Carhart discusses the Helmholtz equation,
as applied to amalgam cells. (Phys. Rev., March, 1908). In a yet more recent
paper by Hulett and De Lury, published after the conclusion of the present work,
the work of Richards and Forbes is in part repeated and extended to more dilute
solutions. In so far as the two investigations overlap, they confirm one another
(J. Am. Chem. Soc., 30, 1812 [1908]). Another theoretical paper, by van Laar
(Arch. Neerl. d. Sci. ex. et nat. [n] vm, 296), should perhaps be mentioned.
OF THALLIUM, INDIUM, AND TIN
VALUES OF CONSTANTS.
In the discussion which follows, all the experimental work is viewed in
the light of three mathematical expressions :
<*>
In these expressions,
TT electromotive force. c t = concentration of more concen-
F Faraday's equivalent = 96,530 trated amalgam.
coulombs. c 2 = concentration of less concen-
R = the gas constant. trated amalgam.
r=the absolute temperature. 7= the change of total energy in-
v valence. volved in the dilution of the
In = natural logarithm to the base e. amalgam.
The first of the numbered equations is the well-known expression of
Helmholtz (sometimes called the Gibbs-Helmholtz equation) ; the second
contains the substance of the proposal of von Turin and G. Meyer; and
the third is the suggestion of Cady and Lewis. Both of the last two may
be said to be the outcome of other work of Helmholtz, and to be covered by
the equation of Nernst. Before denning the quantities whose symbols are
given in the foregoing list, it may be well to say a word about these funda-
mental equations themselves.
Equation (i) needs no comment. Equation (2) has been reached in
somewhat different ways by a number of thinkers ; it is based essentially
upon the epoch-making discussion by Helmholtz of the concentration cell.*
The forms in which the several investigators have expressed their results
appear to be different, although they express essentially the same idea;
the equation, as given here, is not exactly like that of any of them.
Nernst, 1 who did not himself at first apply his equation to cells of the type
under consideration, used the ratio of pressures instead of the ratio of
concentrations, and would have expressed the result thus
'Helmholtz, Monatsberichte d. kgl. pr. Akad., Berlin, 1877, p. 713. Helmholtz's
other well-known paper on the thermodynamic equation numbered (l) above was
published in the Sitzungsberichte der kgl. pr. Akad., Berlin, in February, 1882, p. 22.
'Nernst, Zeitschr. phys. Chem., 4, 129 (1889).
4 ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS
In this equation P and P' represent the unknown solution-pressures,
whose ratio alone is to be inferred, and p the osmotic pressure of the
appropriate ion in the electrolyte. The latter cancels, being common to
r> rr* r>
both electrodes, and the expression becomes ir =pln~^,. If no other
source of free energy other than osmotic effect is present, -, may be taken
as equal to and the equation reduces to ours. In this expression the
c*
absence of association in the dissolved metal is assumed. Both Nernst's
expression and that given above are calculated on the basis of the
gram-atom.
On the other hand, von Turin * and Meyer ' expressed their equations
in terms of concentration, and calculated them on the basis of the electro-
chemical equivalent in terms of grams per coulomb; and both introduced
the molecular weight (M or p) of the dissolved metal although, to be
sure, von Turin seems to have accidentally omitted this quantity from his
final statement. 8 Their equation, reached in different ways, reads T
|,8. 32 r( 2 . 3 o 3 toft,*) =
gram-atomic weight
Bearing in mind the fact that their q meant = - - - and that
we have made the additional assumption (based upon the measurements
of many investigators) that M = gram-atomic weight, it is seen that their
form is essentially identical with that given above. Our form will be
called in future merely " the concentration-equation," as its ascription to
any one author might under the circumstances seem invidious.
Attention should be called to the fact that Helmholtz, himself, insisted
that his original concentration-equation holds true only when there is no
heat of dilution involved in the reaction, 8 a condition reiterated by von
Turin. The same limitation applies, of course, to the equation in its
present simplified form ; but this limitation does not necessarily apply to the
equation of Nernst, involving solution-pressures instead of concentrations.
The term solution-pressure must be interpreted as including combined
effect of all the tendencies affecting the escape of the dissolved metal from
4 von Turin, Zeitschr. phys. Chem., 5, 340 (1890) ; 7, 221 (1891).
S G. Meyer, Zeitschr. phys. Chem., 7, 447 (1891).
* See von Turin on the bottom of page 221, Zeitschrift fur physikalische Chemie,
7 (1891).
By a coincidence of misprints, of which there are many in the papers of both
von Turin and Meyer, the decimal point of the factor 19.1 has been misplaced in
each case and reads 1.91. This mistake was inadvertently copied in reporting the
history of their work in Publication 56 of the Carnegie Institution of Washington.
8 Helmholtz, Berliner Monatsbericht, November, page 713 (1877).
OF THALLIUM, INDIUM, AND TIN 5
the amalgam, except the osmotic pressure of the ion dissolved in the
electrolyte. Thus P and P' include the effect of the chemical free
p
energy change connected with dilution ; and if such exists - t can not be
equal to . This explanation appears to be necessary, because of the
Cl
misconception of Carhart concerning the significance of the Nernst
equation.'
The equation of Cady 10 and of Lewis u is an attempt to take account of
the heat of dilution, thus resolving the tendencies P and P' into their most
important components. This equation may only be supposed to hold true
when there is no change of heat capacity during the reaction. Further
explanation may be deferred until the present research has been described,
when a still more recent suggestion of Lewis, concerning the application
of the law of Raoult ( = ^ ) to osmotic work, will also be con-
\p N+nJ
sidered.
Before beginning a description of our experimental work it will be well
to consider the accuracy with which the various quantities in the equations
are defined.
In a previous contribution from this laboratory" the results of Ray-
leigh, 18 F. and W. Kohlrausch," Kahle," and Patterson and Guthe, 1 ' con-
cerning the value of Faraday's equivalent F, have been compared ; and
the conclusion was reached that 96,580 coulombs are associated with 107.93
grams of silver, if the silver is weighed in a form free from mother-liquor,
after having been deposited in a manner avoiding anode complications.
The more recent work of Smith, Mather and Lowry, and others, has not
changed our opinion on this point." Since Richards, Collins and Heim-
rod, 18 and Richards and Stull 19 have established the universality of Fara-
day's law on a firmer basis than ever, the same value can be used for a
gram equivalent of thallium or indium with reasonable accuracy. If the
atomic weight of silver is taken as 107.88, a value probably nearer the
H. S. Carhart, Phys. Rev., 26, 216 (1908).
10 Cady, Journ. Phys. Chem. 2, 551 (1898).
11 Lewis, Proc. Am. Acad. 35, 34 (1899).
12 Proc. Amer. Acad., 37, 415 (1902).
"Phil. Trans., 175, 411 (1884).
"Wied. Ann., 27, I (1886).
15 Wied. Ann., 67, i (1889).
16 Phys. Rev., 7, 257 (1898).
17 Smith, Mather and Lowry, Phil. Trans. Roy. Soc. London, Series A, 207, 545
(1908); also see especially T. W. Richards, Proc. Am. Acad., 44, 91 (1908). The
Report of the International Conference on Electrical Units and Standards, " Science,"
28 (1908), recommends F = 96,540 for the same atomic weight without these pre-
cautions. This probably amounts to about the same thing.
"Zeit. phys. Chem., 32, 301 (1900).
19 Proc. Amer. Acad., 35, 123 (1899).
6 ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS
truth, the value F must be diminished by 0.05 per cent, and becomes 96,530
coulombs per gram equivalent. This latter value is used in the work
which follows, and all atomic weights also are referred to this standard.
The symbol v represents the valency of the metallic ion in the electrolyte
of the cell. Since thallous sulphate and indium sulphate were used as
electrolytes in the cells of thallium and indium amalgams, it is difficult to
conceive how the valency of the ions of thallium and indium could be
other than I and 3 respectively. The valency of tin will receive especial
consideration when that metal is discussed; in our experiments it was
undoubtedly 2, not 4.
The work of Daniel Berthelot " probably affords the most accurate value
of R, which we may express conveniently in mayers. A mayer is the heat
capacity which is warmed I degree centigrade by I joule. According to
Berthelot's work, the space occupied by a gram-molecule of a perfect gas
at 760 mm. pressure, 45 latitude at the sea-level, may be taken as 22.412
liters (the atomic weight oxygen being 16.000), and the absolute zero at
273.08 C. These values are probably accurate at least to within 0.05
per cent. The value of R on this basis will be
^76.00x13.596x980.6x22,412^ 6
273.08 XIO T
T, by which R is multiplied in the formula, is the temperature of the cell
referred to the hydrogen scale. This was fixed in our experiments by
means of four exactly known thermometers. Over the range of tempera-
ture employed in the following measurements these readings are closely
comparable with the corresponding thermodynamic temperatures. More-
over, the experimental determination of the temperature to within 0.01
would fix the value of -J 1 within one part in 30,000, a degree of accuracy
Jo
far greater than can be attained with the rest of the data used in calculat-
ing the electromotive forces.
It appears, then, that the values of v, R, T, and F are known with
considerable accuracy, and it now remains to consider the concentration
ratio -L. An error of o.i per cent in this ratio would cause an error of
Ct
o.ooooi volt in the electromotive force, and it is clear that the early investi-
gators have not determined this ratio with sufficient accuracy. If a weight
w of amalgam of concentration c is mixed with a weight nw of mercury
to form a new amalgam of concentration c 2 , it is not permissible in accurate
work to write
*"Trav. et Mem. du Bureau internat. des poids et mesures, 13, 113 (1903).
OF THALLIUM, INDIUM, AND TIN 7
as seems to have been the custom of previous workers in this field.
Richards and Forbes have shown the necessity of applying a correction
for the difference in density of the two amalgams being compared. For
example, let w be the weight of an amalgam of concentration c^ diluted
with w He grams mercury to form a new amalgam c 2 . Now, if D^ and D 2
are the densities of the amalgams, we have
Careful determinations were made of the densities of the several amal-
gams at various concentrations; and corresponding corrections were
applied to the calculated values of the concentration ratio. These determi-
nations will be considered later in their proper place. The densities were
all measured at 20 ; their relative values undoubtedly change slightly
with the temperature, but not enough to affect appreciably the calculation
in question.
In calculating the thermochemical results, one 18 calorie was taken as
equal to 4.181 joules.* 1
A number of typical cadmium standard cells, containing crystals of
cadmium sulphate, prepared from different pure materials at different
times, were used as the standard of electromotive force. As these all
agreed within the tenth of a millivolt, their value was taken as
1.0184 0.00004 (t 20) international volts
and this value was used as the standard of electromotive force.**
"Callendar and Barnes, Phil. Trans., A, 199, 149 (1902).
11 See Report of International Conference on Electrical Units and Standards,
1908 published in many places, for example, "Science," 28, 743 (1908).
8 ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS
PREPARATION OF THE AMALGAMS.
The thallous sulphate used in preparing the thallium amalgams was a
sample which had been many times recrystallized, both as acid sulphate
and as sulphate. The original preparation had been of a high grade of
purity. The indium amalgams were prepared from a sample of very pure
indium, which, through the kindness of Professor L. M. Dennis, of Cornell
University, was available for this work. 23 The sample in question had
been carefully purified for use in the determinations of the atomic weight
of indium, although it was not the purest specimen used for this purpose,
and was finally fused in a current of hydrogen. It contained no impurity,
except a trace of iron. Metallic tin was obtained by the electrolysis of an
acid solution of pure stannous chloride, using a pure carbon anode. The
fine needles of tin were washed with distilled water and alcohol and dried
in a desiccator over sulphuric acid.
Pure mercury was obtained as follows: Crude mercury was shaken
first with sulphuric acid to remove the major part of the metallic impuri-
ties and then for some time with dilute nitric acid and mercurous nitrate.
The sample was now wholly free from contamination with the more
electropositive metals. It was then distilled under a pressure of 20 mm.
of hydrogen in an apparatus somewhat similar to that described by
Hulett. 21 The hydrogen was passed through three towers, containing
solid potash, in order to purify and dry it. The entire apparatus, as far
as the connection to the pump, was wholly fused together in order to avoid
rubber connections or glass joints. The pipettes in which the mercury
was kept were themselves used as the receivers of this still, and the
mercury was sealed in them without for an instant coming in contact with
the air. The stopcock, regulating the supply of gas bubbling through the
mercury, was lubricated with sirupy phosphoric acid. The mercury thus
obtained must have been very pure. Distillation in air, recommended by
Hulett, affords an excellent means of oxidizing other metals present; but
our experience leads us to fear that the product contains a trace of
dissolved oxygen. Accordingly, we used hydrogen instead of air.
The water used in making up the solutions was distilled twice, first
from an alkaline permanganate solution, and then from very dilute
sulphuric acid.
Since amalgams of all the metals studied are very susceptible to oxida-
tion, they were made and introduced into the measuring apparatus wholly
out of contact with the atmosphere, and the mercury from which they
were made was never allowed to come into contact with the air after its
distillation in rarified hydrogen.
33 For details of purification of this indium see Jour. Amer. Chem. Soc., 29 (1907).
M Zeit. phys. Chem., 33, 611 (1900).
OF THALLIUM, INDIUM, AND TIN 9
It was found that the thallium amalgams could be most conveniently
prepared by the electrolysis of a solution of thallous sulphate, using a
mercury cathode. Addition of ammonium oxalate prevented the formation
of peroxide on the anode. The complete apparatus used in preparing and
transferring the amalgam is shown in fig. i.
Hydrogen
Pump
Fig. I. Apparatus (or Making and Preserving Amalgams.
The amalgams were prepared by electrolysis in the flask H. Connection
was made to the mercury cathode by means of glass tube passing through
the stopper carrying the wire K. The anode 7 terminated in a spiral of
platinum wire. The anode was inclosed in a small linen bag (not shown
in the figure), in order to prevent any peroxide which might be formed
from falling on the cathode. The amount of thallium deposited was
measured by a silver coulometer included in the circuit. The coulometer
was of the form used by Richards and Heimrod. The porous cup was
cleaned with concentrated nitric acid and then boiled with many portions
of water before use. The anode was a bar of pure silver which had been
prepared for use in an atomic weight research. Care was taken to keep
the level of the liquid within the porous cup lower than that outside in
order to prevent outward filtration. An amperemeter, also in the circuit,
served for an approximate measurement of the current strength.
10 ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS
A weighed amount of pure mercury was run into the flask H, which
was then nearly filled with a saturated solution of thallous sulphate con-
taining about ten grams of ammonium oxalate. The stopper was inserted,
care being taken that the cathode and the tube T leading to the flask C
were immersed in the mercury. The current was now allowed to run
until the desired quantity of thallium had been deposited. The time neces-
sary for this could be calculated approximately from the readings on the
amperemeter. On breaking the circuit, the amalgam was immediately
sucked up into C by cautiously opening the stopcock S 4 . The platinum
crucible containing the deposited silver was washed with water, dried at
200, and weighed. From the weight of the silver deposited, the concen-
tration of the amalgam could be calculated.
The arrangement employed in transferring the amalgams was essentially
similar to that used by Richards and Forbes. Hydrogen, prepared from
pure hydrochloric acid and zinc, and purified by passing through four
towers containing concentrated potassium hydroxide solution and dry
fused potash, was supplied through the tube G. The pipette B communi-
cated through A with either the hydrogen supply or the vacuum-pump.
The outlet tube of B, terminating in a thick capillary, passed through a
tightly fitting rubber stopper into the flask C. (The rubber stopper had
been boiled with alkali, thoroughly washed with water and finally covered
with soft paraffin.) The flask C was supplied with two side necks. The
tube F communicated with the vacuum-pump, while T was bent down
and passed to the bottom of the flask H.
The whole apparatus being thoroughly clean and dry, it was manipu-
lated as follows: First S, 6\, and S 6 were closed and S 2 and S 3 were
opened ; the pressure in B and C was reduced to 1 5 mm. of mercury, and
S t was closed. The manometer, R, proved that the apparatus was free
from leakage. By cautiously opening S 6 the system was now filled with
hydrogen ; and the exhaustion and filling with hydrogen were repeated
three or four times. Care was taken to expel the air in the capillary also
by a stream of hydrogen. In order to force the hydrogen through the
shallow layer of mercury in the bottom of H, the pressure in H was
slightly diminished by suction through S 7 . After the amalgam had been
drawn up into C, a rapid stream of dry hydrogen was bubbled through it
by opening S 6 and S a , at the same time maintaining a low pressure in C.
This served to dry the amalgam and to mix it thoroughly. After 10 or 15
minutes S 2 was closed and the system was allowed to fill with hydrogen.
S l was then opened and B exhausted. By opening S 5 the amalgam could
be drawn up into B. S 5 was finally opened and normal pressure restored
in B, which was then sealed off at A by using a small blast flame. F was
cut with a file and the flask C detached. The capillary tip of the pipette-
OF THALLIUM, INDIUM, AND TIN
II
like tube of B was immediately sealed with wax to protect it from air.
The pipettes were kept in a rack, shown in fig. 2.
Precisely the same mode of procedure was followed in preparing and
protecting the electrolyte used in the cell. The stream of hydrogen was
allowed to bubble through C for some time to remove the last traces of air
from the solution. It was then drawn up into the pipette and sealed off
as before. When the solution was wanted its weight was, of course, not
sufficient to draw it out; accordingly the following method was used to
follow it up with hydrogen : A clean rubber tube, delivering a stream of
pure hydrogen, was slipped over the drawn-out portion, and the tube was
then broken ; in opening the stopcock, the solution readily flowed out.
Fig. 2. Rack with Pipettes containing Amalgams.
The amalgams of indium and tin were prepared in the same apparatus.
It was found more convenient to prepare the latter amalgams by adding
the metals directly to the mercury in the atmosphere of carbon dioxide in
the flask H, for they are far less readily oxidized than the others ; but
afterwards the amalgam was treated just as the others.
12 ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS
DENSITIES OF THE AMALGAMS.
It has been pointed out K that a knowledge of the densities of the various
amalgams is essential in order to fix accurately the value of the concen-
tration-ratio in calculating the theoretical potentials of the cells. More-
over, such data make possible the calculation of the contraction or expan-
sion occurring on the amalgamation of the various metals. For these
reasons numerous determinations were made of the densities of the amal-
gams of thallium, indium, and tin.
The pycnometer used was of the Sprengel type, as modified by Ostwald ;
its capacity was about 3 cc. and its tubes i mm. in diameter. Before use it
was thoroughly cleaned with appropriate reagents, and, after washing with
water, dried by suction. The weight of the pycnometer filled with mercury
at 20 was then carefully determined. Since in filling the pycnometer
with the amalgams, it was sometimes difficult to adjust the contents exactly
to the marks, the weight of a centimeter length of mercury in the capillary
was determined, and a suitable correction was applied. The length of any
excess in the column of amalgam was accurately determined with dividers.
Since the correction was small, never amounting to more than 0.15 gram,
the difference in density between mercury and the amalgam would cause
no appreciable error. All the densities were determined at 20. The
amalgams used in these determinations were prepared in the manner
already described. When all was ready, a sufficient quantity of the
amalgam was run out into a small weighing bottle, filled with carbon
dioxide, and hastily drawn up into the pycnometer. By working in this
fashion, no serious oxidation occurred. The thread of mercury was
adjusted only after the pycnometer had been in a thermostat at 20.0 for
some time.
The data of a typical determination are as follows :
Weight of pycnometer and
mercury 53.228
Weight of pycnometer alone 18.134
Weight of mercury 35.094
Weight of pycnometer and amal-
gam 53-121
Weight of pycnometer alone 18.134
Weight of amalgam 34.987
The density of mercury at 20 is 13.545, therefore the density of the
amalgam is
1^X13.545 = 13.504
This amalgam contained 1.845 P er cent thallium.
Table I contains the results with amalgams of thallium, indium, and tin.
There are given also imaginary values which the densities would have
shown if no contraction or expansion had taken place on amalgamation.
'"Richards and Forbes, Publication of Carnegie Institution of Washington, No.
50, ii (1900). Also, pp. 6 and 7 of the present monograph.
OF THALLIUM, INDIUM, AND TIN
The values of the densities of the pure metals used for this calculation are
given in the first column of the table. The value for the density of pure
indium is the mean of two closely agreeing determinations made by us
with Professor Dennis's pure sample of the metal, because the values
previously obtained, 7.421 by Winkler and 7.12 by Thiel, are in very poor
agreement. Our data are as follows :
First Determination:
Weight of pycnometer : Grams.
With air-free water (20.0 ) 10.1338
Alone 7.0012
With indium alone 10.2568
With indium and water 12.9420
Result : Density 7.277
Second Determination:
Weight of pycnometer :
With indium alone 10.0045
With indium and water 12.7525
Result : Density 7.291
The mean value is 7.284.
indium is found to be 7.277.
Corrected to vacuum the true density of
TABLE i. Densities of Amalgams.
Metal.
Per cent of
solid metal
in amalgam.
Correct
weight of
liquid needed
to fill pyc-
nometer.
Actual
density of
liquid.
Calculated
imaginary
density of
amalgam.
Thallium (density 11 .85)
1.854
34.987
I3.504
13.509
I.4IO
35-017
I3.5I5
13.520
0-793
35-049
13.527
13-530
Indium (density 7 28)
I 020
Q
^3-334
13 .324
i yOT*
1.430
1.090
34.703
34.784
13-394
13.426
13.380
13.419
0.928
34.835
13.446
13-439
0.770
0.468
34-867
34-949
13-457
13.489
13-455
I3.490
Tin (density 7 29)
O.45
35.012
13.513
I3.493
0.30
35-027
13.519
13.510
0.21
35-053
13.529
13.519
Mercury, pure (density 13.545)
35-095
13-545
13-545
The density curves for the thallium, indium, and tin amalgams are
shown in fig. 3. The dotted lines give the imaginary values that would
be obtained if neither expansion nor contraction took place on mixing.
Indium and tin contract on amalgamation, while in the case of thallium
there is a slight expansion.
ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS
1334
036
13.38
13.40
13.42
13.44
13.46
13.48
13.54
'>
/'/
/
/
//
/
//
/
//
7
In
/ /
?
'*/
?_
/
/
6
^Sn
^~~
Tl_
^ -
-0-^
/
7
- "^"-^
^-***
0.2 0.4 as 0.8 1.0 1.2 1.4 1.6
Fig. 3. Densities of Thallium, Indium, and Tin Amalgams.
Densities are plotted as ordinates, per cents by weight of solute in amalgam as ab-
scissae. The continuous lines represent actual densities, the dotted lines
the averaged densities of the components, that is, the density which the
amalgam would have possessed if there had been no change of volume on
mixing. The dotted line for tin coincides essentially with that for indium.
OF THALLIUM, INDIUM, AND TIN 15
THE CELL.
The multiple cell used in all the measurements of electromotive force is
shown in fig. 4. This apparatus, devised by Richards and Forbes, must be
very carefully annealed, for even at the best the glass receptacle is very
fragile. The body of the vessel is used to hold the electrolyte ; the four
cups contain the amalgams to be measured. The advantage of the four
cups is obvious : six different measurements may be made at one filling,
and at the same time important checks can be secured on the accuracy of
the readings.
Fig. 4. Amalgams in Cell ready for Potential Measurement.
The glass receptacle was carefully cleaned and dried, and fused at A to
the delivery tube of an apparatus supplying pure hydrogen. A vacuum
pump was now attached at S z and the whole cell exhausted as far back as
the stopcock S^ The tops of the tubes, B, C, D, and E were closed with
small pieces of rubber tubing and glass rod. When the pressure had been
reduced to about 20 mm., the stopcock S 2 was closed and the cell allowed
to fill with hydrogen through 3\. This was repeated four times. The
glass rod was now removed from one of the tubes and the fine tip of a
pipette, containing the proposed electrolyte, inserted. The issuing stream
of hydrogen prevented the diffusion of air into the cell. When the vessel
was about half full of the aqueous solution, the pipette was withdrawn and
the stopper was replaced. In the same manner suitable amounts of the
l"6 ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS
various amalgams and mercury were introduced into the four cups.
Finally, the electrodes, sealed into narrow glass tubes, were introduced
care being taken that the platinum points did not touch the glass. S^ was
now closed, the coil broken off from the hydrogen supply, and the vacuum
connection removed from S 2 . After gentle shaking for several minutes,
the completed cell was transferred to the thermostat, and the measure-
ments soon begun.
Amalgams prepared thus remained bright as long as was necessary and
showed no signs of oxidation. It is evident that Hulett and De Lury did
not fully read the somewhat similar description by Richards and Forbes,
or they would not have suggested that the method contained faults which
existed only in the preliminary work, not in the procedure finally adopted. 24
The manner of adjusting the wires connecting the potentiometer to the
cell should be mentioned. In the first trials long platinum wires dipping
in the various amalgams were connected with the copper wires by means
of mercury cups. The junctions of unlike metals were thus outside
of the thermostat an objectionable feature. Accordingly, in the final
measurements only a short length of platinum wire was fused in the
bottom of each tube dipping into the cell, and above this was placed, inside
the tube, a drop of mercury. The copper wires were now pushed down the
narrow tubes until connection was made with this drop. The contact of
unlike metals was now deep in the cell and, being at constant temperature,
could cause no disturbance.
Most of the potentials were measured at 30 and o, and many of the
thallium cells were also measured at 15. The temperature of the 30
bath was kept constant by means of a sensitive electrical regulator. A
large heating coil was used in place of an incandescent lamp as the source
of heat, since it avoids any disturbing effect due to radiant energy when
the heater is in frequent operation. The temperature of this bath was
always constant within 0.01. The 15 bath was exactly similar except
that it was equipped with a cold-water coil in order to compensate for the
higher temperatures of the surroundings. For the zero bath a metal
trough was filled with clean, finely crushed ice, covered with distilled
water. This trough was placed in a larger one, the space between being
filled with ice, and the box in turn was tightly packed in sawdust. This
arrangement gave a very constant temperature. The temperatures of all
the thermostats were determined with small Beckmann thermometers,
capable of being read to within 0.005 ; they were standardized by com-
parison with a very accurate Reichsanstalt thermometer, taking all the
precautions necessary for ascertaining the temperature to within o.oi.
M Compare Hulett and De Lury, Journ. Am. Chem. Soc., 30, 1809 (1908) with
Richards and Forbes, Publication of Carnegie Institution of Washington, No. 56,
page 40 (1906).
OF THALLIUM, INDIUM, AND TIN 17
THE POTENTIOMETER.
Considerable time was spent in the elaboration of a suitable potentiom-
eter for use in this work. The arrangement used by Richards and
Forbes, while probably accurate to 0.000005 of a volt, was complicated
and involved troublesome calibrations. Moreover, it seemed desirable to
dispense with the one-volt element and compare the drop of potential
directly with a standard Weston cell. The arrangement finally adopted is
shown in fig. 5. It was elaborated with the help of R. N. Garrod-Thomas,
and was used also for his work, to be described later.
E
o -
o
o
o
A o
o
o
o
o
o
T
T
x
Fig. 5. The Potentiometer.
A large Daniel cell F was used as the source of the fall of potential.
When in use, it was found best to keep it short-circuited through a resist-
ance of about 300 ohms in the box E. The rough box D was so adjusted
that the fall of potential between the points U and V was equal to 1.0184
volts, as measured against the normal cell H. C was a constant resistance
of 9000 ohms. A and B were resistance boxes of mi ohms each, and
MN was a manganin wire of 1.063 ohms resistance. At the commence-
l8 ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS
ment of a measurement, the plugs were all placed in the box A and all
removed from B. The resistance between U and V under these conditions
was 10,112.06 ohms, embracing a drop of potential of 1.0184 volts, as
given above. By removing plugs from A to the corresponding place in B,
in order to keep the drop of potential constant, and manipulating the slider
X, it was easy to compensate the potential of the unknown cell by opposing
potential tapped from the box A and the slide-wire bridge, since the poten-
tials measured never amounted to as much as o.i volt.
Suppose the total reading of the box A and the slide wire to be a ohms.
Then the potential of the cell measured would be -p X 1.0184 volts.
10,112.06
The factor *' I ^ being a constant value, its logarithm was found once
for all, and entered into all calculations.
In following this mode of procedure, the only portion of the resistance
which needs very accurate calibration is the box A. The wire MN was
65 cm. in length, and was divided by a scale into divisions 6.10 mm. long,
each of these corresponding to the millionth of a volt. Since the total fall
of potential in the wire was only about o.oooi volt and preliminary calibra-
tion showed it to be very uniform in resistance, no correction was deemed
necessary for the readings of this scale under the wire. PQ was a three-
way switch. When thrown towards P, the standard cell H was balanced
against the fall of potential between U and V. When thrown toward Q,
the potential was ready to be balanced against a portion of the bridge M N
and box A. The galvanometer G of the d'Arsonval variety was manu-
factured by the Leeds and Northrup Company, of Philadelphia, and is
designated by them as Type H. It was read with a telescope and scale
at a distance of 60 cm. .S was a double-rocker switch, the base of which
was a thick plate of ebonite. It was so arranged that the galvanometer
was either in the circuit or short-circuited itself. The galvanometer was
extremely sensitive, and when short-circuited it returned to zero without
any oscillations whatever. The whole potentiometer with the exception
of the galvanometer was placed inside of a large glass case with a swing-
ing door in order to avoid disturbing effects from changes of temperature
and impurities in the atmosphere.
The apparatus, as described above, was used in the measurements on
thallium amalgam cells and was easily accurate to within three or four
millionths of a volt. Since thallium under the conditions of the measure-
ments was univalent, and consequently gave comparatively large poten-
tials, the above accuracy was fully sufficient ; but in the case of trivalent
indium, which for equal concentrations gives potentials only one-third as
large as those of a univalent metal, even greater accuracy was desirable.
OF THALLIUM, INDIUM, AND TIN 19
As has been previously mentioned, the portion of the bridge wire MN
corresponding to one ohm was divided into 100 parts, giving direct read-
ings to o.oooooi volt for each 6 mm. of wire. The graduation of the
instrument was therefore adequate ; improvement was to be attained only
by eliminating all irregularities ; and prominent among these, as every one
knows, are thermoelectric effects due to junctions of dissimilar metals.
Two ways of suppressing thermoelectric effects are available: one, to
use only one metal ; the other, to keep the temperature the same through-
out. The latter method was in the present case the more convenient. It
was at first found that the temperature at the two ends of the glass case
containing the potentiometer differed by as much as 0.5. Part of this
difference was traced to the proximity of an incandescent light, which
was removed ; but there still remained a considerable variation. This was
finally overcome by the use of a small revolving fan which was attached
to an axle run through one of the corners of the case and driven at high
speed by a motor. Thus the air was stirred and kept at the same tempera-
ture throughout. Contact of the operator's hand with the bridge slide
was obviated by the use of two cords attached to opposite sides of X and
passed through small holes in the ends of the case ; and the final adjust-
ment was made on the bridge with the case closed. In this way another
frequent source of irregularity was avoided and the readings were im~
proved. The room in which all the apparatus was placed was kept as
constant in temperature as possible.
In seeking for the causes of the yet remaining fluctuations, it was found
that the galvanometer was influenced by the proximity of the observer,
and even more so by heat-effects due to the operation of the rocker switch
S with the hand. Therefore, the galvanometer was removed some dis-
tance from the apparatus and screwed against a very firm wall, the con-
nections being made by insulated copper wires incased in glass tubes. The
case of the galvanometer was packed in felt and covered with a sheath
of copper, a small hole permitting a view of the mirror ; and the instru-
ment was read by a telescope and scale placed at a distance of about
130 cm. The rocker switch 5" was placed inside the case and operated
from outside by means of a long cord, the observer being seated at the
telescope some distance away.
The resistance box A was standardized by substitution. A sensitive
Wheatstone bridge was used and the corrections on the various resistances
were determined and tabulated exactly as if they were weights.* 7
Only two of the corrections thus found were as much as o.oi ohm, and
since each o.oi ohm corresponds to very nearly o.oooooi volt, it is easily
seen that all others were negligible. The two in error were the 300 and
"Richards, Proc. Am. Chem. Soc., 22, 144 (1900).
20 ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS
400 ohm coils ; and the deviation of these amounted to only 0.000002 and
o.oooooi volt respectively. The boxes B and C were of the same quality
as A and a preliminary standardization showed them to be fully as accu-
rate. Since the resistances in B and C need be known only one-tenth as
accurately as those in A, any corrections on these boxes would be super-
erogatory. The one important point, that 1000 ohms in A should be
exactly one-ninth of the 9000 ohms in B, within o.oi per cent, was demon-
strated.
The standard Weston cells were made up from pure material as recom-
mended by Hulett. These cells were compared with one another and also
with three similar cells kindly loaned by Dr. H. L. Frevert. They all
furnished the same value to within o.oooi volt at 20, and for their value
the electromotive force 1.0184 was accordingly assumed.
The improved potentiometer described above appeared to be accurate to
within a microvolt (o.oooooi volt) a high degree of precision.
ELECTROMOTIVE FORCE BETWEEN THALLIUM AMALGAMS.
With the apparatus and materials which have been described, measure-
ments upon a variety of amalgams were executed. The description of a
preliminary experiment will be given in detail, in order that the method
may be more thoroughly understood. Amalgam I was prepared in the
closed apparatus by depositing into 180.557 grams of mercury the amount
of thallium equivalent to 0.9473 grams of silver (deposited in a coulometer
in the same circuit), that is to say, 1.7915 grams of thallium, if silver and
thallium are assumed to have the atomic weights of 107.88 and 204.03
respectively. Hence the amalgam contained 0.9822 per cent of thallium
by weight.
One portion of this amalgam was introduced into one cup of the multiple
cell, and another weighed portion was introduced out of contact with air
into another cup, being diluted by the addition of a weighed amount of the
pure mercury, which had been preserved in hydrogen as previously
described. The second cup contained 36.513 grams of mercury, and
received 25.721 grams of amalgam. It is easy to calculate that the dilute
amalgam must have contained 0.4059 per cent of thallium. In order to
mix thoroughly the amalgams and mercury in the second cup, the cell was
gently shaken for some time, great care being taken to avoid any splashing
from one cup to another. The cell was then introduced into the 30 ther-
mostat and, after it had acquired the temperature of the bath the readings
were begun. Two measurements of the cell gave values of 25.235 and
25.238 millivolts respectively, in mean 25.237.
The potential remained very constant over a considerable interval of
time. Two entirely separate measurements taken with the same cell 48
OF THALLIUM, INDIUM, AND TIN 21
hours later gave the values 25.231 and 25.243, in mean 25.237, exactly the
same as before. In subsequent work the agreements were of this order
of accuracy ; usually average values alone will be given.
It is worthy of remark in this connection that the electrolyte was not
found to be the least alkaline to phenolphthalein after thus standing for
48 hours over a thallium amalgam. This fact is very satisfactory, not only
with regard to thallium, but also in its implication concerning the probable
integrity of amalgams of less easily oxidized metals, whose oxides are less
easily detected.
It is interesting to compare the result with the ideal value calculated
from the gas law. The theoretical potential, calculated according to the
formula
T -8-3i6x (273-09 ) x 2.3026 .q,
96,530 * Cn
is 23.064 millivolts. This is 2.183 millivolts, or nearly 10 per cent, less
than the observed value 25.237.
Having thus cleared the way by this preliminary work, four series of
more accurate measurements were made. Four multiple cells containing
thallium amalgam, designated A, B, C, and D, were prepared. In each
case an amalgam prepared electrolytically was placed in cup I ; and cups
2, 3, and 4 were filled with the same amalgam diluted (in an atmosphere of
hydrogen) with weighed amounts of mercury.
The " parent amalgam " in cups Ai and Bi was made by depositing in
197.33 g r a m s of mercury the amount of thallium equivalent to 0.4290 gram
of silver. This amalgam was diluted as follows :
grams of amalgam. grams of mercury.
13.272 + 82.933 in A2
15.679 4L938 A3
23.710 32.791 62
6.838 97-483 63
11.736 83.642 64
The " parent amalgam " in cup Ci was made by depositing in 168.361
grams of mercury the amount of thallium equivalent to 1.6738 grams of
silver. This amalgam was diluted as follows :
grams of amalgam. grams of mercury.
12.487 +31.420 in 2
10.710 75-495 C3
10.448 112.095 C4
Finally the " parent amalgam " in cup Di was made by depositing in
213.65 grams of mercury the amount of thallium equivalent to 0.2289
grams of silver. This amalgam was diluted as follows :
grams of amalgam. grams of mercury.
14.967 +29.589 inD2
8.851 75453 D3
9.461 122.984 D4
22
ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS
The electrical measurements made with these amalgams are summarized
in table 2, together with the theoretical values calculated upon the assump-
tion that the gas law applies with exactness, according to the concen-
tration equation:
RT . c m
TABLE 2. Electrical Measurements of Thallium Amalgams.
Designation
of cup
containing
amalgam.
Approxi-
mate
per cent of
thallium in
amalgams.
Exact
value of
'_:
Electromotive force between each pair of cups, in millivolts.
0C.
15C.
30C.
Observed.
Theo-
retical.
Observed.
Theo-
retical.
Observed.
Theo-
retical.
Ai
0.410 ,
O.III |
0.0565*
0.410 ,
0.172 1
0.05I2J
0.0269
1.8456-,
0.5249!
0.2294 j
0.1575^
0.220 -j
0.074 1
0.0231 |
0.0157^
0.56502
0.29408
0.37694
0.53272
0.27338
0.54518
0.35943
0.16340
0.47203
0.50556
0.16729
3L543
16.360
30.608
15-080
33.166
17.238
32.290
16.858
34.810
18.110
23-523
32.408
16.531
37.134
22.610
10.090
28.064
30.592
10.114
33-971
17-735
22.664
32.026
16.436
32.775
21.610
9.824
28.379
30.455
10.058
A2
A3
Bi
B2
83
B 4
Ci
C2
C 3
C 4
Di
D2
D 3
D 4
33.897
20.485
9.II8
29.533
19.471
8.852
35-5"
21.530
9.601
31.155
20.541
9.338
The measurements with cell B at the lower temperatures were unsatisfactory,
and were rejected; cell D was measured only at 30.
Each observed figure is the mean of at least three measurements. For
example, the Di-D2 was found to have a potential of 28.969 millivolts
by direct measurement. Di-D3 was found to be 59.551, and D2-D3,
30.596. Subtracting, we find again D 1-02 = 28.95 5. ^ n the same way,
by subtracting the observed value for D2-D4 from that for Di-D4, the
value 28.969 is found. The mean value 28.964 is given ; the same practice
was adopted in all cases.
OF THALLIUM, INDIUM, AND TIN 23
The difference between the observed and the ideal values is usually
great; in the case of the concentrated cell, Ci-C2, it amounts to 13 per
cent. Further study of the figures shows that as the dilution is increased,
this difference between the observed and calculated potentials diminishes,
becoming only about 0.6 per cent in the case of the very dilute cell D3-D4.
Deviations from the theoretical are always positive ; the cell always gives
a potential higher than the value computed simply from its concentrations.
Cells of thallium amalgams thus appear to behave in a fashion similar to
those of cadmium with increasing dilution, although in the case of the
thallium cells the deviations are larger. Zinc varies in the opposite
direction.
The results of these measurements and calculations are plotted graphi-
cally below according to the method employed by Richards and Forbes,
which affords a convenient method of noting the departure of the cells
from the gas law. In fig. 6 there are plotted as abscissae the logarithms of
the volumes occupied by a given weight of amalgamated thallium, taking
the volume of the most concentrated amalgam in cup Ci as unity. The
progress of the curve in the direction of ordinates between the points
corresponding to any two volumes indicates the extent of the deviation
from the theory of the electromotive force of the cell made from the two
indicated amalgams. The curve is built up by plotting first the results
with cell C, then those with cells A and B, and finally those with cell D.
In each case as the drawing progressed the " parent amalgam " was
started at its proper concentration on the curve already drawn ; and this
proceeding of necessity fixed the other points obtained from that particular
cell. If into each cell a two-phase amalgam, having a constant potential,
had been introduced, according to the excellent suggestion of Hulett and
De Lury, the construction of this curve would have been somewhat facili-
tated ; but the final result would have been identical. In this case greater
care about perfect constancy of temperature would have been necessary.
The regularity of the curve affords strong evidence of the accuracy of the
measurements.
The curve for the thallium amalgams, like those for both zinc and
cadmium, shows that as dilution is increased the potential of any cell
approaches nearer and nearer to the requirement of the simple concentra-
tion law ; that is to say, the slant of the curve becomes less and less. Com-
plete horizon tality would indicate complete fulfilment of the gas law. The
regular form of the curve indicates the absence of oxidation in the more
dilute amalgams, one of the most insidious sources of error in this sort of
work. Thallium amalgams are extremely sensitive to oxidation and its
elimination in these measurements is a source of gratification.
The results depicted by this curve will be discussed later in connection
with the results for the other metals.
24 ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS
+ 7
+ 1
Iog4 Iog8 log 16 log3Z Iog64 log 128 log 256
Fig. 6. The Deviations of the Electromotive Force of Thallium Amalgams.
Deviations from the expression = ^F '* 7 are P lotted in millivolts as ordinates,
the logarithms of the concentration ratios as abscissae. The most concen-
trated amalgam contained 1.85 per cent by weight of thallium and 98.15
per cent by weight of mercury. A horizontal line on the diagram would
indicate complete fulfilment of the concentration law. This curve is almost
if not quite independent of temperature, at least between o* and 30.
OF THALLIUM, INDIUM, AND TIN
ELECTROMOTIVE FORCE BETWEEN INDIUM AMALGAMS.
Amalgams of indium were now studied in the same manner. They had
been prepared in the fashion described on page 9, and all the dilutions
were made inside the cell in an atmosphere of hydrogen with the same
precautions as in the case of thallium. Density corrections were applied
in the calculation of the concentration ratio.
Three parent amalgams, Ei, Fi, and Gi, were prepared. The first, El,
contained 3.0014 grams of indium dissolved in 152.783 grams of mercury;
the second, Fi, 23.276 grams of this amalgam with 116.472 grams more of
mercury, and the third, Gi, contained 40.812 grams of Fi with 72.926
grams more of mercury.
These " parent " amalgams were diluted as follows :
grams of
amalgam.
10.368 Ei
9-732 El
8.074 El
11.727 Fi
grams of
mercury.
+ 41.883
+ 68.490
+ 123.133
+ 36.564
in E2
E3
4
F2
grams of
amalgam.
8.498 Fi
8-543 Fi
8.177 Gi
9.328 Gi
grams of
mercury.
+ 71.897
-j- Il8.68o
+ 58.144
+ 102.808
in Fj
F 4
G2
G3
The measurements of electromotive force, and the theoretical values
calculated from the concentration law, are given in table 3.
TABLE 3. Electrical Measurements of Indium Amalgams.
Electromotive force between each pair of cups, in millivolts.
Designation
of cup
containing
amalgam.
percent of
indium in
amalgams.
Exact
value of
* Z
0C.
30C.
Observed.
Theo-
retical.
Differ-
ence.
Observed.
Theo-
retical.
Differ-
cnce.
El
1.92 i
0.69705
14-455
12.587
1.868
15.786
13.967
I.8I9
E2
0.384
0.20III
3.823
3.631
0.192
4-23I
4.030
0.201
E3
0.242
0.30466
5.692
5-501
O.I9I
6.287
6.106
O.lSl
E 4
0.120
Fi
0.319
0.6l38l
H.387
II.083
0.304
12.616
12.301
0.315
F2
0.078
0.36079
6.588
6.515
0.073
7-3II
7.231
0.080
F3
0.034
0.19750
3.666?
3.566
O.IOO?
3-989
3.958
0.031
F4
0.021
Gi
0.016 )
0.31887
5-775
5-758
0.017
6.411
6.390
0.021
G2
0.008
O.I094I
3-035
3-003
0.032
3-430
3-390
0.040
G 3
0.00 '
26
ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS
Comparison of the observed and calculated potentials of the indium
amalgam cells shows the behavior of these cells to be similar to those of
thallium, but in a less degree. The cells with concentrated amalgams show
considerable deviation from the theoretical value, not so much, however,
as with thallium amalgams of the same concentration. On the other hand,
at great dilutions the agreement between the observed and calculated
values is exceedingly close. The cell Gi-G2 differs by only 0.000019 volt
or 0.3 per cent from the theoretical potential.
The significance of the results of these measurements can best be illus-
trated by the same sort of curve as was employed in the case of thallium
amalgams. The curve for indium amalgams is shown in fig. 7. As before,
the common logarithms of the concentration ratios are plotted as abscissae
and the value of the deviations from the simple concentration law as
ordinates. The sign of curvature is the same as with thallium, since both
deviate in the same direction from theory.
The significance of this curve also will be discussed later.
+ 3
-H
logZ Iog4 Iog8 log 16 Iog33 Iog64 logIZS Iog256
Fig. 7. The Deviation* of the Electromotive Force of Indium Amalgam*.
Deviations from the expression
are plotted in millivolts as ordinates.
the logarithms of the concentration ratios as abscissae. The most concen-
trated amalgam contained 1.92 per cent by weight of indium and 98.08
per cent by weight of mercury. A horizontal line on the diagram would
indicate complete fulfilment of the concentration law. This curve is almost
if not quite independent of temperature, at least between o* and 30.
OF THALLIUM, INDIUM, AND TIN
ELECTROMOTIVE FORCE BETWEEN TIN AMALGAMS.
The tin amalgams were prepared in a manner similar to that employed
with indium. The electrolyte used in the cells was a solution of stannous
chloride, about half normal. Before use it was allowed to stand over pure
tin and was then preserved under hydrogen. Great care was taken to
insure the absence of stannic compounds.
Since concentrated tin amalgams deposit a solid phase on cooling to o,
the first series of measurements were performed by the dilution of an
amalgam containing 0.66 per cent by weight of tin less than half of the
higher concentration used by Cady. As even this was found to separate
a solid at o, another series was made beginning with an amalgam con-
taining only 0.21 per cent of tin.
The data concerning the preparation and dilution of these amalgams
were as follows: 1.0766 grams of metallic tin were dissolved in 161.161
grams of mercury to make amalgam Hi. This was diluted as follows :
grams of amalgam.
17-351
I3-279
10.391
grams of mercury.
+ 39-593
+ 99.824
+ I47-265
in H2
H3
H 4
The more diluted series was made from a " parent " amalgam obtained
by dissolving 0.3116 grams of tin in 149.021 grams of mercury. From
this were prepared:
grams of amalgam.
18-537
16.436
9.919
grams of mercury.
+ 44.845
+ II3-3I2
+ 117-947
in J2
TABLE 4. Electrical Measurement of Tin Amalgams.
Electromotive force between each pair of cups, in millivolts.
tion of
cup con-
mate
per cent of
Exact
value of
1 Cm
0C.
30C.
taining
amalgam.
amalgams.
l0g c.
Observed.
Theo-
retical.
Difference.
Observed.
Theo-
retical.
Difference.
Hi....
0.66
0.51495
7.632
13-949
-6.317
I3.I82
15.480
-2.208
H2....
0.20
0.41401
I0.6I4
11.213
-0.599
11.820
12.447
-0.627
H 3 ....
0.077
Ji
0.210 i
0.53655
I3.6l2
I4.532
0.920
15.156
16.128
-0.972
J2
0.061
0.36025
9.548
9.758
-0.210
10.622
10.829
-0.207
J3
0.027
0.21345
5.715
5.781
-0.066
6.371
6.416
-0.045
J4
0.016
ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS
Examination of these results shows that the observed potentials of the
amalgam cells of tin, like those of all the other metals thus far studied,
approach the theoretical requirements more and more closely as the dilu-
tion is increased. The results are depicted graphically by the curve in
fig. 8. It should be noted that the sign of curvature is exactly the reverse
of that of the otherwise similar curves obtained with cadmium, thallium,
and indium amalgams, since tin amalgams deviate in the opposite direction
from theory. In this respect tin is similar to zinc.
-2
-3
log a Io44 logS log 16 log3Z log 64
Fig. 8. The Deviations of the Electromotive Force of Tin Amalgams.
Deviations from the expression IT = ^^ / c - are plotted in millivolts as
ar c-2
ordinates, the logarithms of the concentration ratios as abscissae.
The most concentrated amalgam contained 0.66 per cent by weight
of tin and 99.34 per cent by weight of mercury. A horizontal
line on the diagram would indicate complete fulfilment of the
concentration law. This curve is for 30. The most concentrated
amalgam separates solid at o.
In the case of the tin amalgam cells complete exclusion of oxygen is
necessary, not only on account of the amalgams, but also in order to
insure the stability of the electrolyte, since stannous chloride when exposed
to the air quickly becomes basic according to the equation :
3$>nC\ 2 + y 2 O 2 + H 2 O=2SnClOH + SnCl 4
When the solution is in contact with tin amalgam in the air this reaction
proceeds very rapidly, perhaps because the stannic chloride is reduced by
the amalgam. The formation of stannic chloride would be expected to
lower the potential, and the constancy observed in the values of the various
cells proves the complete elimination of any such disturbing effect.
OF THALLIUM, INDIUM, AND TIN 2Q
With the idea of testing the effect of stannic chloride, but without much
hope of obtaining results fully corresponding to a quadrivalent ion, a
further attempt was made to measure a tin amalgam concentration cell,
using an electrolyte containing at first pure stannic chloride. Pure tin was
dissolved in aqua regia and the nitric acid was removed by boiling
repeatedly with fresh portions of hydrochloric acid. The solution was then
diluted with water, most of the free acid was neutralized with sodium
hydroxide, and the solution containing all its tin in the state of highest
oxidation was placed in the cell.
No constant readings could be obtained with any of the tin amalgams
under these conditions. Evidence was obtained, however, that this electro-
lyte tended to give lower potentials than those obtained with stannous
chloride. For example, with a cell whose calculated potential would be
0.01605, if the tin were quadrivalent, and 0.0321, if bivalent, a value of
0.0262 was obtained. Clearly, as we had expected, ionized quadrivalent
tin is not in a state of electrochemical equilibrium with tin amalgam.
Cady 28 supposed that he attained this equilibrium by using potassium
stannate as an electrolyte, but in our opinion it is extremely doubtful if in
a solution of a stannate, the quadrivalent tin ion is in reversible equilibrium
with a tin amalgam. Our practical experience confirms this conclusion.
We attempted to measure a cell with a solution of sodium stannate as its
electrolyte, but were unable to obtain anything approaching constant
potentials.
We regret to state that another fact also points to the conclusion that
Cady's work with tin was questionable. Roozeboom and van Heteren
have shown that at 25 tin amalgams containing from 1.2 to 99 "atom
per cent " of tin give the same potential, there being present two phases
of invariable composition a liquid phase containing 1.2 "atom per cent"
tin and a solid phase of 99 per cent tin. But Cady supposed he had made
a tin amalgam of 1.73 per cent by weight or nearly 3 atom per cent, when
he used potassium stannate as electrolyte in the attempt to obtain the
potential of a cell in which tin behaved as quadrivalent. He calculated
the concentration ratio on the basis of his supposed percentage." In
the light of the work of Roozeboom and Van Heteren this work is evidently
faulty, since the strongest liquid amalgam in the cell could not have
exceeded 0.8 per cent by weight of tin, and the more dilute amalgam
might have been affected by crystals of tin dissolved on dilution. Clearly
Cady's work on tin is without significance.
"Jour. Phys. Chem., 2, 551 (1898). Attention should be called to another serious
error in Cady's paper, of which due acknowledgment was made. (Ibid., 3, 107
[1899]). All this work of Cady's was done under the direction of W. D. Bancroft.
" Professor Cady has kindly looked up his data in his original note-books, and
finds that the mistake was not an error of proof-reading, but arose from lack of
knowledge of the solubility of tin in mercury.
30 ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS
THE TEMPERATURE COEFFICIENT OF THE AMALGAM CELLS.
Since all the potentials have been measured at two or three tempera
tures, interest next centers in the computation of the temperature coeffi-
cients of the various cells. The temperature coefficient ^ over a finite
range of temperature is conveniently divided by the potential at o, in
order to compare the values obtained from the various amalgams with the
same range.
The values of the quantity thus obtained,^,, for the thallium, indium,
and tin amalgams are given in the following table as calculated from the
electromotive forces already recorded. The change of electromotive force
between o and 15 was almost always essentially identical with that
between 15 and 30. On account of the comparatively small change of
electromotive force, 15 is rather a small range for this purpose ; therefore
the whole range of 30 is given below as the basis for computing the
temperature coefficient.
The values given in table 5 are arranged in the order of the concen-
tration of the most concentrated amalgam in each cell. Thus the effect of
concentration upon the temperature coefficient is to be ascertained at a
glance.
TABLE 5. Temperature Coefficients of Electromotive Force.
Thallium amalgams.
Indium amalgams.
Tin amalgams.
Per cent
Per cent
Per cent
of
of
of
thallium
ATT
indium in
ATT
tin in
ATT
Designa-
of most
Designa-
the more
Designa-
the more
tion of
concen-
^"0^ T
tion of
concen-
TnA T
tion of
concen-
Tfp&T
cell.
trated
cell.
trated
cell.
trated
amalgam
0to30C.
amalgam
0to30C.
amalgam
0to30C.
in each
in each
in each
cell.
cell.
cell.
CI-C2
C2-C 3
I.8 S
0.52
0.00319
0.00350
EI-E2
E2-E 4 *
1.92
0.38
0.00309
0.00350
JI-J2
H 2 -H 3
0.21
0.20
0.00378
0.00380
Ai-A2
0.41
0.00346
Fi-F2
0.32
0.00360
J2-J4
0.06
0.00378
C3-C 4
0.23
0.00355
F2-F4*
0.08
0.00354
A2-A3
O.II
0.00357
Gi-G2
0.015
0.00364
* The cells E2-E3 and F2-F3 had such small electromotive forces that the accu-
rate measurement of the temperature coefficients was beyond the range of the
apparatus. Therefore those cells were combined with cells E3-E4 and F3-F4 re-
spectively, for the present purpose. It should be pointed out that the error involved
in calculating the temperature of the indium cells is rather large, since the poten-
tials are small, the metal being trivalent.
Although these results are not perfectly regular, and show evidence of
experimental imperfection, their general tendency is clear.
OF THALLIUM, INDIUM, AND TIN 3!
The temperature coefficients of the thallium and indium amalgams
exhibit very similar behavior. The concentrated amalgams give a value
much lower than 0.00366 (the coefficient of expansion of the unit volume
of perfect gas), but as the dilution is increased, the coefficient approaches
nearer and nearer to the ideal value. The most dilute indium cell measured
gave a value 0.00364, very nearly the theoretical coefficient. This same
cell gave a potential only 0.4 per cent different from that demanded by
the formula of von Turin; thus, as the electromotive force approaches
the requirement of the gas law, the temperature coefficient does likewise.
APPLICATION OF THE EQUATION OF CADY.
The equation of Cady claims that the deviations from the simple equa-
tion of von Turin are due to the heat of dilution of the amalgams.* On
comparing this equation
with the equation of Helmholtz
it is apparent that if the former really held true, the last terms of the
equations would be identical. This was pointed out by Cady.
Placing the second members equal to one another and dividing through
by T we obtain the expression
R . C m d-rr , ^
VF ln 7n=dT U)
That is to say, the temperature coefficient should depend upon the relation
of the concentrations, not upon the electromotive force which they hap-
pen to exert.
This consequence is readily tested by the data in hand. Take for
example the cell Ci-C2. Here =3.516, and its natural logarithm is
1.2574. Hence the first member of the above equation (4) becomes
8.316X1.2574 =0.0001082
1X96,530
and the second member becomes
0.037I34-0-033887 = o .oooio8i
30.0
The agreement is so striking that other cases should be studied.
*Journ. phys. Chem., 2, 551 (1898).
32 ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS
Take for example 62-63. Here =3.4104, and its natural logarithm
is 1.2268. Hence the first member of the equation becomes
8,316x1^268 =aooo
1x96,530
and the second member becomes
0.032408-0029303 =0.000^35
30.0
Here the agreement is not so good ; but, on the other hand, it might be
worse. Another thallium amalgam cell, Ai-A3, taken at random, shows
essentially the same relation, the terms being as follows :
8.316x1.9808 =0iOOOI700 52.920-47.903 =0.0001670
96,530 30.0
In the case of indium, a somewhat less percentage accuracy in fulfilling
the requirements of the Cady equation is shown. For the cell Ei-E2 the
terms are these:
8.316x1.6082 ^ Q 6l 15.786-14.455 = 0.0000444
3 x 96,530 30.0
With tin, about the same order of agreement is to be found. For
example, in the cell, Ji-j2, the first member of equation (4) becomes
and the second member becomes
a difference of about 3 per cent, or about like that found in the case of
indium.
One conclusion drawn from these partial agreements is the same as
that drawn from the case of cadmium studied by Richards and Forbes,
namely, that the equation of Cady does not contain an exact representation
of all the influences producing electromotive force. On the other hand,
the new results strongly reinforce the hope expressed in the earlier paper
that this equation, although not wholly exact, is really a step in the right
direction. For it is inconceivable that all these cells, possessing very
different temperature coefficients, one as much as 13 per cent different
from the requirement of the gas law, should all come within 3 per cent
of the fulfilment of equation (4), if the equation were without meaning.
Expressed in other words, the meaning of the results and mathematical
considerations just detailed may be stated as follows : The reason for the
deviation of the actual electromotive forces of amalgam cells from the
values calculated from the concentrations is found to be primarily in the
free energy of the change of chemical affinity involved in the dilution of
OF THALLIUM, INDIUM, AND TIN 33
the amalgams. The electromotive force may be looked upon as being due
to at least two entirely different phenomena superposed : one, the " chemi-
cal free energy," which manifests itself as heat on dilution, and the other
the " osmotic energy," due to the difference of concentration of the two
different amalgams. In these cells all the free energy of the essentially
chemical part of the change may be supposed to appear as heat, because
the heat capacity of the system is essentially unchanged during the reac-
tion ; hence the system is peculiarly well adapted for tracing the mechanism
of the chemical production of electromotive force. 31 This was indeed the
reason why the whole investigation was undertaken. The probable reasons
for the lack of exactness in the application of the equation of Cady will be
discussed in the second half of the monograph, when other results have
been presented.
APPLICATION OF THE EQUATION OF HELMHOLTZ.
The importance of the heat of dilution in the case of amalgam cells
leads one to inquire concerning its exact values under the conditions
of the present experiments. These values are most readily calculated
from the well-known equation of Helmholtz, whose verity is undoubted.
The only difficulty in the present case lies in the fact that the temperature
coefficients were perforce determined over a rather large range of tem-
perature 30 on account of their otherwise too insignificant magni-
tudes. Moreover, even then their determination carries with it by far the
largest percentage error of any part of the work. Fortunately the nearly
if not quite linear nature of the coefficients with these metallic cells
prevents the introduction of any considerable error from the large range
needed.
In 1882, Helmholtz, in a paper already referred to, evolved the equation
^F-U=vFT^ (5)
an expression already given in a somewhat different arrangement as
equation(i). According to this expression the sum of the heat of reaction
and the product of the absolute temperature and the temperature coeffi-
cient of the change of free energy should equal the change of free energy
itself.
The experimental work already described furnishes sufficient data for
applying this equation to the amalgam cells of thallium, indium, and tin.
Take, for example, the thallium cell Ci-C2. Here ^=0.033897,
A?r =0.003237, AT=3O.oo, T=273.O9, v=i, and F=
"Richards, Proc. Am. Acad., 38, 293 (1902) "The relation of changing heat
capacity to change of free energy, etc." This theorem has been recently expanded
mathematically by Nernst, with the help of an interesting assumption concerning
the extrapolation to the absolute zero.
34 ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS
Then
ir vF= 3272.1 joules
Fv ^ ^~T~ 2844.4 joules
Difference U = + 427.7 joules
Thus upon the dilution with mercury of an amalgam containing nearly
two per cent (1.846 per cent) by weight of thallium to about treble its
volume (more exactly, 3.5 fold) we should obtain 428 joules or 102 small
calories for every 204 grams of thallium.
Again, in cell C2-C3, TT O = 0.020485, A*-= 0.002 125, AT =30.00,
7=273.09, v= i, and F = 96,530. Then
ir vF = 1978 joules
fvTr^ = 1869 joules
Difference U 109 joules
Turning now to the indium amalgams, we may consider for example
the cell Ei-E2, in which * = 0.014455, ATT = 0.001331, A7 = 30.00,
7=273.09, v=3, F= 96,530.
Then
KvF=4i86 joules
vFT ji = 3509 joules
Difference U = 677
This difference, the heat of dilution, is here much larger even than in the
concentrated thallium cell, because the electrochemical equivalent of
indium is only about one-sixth as great as that of thallium. In the case of
a cell with very dilute amalgams, on the other hand, the heat of dilution is
almost negligible, as is shown by the following calculation of cell Gi-G2,
about a hundred times as dilute as the previous example. There
wF =1858 joules
vFT ^ = 1862 joules
Difference U = - 4 joules
The agreement here is very satisfactory, being about 0.25 per cent.
The minus sign can hardly be significant, as the probable error of the
measurements is as great as 4 joules.
There now remains to be considered only the tin amalgam cells. For
example, we have in one cell, H2-H3: 7r =o.oio6i4, A7r=o.ooi2o6,
AT=30.oo, 7=273.09, v=2, ^=96,530. Then
KvF= 2284 joules
vFT^j.= 2353 joules
Difference U= 69 joules
OF THALLIUM, INDIUM, AND TIN 35
Thus the dilution of the tin amalgams gives a small cooling effect a
conclusion wholly in accord with the deviation of its potential from the
equation of von Turin and Meyer. If more concentrated amalgam could
have been used, the result would undoubtedly have been greater.
If possible, it would be well to verify these values of heats of dilution
by actual experiment. Unfortunately, however, an accurate determination
of the heat of dilution is only possible with the more concentrated amal-
gams, and even in these cases it is difficult. Five millionths of a volt in
the potential of a concentration cell corresponds to the development of
one joule during the transport of an univalent gram-atom. A mass of
amalgam containing a gram-atom of thallium dissolved in 99 times its
weight of mercury, when diluted with an equal volume of mercury would
involve a heat capacity not far from 6000 mayers ; hence one joule would
produce a temperature change of less than 0.0002. On account of the
high inertia of mercury, the liquids do not mix easily ; and for the same
reason the plentiful stirring evolves much heat. The exact evaluation of
the stirring correction is very difficult. Moreover, the dilution must be
carried out in an indifferent gas in order to avoid oxidation with its
attending heat effect.
Nevertheless, in spite of these difficulties the attempt was made to
determine the heat of dilution in the cases of the more concentrated amal-
gams of thallium and indium. 1226 grams of a I per cent thallium amal-
gam were diluted with an equal bulk of mercury and found to cause a rise
of 0.015 in a calorimetric system having a heat capacity of 431 mayers.
On further diluting by an equal bulk of mercury the mixture resulting
from this first experiment, the increased system (having now a heat
capacity of 762 mayers) was raised through only 0.002. These effects
were in the expected direction, but not of the expected magnitude.
The experiments were conducted in the apparatus of Richards and
Forbes, in which the mixing was conducted by a clock-work stirrer. Lack
of time had prevented the proposers of this apparatus from testing it
thoroughly. Our present experience indicates that the clock-work stirring
was inadequate, and hence that an inadequate change of temperature must
have been observed in all cases. Nevertheless, in spite of the quantitative
inadequacy of these results, they are qualitatively of value ; for they afford
experimental evidence that the conclusions drawn from the equation of
Helmholtz are at least in the right direction, and therefore that the data
upon which the conclusions are based are not seriously in error.
In the case of indium, 150 grams of an amalgam containing 1.92 per
cent of indium was diluted with 600 grams of mercury in a small calo-
rimeter, the total heat capacity being 157 mayers. Here, in this smaller
apparatus, the stirring was more effective, and the temperature rose 0.048,
36 ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS
a result more nearly in accord with the expected value, but still below its
full magnitude. The computation of the result is not worth while, as there
can be no doubt that this experiment, like the others, has no more than
qualitative value.
The small per cent of tin in a tin amalgam which remained wholly
liquid at o corresponds to a heat of dilution which would cause a change
of only 0.002 in the calorimeter -an amount too small to be determined
within 50 per cent by means of our thermometers. Hence an attempt to
carry out this experiment was without object.
In view of all these circumstances, we are inclined to agree with Carhart
in thinking that the electrical method of determining the heats of dilution
of amalgams is to be preferred to the thermochemical method.
It is worthy of note, in this connection, that the Helmholtz equation
shows at once why the temperature coefficient of the electromotive force
divided by the electromotive force approaches the coefficient of expansion
of a perfect gas as the dilution of the amalgam proceeds. To illustrate
this relation, the equation may be cast into a somewhat less familiar form.
The normal form, transposed, is thus:
Dividing through by vF-nT, we obtain
^L- _!_ u
7rAT~~ T vF-jrT
Evidently, because U, the heat of dilution, diminishes as the dilution pro-
ceeds, the last term will become smaller and smaller. Finally, when the
heat of dilution becomes negligible at great dilution, the equation will
become simply = .
Simultaneously, the equation of Cady
_RT 1 c m U
-W ln ~^~^F
loses its last term, and becomes the simple concentration equation.
It is equally clear that a positive heat of dilution ( + U} will cause the
potential to be high and the temperature coefficient to be low. In the case
of thallium and indium, this was found actually to be the case. On the
other hand, with a negative heat of dilution ( C7) the potential will be
low and the temperature coefficient high. This was found to be the case
with tin, and by Richards and Forbes with zinc.
Thus the theory of these cells seems to be complete, except for the
quantitative understanding of the minor deviations from the equation of
Cady. These deviations, which are probably to be traced primarily to the
inaccuracy of the simple concentration ratio ? as an index of the precise
OF THALLIUM, INDIUM, AND TIN 37
osmotic work to be obtained from the dilution of an amalgam, may best
be discussed in the light of the further data presented in the next paper.
Hence they will be deferred to the conclusion of the monograph.
In conclusion, it is a pleasure to express our indebtedness to the
Carnegie Institution of Washington for the apparatus and materials used
in this work.
SUMMARY.
The main points of the present research may be summarized as follows :
(1) The potentials between various liquid amalgams of thallium,
indium, and tin were investigated at 30 and o. Many precautions were
taken against experimental errors. The potentials of the thallium cells
are thought to be reliable within o.ooooi volt; those of the indium and
tin cells within 0.000005 volt.
(2) Thallium and indium amalgams gave potentials higher than those
calculated from the simple concentration law ; and tin amalgams gave
potentials lower than those calculated from the simple concentration law.
(3) The temperature coefficients of the various cells have been calcu-
lated and found to approach the ideal value 0.00366 for a unit potential
as infinite dilution is approached.
(4) The equation of Cady was applied to the results, and found to
afford a fairly accurate explanation of the deviations from the concentra-
tion law in all three cases.
(5) The equation of Helmholtz was used for the calculation of the
heats of dilution, and was found to account for the changes in the tempera-
ture coefficients.
(6) It was found impossible to obtain satisfactory results with an elec-
trolyte containing tin in a quadrivalent condition, either as stannic chlo-
ride or as sodic stannate. In this connection it was pointed out that Cady
must have had a two-phase amalgam in his tin cell, and that his results
with tin were illusory.
(7) The density of pure indium was determined and found to be 7.28.
(8) The densities of various liquid amalgams of thallium, indium, and
tin were carefully measured and compared with the calculated values.
SEPTEMBER 1907 TO JANUARY 1909.
209154
II.
Electrochemical Investigation of Liquid Amalgams of Zinc,
Cadmium, Lead, Copper, and Lithium.
BY THEODORE W. RICHARDS AND R. N. GARROD-THOMAS.
INTRODUCTION.
Simultaneously with the work described in the foregoing paper a
similar investigation upon other metals was begun in the laboratory. The
parallel progress of these two investigations was an assistance to each,
for not only were the potentiometer and other apparatus used in common,
thus economizing time for each investigator, but also the experience gained
in the one was immediately helpful in the other. The object of the work
to be described was, of course, similar to that of the work just chronicled,
namely, to extend as far as possible the study of liquid amalgams in their
relation to thermodynamical theory and to the essential nature of solu-
tions and the galvanic cell. The present paper contains, as its title indi-
cates, an experimental study of the liquid amalgams of zinc, lead, copper,
and lithium. It will be seen that the theoretical discussion of these results
together with those concerning cadmium, thallium, indium, and tin, already
described, furnishes much light upon these general questions and the out-
come will be seen to have justified the time and trouble spent upon the
somewhat exacting investigation.
ZINC AMALGAMS.
The energy changes involved in the dilution of zinc amalgams have
recently been studied in this laboratory by Richards and Forbes." Zinc
amalgams of different concentrations, ranging from 0.9 per cent to about
0.015 P er cen t f zinc, were connected by means of an electrolyte consist-
ing of zinc sulphate in water ; and the potentials of the resulting concen-
tration cells were measured, and were compared with the theoretical poten-
tial deduced from an equation derived from that of von Turin : "
"Carnegie Institution of Washington, Publication No. 56, p. 36 (1906).
"Zeit. phys. Chem., 5, 340 (1890).
39
4O ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS
An attempt was made also to determine the heat which the amalgam
of concentration c would evolve or absorb on dilution to concentration c 2
in the case of one cell. In this trial a 0.9 per cent zinc amalgam on dilu-
tion by its own weight of mercury absorbed 52 joules per gram-atom of
zinc.
It seemed very desirable that this thermochemical result should be
verified by the application of the equation of Helmholtz:
through the determination of the temperature coefficient of the electro-
motive force. Lack of time prevented this in the earlier work ; accord-
ingly the present investigation was undertaken.
The problem obviously involved simply the extension of the work of
Richards and Forbes to two different temperatures, but the execution of
the work was less easy than had been expected. Since the value of A?r
which would be expected in the case of the above cell is very small, it was
found necessary to make AT somewhat large. Measurements were at
first made at 30, 15, and o, but the interval of only 15 is too small to
allow of an accurate measurement of the temperature coefficient, and so
in the final experiments measurements were made at 30 and o C. only.
Most of this investigation was carried out in identically the same way as
the earlier work, and the densities of the amalgams were taken from those
results. The methods of purification of the zinc, zinc sulphate, and
mercury, the methods of preparing the amalgams, of sealing them in
hydrogen, and of introducing them into the cell, and diluting them with
mercury, which had been distilled and sealed in hydrogen, were identically
the same in every respect.
The potentiometer used was, however, considerably modified. If in a
cell of a bivalent metal where =2, it is desired to distinguish between
c z
a temperature coefficient of 0.00366 and 0.00367, the potential of the cell
at 30 and o must be measured with an error of not more than 0.000002
volt. Hence it was clear that a potentiometer more sensitive than that
employed by Richards and Forbes would have to be used. Accordingly,
much time was spent, with the help of J. Hunt Wilson, in elaborating a
suitable potentiometer. As this instrument is described in detail in the
foregoing paper," any further account of it is unnecessary here.
The thermostats, also, were the same as those described there ; they
could be relied upon to keep at a temperature constant within 0.01. The
thermometers were accurately standardized by means of instruments bear-
ing the certificate of the Reichsanstalt.
M This monograph, pp. 17 to 20.
OF ZINC, CADMIUM, LEAD, COPPER, AND LITHIUM
ELECTROMOTIVE FORCE BETWEEN ZINC AMALGAMS.
The first series of results with zinc amalgams, although not of sufficient
accuracy to yield trustworthy temperature coefficients, are worth recording
as a corroboration of the results obtained during the previous investigation
of Richards and Forbes.
In the first case the most concentrated amalgam contained 0.90 per cent
of zinc. It was placed undiluted in the first cup of the multiple cell
described in the foregoing paper," was diluted with mercury in the third
and fourth cups, and finally the parent amalgam was again put undiluted
in the remaining second cup, in order to be sure that no change had taken
place in the amalgam during the filling of the cell, and also that the
amalgam had been in the first place thoroughly mixed. This precaution
was usually taken in the subsequent work also, but only in one case,
mentioned later, was a difference greater than 0.000002 volt ever found
between the first and the last portions of amalgam. As is shown below,
the maximum difference in the present case was only one millionth of one
volt.
In addition to this series of measurements, another was made upon three
more dilute amalgams, in order to show the increasingly near approach
of the potential to the gas law. Table 6 gives both series of measure-
ments at 30. The details of dilution, etc., need not be given as regards
these preliminary results. The theoretical potential given below is calcu-
lated according to the simple concentration equation.
TABLE 6. Preliminary Electrical Measurement of Zinc Amalgams.
Designation
of cup
Approximate
per cent of
Exact
value of
Electromotive force, in millivolts, be-
tween each pair of cups. 3(PC.
amalgam.
amalgams.
108 g
Observed.
Theoretical.
Difference.
Ki
0.000,
f '
0.0000
0.001
0.000
O.OOI
K2
0.000
f '
0.37045
10.175
11.129
0.954
K 3
0.384
I"
0.21459
6.123
6.446
0.323
K 4
0.234'
Li
0.100 i
\"
0.44404
13.262
13.341
0.079
L2
0.036 I
0.26303
7.828
7-903
0.075
L3
0.020 '
'This monograph, p. 15.
ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS
These results confirm wholly the work of Richards and Forbes, carried
out at 23, showing that cells of zinc amalgams give a much lower electro-
motive force than that required by the concentration law. The quantita-
tive agreement of the two series of results is shown in the accompanying
diagram (fig. 9), where the points surrounded by single circles are the
points found by the earlier work, and those surrounded by double circles
the present data. This curve is drawn on the same scale as that used in
the other similar curves in this monograph.
The cells were measured also at 15 and o. In no case did the poten-
tial between cups I and 2 exceed o.oooooi volt. At 30 the other measure-
ments also were sufficiently concordant and convincing. At o the more
dilute amalgams gave less consistent results, and evidently were not so
logE Iog4 logS log 16 log 32 log 64 logJ28 log 256
Fig. 9. The Deviations of the Electromotive Force of Zinc Amalgams.
Deviations from the expression w = ~ i n c are plotted in millivolts as ordinates,
the logarithms of the concentration ratios as abscissae. The most concen-
trated amalgam contained 0.9 per cent by weight of zinc and 99.1 per cent
by weight of mercury. A horizontal line on the diagram would indicate
complete fulfilment of the concentration law. This curve is almost if not
quite independent of temperature, at least between o and 30. Single circles
depict points found by Richards and Forbes; double circles depict points
found by the present investigation.
trustworthy. As the technique and accordingly the consistency of the
results were both greatly improved later, these early measurements need
not be given in detail. It is enough to say that there was undoubted
evidence of the truth of the prediction of Richards and Forbes that the
temperature coefficient is greater than 0.00366, demanded by the gas law.
Moreover, it was clear that the value approached more and more nearly
that required by the gas law as the dilution became greater.
OF ZINC, CADMIUM, LEAD, COPPER, AND LITHIUM 43
DETERMINATION OF THE TEMPERATURE COEFFICIENTS OF CELLS
CONTAINING ZINC AMALGAMS.
The previously described measurements had all been made with the
potentiometer in its original less complete condition. For further more
accurate experiments, the potentiometer was modified with a view of
eliminating all thermoelectric currents, as has been already described."
The air in the case containing the potentiometer was stirred by means of
a fan, worked by an electric motor outside the case, so that the tempera-
ture inside was sensibly uniform. It was also arranged that all final
adjustments on the potentiometer could be made from outside the case,
thus avoiding all danger of thermal effects due to heating by the warmth
of the operator. Moreover, the connections with the cell were made so
as to avoid thermoelectric effects ; contact was made between copper and
mercury well under the surface of the thermostat and inside the cell, so
that all unequal heating of junctions of dissimilar metals was avoided.
A series of test experiments with this improved potentiometer showed
that although thermal currents had been completely eliminated, so that the
potentials could be read to even less than o.oooooi volt, nevertheless, the
amalgam cells themselves were not constant to this same degree. It was
thought that the irregularities might be due to the formation of a basic
salt by the action between the amalgam and water. To test this, in one
case the electrolyte was made slightly acid (about 0.02 N. with H 2 SO 4 ) ,
but no effect was observable, and hence in the final experiments neutral
electrolyte was again used.
In all the measurements thus far recorded the potential at 29.96 was
first measured, and then the potential at o, and finally the readings
repeated at 29.96 and at o again. It was always found that the reading
at 29.96 remained throughout constant to about 0.000005 vo ^, while the
value at o showed much greater change, sometimes even as much as
0.000030 volt. If the cell at 29.96 was shaken, the values were only
temporarily altered, while at o this treatment caused a more permanent
change, which did not completely vanish even if the cell was heated to
29.96, and cooled to o again.
Being unable to eliminate the difficulty, we sought to arrange the experi-
ments in such a way as to minimize its influence. In the final set of read-
ings to be recorded, the amalgams and electrolyte were cooled before using,
and were put into the cell as cold as possible. The readings at o were
first taken and then the readings at the higher temperature. Finally the
cell was cooled to o and measured again. The first readings at o and
the readings at 30 were constant, even if the cell was shaken, but the
second series at o showed after a time the former irregularities.
"This monograph, pp. 17-20.
44
ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS
In order to make these results as definite as possible, it was decided to
carry out two sets of experiments simultaneously, the two cells containing
the same amalgams. To effect this, the usual method of diluting a
"parent" amalgam in the cell was, of course, impracticable, and four
separate amalgams had to be made and sealed in the pipettes. The con-
centration of these amalgams was known to within about 0.5 per cent
a degree of accuracy, which, although not sufficient to admit of the theo-
retical potentials being calculated with the utmost precision, was ample
for finding the temperature coefficients with great exactness.
The cells were filled as in table 7.
TABLE 7.
Cup.
Per cent of zinc.
Cell M.
Cell N.
2
3
4
O.QI3
0.296
0.0998
0.0302
0.913
0.303
0.0098
0.0302
The cells were then put into the o bath, and their potentials measured
at two intervals of about an hour, the cell being shaken between. The
greatest change in potential during this treatment was 0.000004 v lt- Cell
N was then put in the 30 bath, and each pair of amalgams was put in
opposite to the similar pair in cell M at o, and hence a direct measure-
ment of the temperature change was obtained. Cell M was then put in
the 30 bath, and the potential of both cell M and cell N determined at
30 ; finally, N was once more packed in ice, but after two readings had
been taken, the familiar irregularities at o became too great for further
accurate work.
A slight mischance prevented the complete fulfilment of the program,
but although this mischance complicated affairs, it did not interfere with
the significance of the results for the present purpose. Probably because
of insufficient mixing in the bulb before the stem was filled, the amalgam
in cup M2 was found to be slightly less concentrated than in N2. This
prevented the direct comparison of these two cups, but did not affect the
results from each separately. The concentrations of the amalgams in these
two cups, as given above, were calculated from their potentials in con-
nection with the others, by the method given at the very end of this paper.
All the other cups were perfectly comparable, as was shown by the precise
equality of each pair, both at o and at 30.
All the figures in table 8, except the last two columns, represent the
actual readings of the potentiometer. The last two columns are obtained
by difference from the appropriate preceding columns.
OF ZINC, CADMIUM, LEAD, COPPER, AND LITHIUM
TABLE 8.
45
Cell.
MatO.
NatO.
Nao-Mo-
Mat 30.
Nat 30.
M.O-NO.
M-M O .
NK-NO.
1-2
1-3
II.8I3
24.236
II-S30
24.241
"2'.79l"
13-211
27.033
12.897
27.029
2.795
1.398
2.793
1.367
2.788
1-4
38.196
38.196
4.327
42.527
42.525
4-330
4-333
4.329
2-3
12.427
12.714
13 831
14 138
I 404
2-4
26.393
26.669
29 . 33 i
29 637
2 0^8
2 - 968
3-4
I3-960
1-544
15.507
15.506
1-543
1-545
1-544
Thus for cups 1-3 there are four results for ATT to be taken directly
from the table, and three more by subtracting the values for the cups 3-4
from those for the cups 1-4. There are also four values for the value of
ir for 1-3 at o two given in the table, and two obtained by subtracting
the values for 3-4 from those for 1-4. These are recorded below in
table 9, in order to give some idea of the accuracy of the work.
TABLE 9.
[Cell Mi-M 3 (or Ni-Na)].
TT O in millivolts.
AT (o to 29.%), in millirolts.
24.236
24.241
24-234
24.236
2.791
2.795
2.793
2.788
Average 24 237
73
2 788
2.785
Average 2 799
"Probable error".. 0.0008
"Probable error". .. o.ooi
Thus this cell with its amalgams containing about 0.0913 and o.ioo
per cent of zinc, respectively, gave a potential of 0.024237 volt 0.0000008
at o, and changed its potential by 0.002799 volt 0.000001 on being
raised to 29.96. The value for -^- is therefore 0.003855 instead of the
value 0.00366 shown by the increase in pressure of a nearly perfect gas
the standard upon which our temperature scale rests.
In the same way, seven results for cell 1-4 give on the average
ATT =0.004332 volt 0.000001 ; and for cell 3-4, seven similar results give
ATT =o.ooi 541 volt o.oooooi. From these results, as well as from the
figures given in the table for the other combinations, the corresponding
values for the temperature coefficients may be readily computed, it being
borne in mind that wherever cup 2 is concerned, the cells M and N must
46 ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS
be calculated separately. When thus treated the final results from the
two are essentially identical, and may be averaged together. As the
details may be worked out from the data, by anyone wishing to verify the
results, further space need not be wasted by their minute presentation.
It is enough to present the final table of values for the function -J_ .
Cup 1-2 0.00397
1-3 0.003855
1-4 0.003794
Cup 2-3 0.00375
2-4 0.003715
3-4 0.003685
Thus it is clear that in the case of zinc amalgams, as in all other cases
thus far studied, the temperature coefficient of the electromotive cell
becomes nearer and nearer the limiting value as the dilution proceeds.
In the most dilute cell measured, whose two amalgams contained respec-
tively about o.io and 0.03 per cent of zinc, the value of the temperature
coefficient had come within 0.7 per cent of the requirement of the gas law.
The significance of these results as regards the theory of the galvanic
cell will be discussed in a later section, after the facts concerning other
cells have been presented.
It will be observed that the first value given for the temperature coeffi-
cient exceeds the ideal value by as much as 8.5 per cent. This high value
for the temperature coefficient, which appears wherever the most con-
centrated amalgam was concerned, might possibly be due to the crystal-
lization of zinc at o. That this, however, was not the case seems almost
certain from the regularity of the results obtained, and from the fact that
the temperature coefficient between 15 and o, and between 30 and o
for even a stronger amalgam than was here used, were nearly the same.
The point was, however, also experimentally investigated in the fol-
lowing manner. Both the limbs of an H tube were filled with a 0.91 per
cent zinc amalgam, and the potential between them at o was measured
and found to be almost zero. Then a small quantity of pasty zinc amalgam
was added to one limb, and a large and permanent potential was produced
in the direction indicated by theory. In another similar cell, one of the
limbs was very slightly diluted with mercury and again a permanent poten-
tial, in the direction foretold by theory, was observed. These facts could
not be explained if the parent amalgam had crystallized out at o, but are
precisely what would be expected from an unsaturated amalgam.
Control experiments were made in which an amalgam known to be more
than saturated replaced the 0.91 per cent amalgam in the above experi-
ments. On the dilution and on the concentration of one of the sides of
the cell no permanent potential greater than o.ooooi volt was obtained,
showing in this case that the presence of the solid phase caused the effec-
tive concentration of the amalgam to become constant.
OF ZINC, CADMIUM, LEAD, COPPER, AND LITHIUM
47
LEAD AMALGAMS.
In order to generalize concerning facts of any kind, it is desirable to
obtain as wide a variety of data as possible. Hence it was decided to
investigate lead amalgams in the same manner. Previous work on the
subject had been done by G. Meyer," and by Spencer," but no data of
sufficient accuracy had been published. The investigation was carried
out in a manner exactly similar to the above-described work, hence
details of manipulation will not be described again.
Commercial " C. P." lead acetate was found to contain traces of iron,
but after one recrystallization with centrifugal filtration this impurity was
eliminated, and after two more such crystallizations the lead acetate was
considered sufficiently pure to be used as the source of the metal, as well
as for the electrolyte.
The metallic lead used was prepared by the electrolysis of the acetate
solution. The crystals of the metal thus obtained were carefully washed,
and were then fused in porcelain boats in an atmosphere of hydrogen, and
the lead thus obtained was used to make the amalgams. The electrolyte
was prepared by taking a solution of the acetate, saturated at o, and
diluting with about one-tenth its volume of half normal " chemically pure "
acetic acid. In this way the formation of basic salts was prevented, and a
perfectly clear electrolyte was obtained. This solution was, as usual,
boiled in a partial vacuum in an atmosphere of hydrogen, and sealed in a
pipette, also in hydrogen.
The amalgams were made by adding a weighed amount of lead to a
weighed amount of hydrogen-distilled mercury, a little very dilute acetic
acid being present to cover the metals and prevent oxidation ; for the
amalgam oxidizes very rapidly in air. The acetic acid was then analyzed,
and was found to contain neither lead, nor iron from the steel knife used
to cut the lead. The amalgams were then sealed in hydrogen in the
before-described apparatus.
TABLE 10.
Concentration
of amalgam
(per cent).
Weight of pycnometer full of-
Density
ataoc.
Amalgam.
Mercury.
1.02
0.684
0.397
48.9587
35-073
35-079
48.9922
35.092
35.092
35.092
13.536
13-539
13.541
13-545
Zeit. phys. Chem., 7, 477.
"Zeitschr. f. Electrochem., 11, 681.
ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS
A series of density experiments of lead amalgams was carried out at
20, and is recorded in table 10, but the necessary correction is insignifi-
cant in this case, because the density of lead is so nearly that of mercury.
The densities were determined by the use of an ordinary Ostwald pyc-
nometer ; the only unusual precaution taken was to displace the air in the
pycnometer by carbon dioxide. On this account very little oxidation took
place when the amalgams were drawn into the tube.
These results are plotted in fig. 10. The imaginary density, supposing
no contraction to have happened, is given by the dotted line. For a I per
cent amalgam this is 13.524 instead of the actually observed value 13.536.
Thus as a matter of fact a slight contraction occurs on amalgamation.
13.53
13.54
13.55
0.2
0.6
0.8
1.0 percent
Fig. 10. Densities of Lead Amalgams at 20.
Densities are plotted as ordinates, per cents by weight of lead in amalgams as abscissae.
The dotted line indicates the imaginary theoretical values.
The electrical measurement of similar amalgams was now undertaken.
The most concentrated amalgam of lead used for the purpose contained,
as before, 1.02 per cent of this metal by weight. Some of this was placed
in the cup labeled Pi. Into cups P2, P3, and P4 were placed respectively
12.684, I2 -6o3> and 10.946 grams of this amalgam, diluted with 19.358,
58.96, and 108.86 grams of mercury respectively. The second series
began about where this left off, with a freshly prepared amalgam contain-
ing 0.0994 per cent of lead. Cup Qi contained this alone, while cup Q2
contained 14.308 grams of it diluted with 74.628 grams of mercury. The
least concentrated amalgam of all, that contained in Q3, was made by
diluting 8.429 grams of material like that in Qi with 115.72 grams of
mercury. The electrical measurement with these two series of cells is
given in table n.
OF ZINC, CADMIUM, LEAD, COPPER, AND LITHIUM
TABLE n. Electrical Measurement of Lead Amalgams.
49
Designation
of cup
containing
amalgam.
Approxi-
mate
per cent of
lead in
amalgams.
Exact
value of
. Cm
Electromotive force between each pair of cups, in millivolts.
0C.
29.96C.
10B *.
Observed.
Theo-
retical.
Differ-
ence.
Observed.
Theo-
retical.
Differ-
ence.
Pi
P2 . .
,
0.404 j
0.180 |
0.0932 '
0.0994,
0.0160 |
0.0068'
0.4023
0.3SI7
0.2850
0-7935
0-3747
8.960
8.839
7.422
21.303
10.077
10.895
9.525
7.719
21.489
10.149
1-935
0.686
0.297
0.186
0.072
10.135
9.841
8.270
23.680
11.186
12.092
10.509
8.564
23.848
11.262
1.957
0.728
0.294
0.168
0.076
P 3 .. .
P4
Ql
Q 2
Q3
The last column in table n shows the great deviation of the strongest
amalgams from the simple equation
RT c
vF ^ C n
and indicates, as usual, that this deviation approaches zero as the dilution
proceeds in the usual fashion. The fact becomes yet clearer when the
results are plotted as the other metals have been. Fig. 1 1 gives this curve,
drawn on the same scale as those previously given.
log a Iog4 Iog8 log 16 Iog32 log 64 loglZB
Fig. 11. The Deviations of the Electromotive Force of Lead Amalgams.
log,256
Deviations from the expression n = -^p In are plotted in millivolts as ordinates,
the logarithms of the concentration ratios as abscissas. The most concentrated
amalgam contained 1.02 per cent by weight of lead and 98.98 per cent by
weight of mercury. A horizontal line on the diagram would indicate com-
plete fulfilment of the concentration law. This curve is almost if not quite
independent of temperature, at least between o and 30.
ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS
The temperature-coefficient functions
ATT
of these cells, calculated in
the usual way from the figures given in table n, are as follows:
Cell Pi-P2 0.00437
P2-P3 0.003805
P3-P4 0.00381
Cell Qi-Cj2 0.00376
CJ2-Q3 0.003677
The first value is much higher even than that for zinc. Here again as
usual, the figures rapidly approach the limiting value 0.00366 as the
dilution proceeds, although the coefficient for cell Pi-P2 containing the
most concentrated amalgams is 16 per cent in excess of this figure.
The theoretical significance of these results will be considered later, in
connection with all the other results. The possibility that the high tem-
perature coefficient of the most concentrated amalgam cell might be due
to the crystallization of the most concentrated amalgam at the lower
temperature was considered, and was experimentally investigated in an
exactly similar manner to that used in the case of the zinc amalgams.
An amalgam containing 1.03 per cent of lead was placed in an H cell and
one side was in one case diluted and in the other concentrated, and in
both cases a permanent potential, in the direction indicated by theory,
was obtained, the measurements of course being made at o C. Control
experiments, using a saturated amalgam with excess of lead, showed no
potential on adding either mercury or lead to one side of the cell.
These results seem to show clearly that the most concentrated amalgam
used, i. e., 1.02 per cent,- is less than saturated at o.
At this point the potentiometer was recalibrated, but no change as great
as o.oi ohm was found in any of the resistance, and hence, as before, cor-
rections were unnecessary.
COPPER AMALGAM.
Seeking all the light available upon this type of cell, the investigators
next turned to the metal copper. Copper amalgams have been examined
in this connection by Meyer and by Spencer. Meyer made an amalgam,
by electrolysis, intended to contain 0.217 per cent of copper. This amal-
gam he dried by filter-paper and standing in a desiccator, and then diluted
portions of it. Table 12 gives his results, the concentration being ex-
TABLE 12. Potentials of Copper Amalgams measured by Meyer.
/.
a.
C2.
Electromotive
(millivolts).
Mol. wt., calc.
17.3
20.8
0.03874
0.04472
0.009587
0.016645
I8.I5
12.4
6 3 . 3
63.7
OF ZINC, CADMIUM, LEAD, COPPER, AND LITHIUM 51
pressed in percentage, and not in parts per unit of mercury, as it is in the
original paper."
The results obtained by Spencer were not so consistent with theory,
but, as will be seen, are more like our own experience. He found great
difficulty in getting constant readings of potential. His results are given
in table 13 ; it will be observed that he used far more dilute amalgams.
TABLE 13. Potentials of Copper Amalgams measured by Spencer.
No. of
cell.
Per cent of copper.
Electromotive force.
|
Cl.
Observed.
Theoretical.
I.
II.
III.
0.0003193
0.001938
0.005399
0.001938
0.005399
0.007205
26.8
6.4
20.9
IO.I
8.8
It will be noticed that at first the actual potential is larger than theory,
and afterwards smaller. The reason will soon become clear.
The next step of the present research was to repeat these experiments
in order to discover the difficulty. Commercial " C. P." copper sulphate
was carefully recrystallized three times with centrifugal filtration, and the
resulting copper salt was used in the experiments. A copper amalgam
was then made by electrolysis, using mercury as the cathode, the amount
of copper deposited being estimated by means of a silver coulometer in
series. The amalgam was found to contain 0.2311 per cent of copper. On
drawing this amalgam into the pipette, preparatory to its being sealed in
hydrogen, a pasty residue was left which would not enter the fine tip of
the pipette. Hence it was clear that the above amalgam was not a solu-
tion, but rather a suspension of copper or of some copper-mercury com-
pound in mercury. The amalgam which had been drawn into the pipette
was used to fill a cell in the ordinary manner.
This cell proved two important points : first that neutral copper sulphate
could not be used as electrolyte, because the amalgam acted on it, giving
Cu 2 O ; and secondly, that a very dilute amalgam, made by diluting the
original sixteen times, gave only an exceedingly small potential with the
original amalgam. Thus it appeared that the diluted amalgam was still
saturated and there could be no doubt that crystals of the solid had not
all been left behind in the pasty mass mentioned above.
It then became necessary to find the solubility of copper in mercury.
Saturated solutions of copper in mercury were made either by allowing
amalgamated copper wire to stand in mercury for a week, or by carefully
filtering a partially solid amalgam, prepared electrolytically, several times
through leather.
' Zeit. phys. Chem., 7, 477.
ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS
The saturated amalgam was then weighed, and the mercury driven off,
at first by distillation in hydrogen, and the last traces by heating to a red
heat in a crucible. The cupric oxide left was then either directly weighed,
or it was dissolved in nitric acid, neutralized with ammonia and the con-
centration of the solution approximately estimated by colorimetric com-
parison with the color of a standard solution of ammoniacal cupric nitrate.
The results are given in table 14.
TABLE 14. Solubility of Copper in Mercury at 20".
Method of preparation.
Weight of
amalgam
(grams).
Method of analysis.
Weight of
<
Solubility
(percent).
Copper + mercury
41 I
Colorimetric
0.08
o 0024
Do
885
Direct weighing
2 OO
o 0023
Electrolysis + filtration
30 o
Colorimetric
o 60
O O02O
Do
mo o
Direct weighing
4 05
o 0027
o 002^"?
Thus the solubility of copper in mercury at room temperature seems to
be very small indeed, about 0.0024 per cent, or about I milligram in 40
grams of mercury. This agrees well with the observations of Sir W.
Ramsay, 40 but is somewhat higher than a result of Gouy.* 1
It was then decided to measure electrically a series in which the start-
ing point should be undoubtedly a real solution. An amalgam containing
about i per cent of copper was made electrolytically. It was then filtered
three times through leather, the last filtration leaving no solid residue.
153 grams of this amalgam were then diluted with 26 grams of mercury
in order to make quite certain that no solid was present. This amalgam
was bottled in the usual way. It was estimated to contain about 0.0020
per cent of copper.
TABLE 15.
Cell.
Electromotive force, in millivolts.
Observed.
Theoretical.
After i hour.
24 hours.
48 hours.
72 hours.
1-2
1-3
1-4
15.20
31-6
43-8
14.70
32.0
40.7
9.1
I7 "i
21.6
5-4
10.8
13-8
H-53
27.38
34.83
*Journ. Chem. Soc., 1889, Trans, n, 532.
41 Gouy, Ann. der Phys. Beiblatter, 19, 758. He found q.ooi per cent of copper,
1.8 per cent of zinc, and 1.3 of lead in their respective liquid amalgams.
OF ZINC, CADMIUM, LEAD, COPPER, AND LITHIUM
53
The cell was then filled, using this amalgam in cup i, diluting it in the
three other cups of the multiple cell, and using a solution of copper sul-
phate in 0.0125 normal sulphuric acid as electrolyte. As table 15 shows,
no constant results could be obtained.
At first the potentials were all higher than the theoretical and later they
all became lower. Evidently the copper reacts with the electrolyte, form-
ing cuprous salt, and this reaction proceeded further in proportion in the
case of the more concentrated amalgam, because of its lesser volume and
larger proportion of exposed surface. 42 Another series of readings was
then tried, with additional precautions. The original amalgam was,
in this case, made by standing amalgamated copper wire in mercury, in an
atmosphere of hydrogen, for several days the mercury being frequently
shaken. It was drawn into the pipettes in the usual way, wholly out of
contact with the air. The electrolyte, again slightly acid, was also allowed
to stand in an atmosphere of hydrogen over a copper amalgam for several
days. In spite of these precautions no more constant results were obtained,
as table 16 shows.
TABLE 16.
Cell.
Electromotive force, in millivolts.
Observed.
Theoretical.
As soon as
possible.
i hour.
6 hours.
24 hours.
48 hours.
1-2
1-3
1-4
10. 60
26.2
29-5
ii. 9
28.5
29.6
^' 3
26.7
29.9
II. I
21.9
24-5
6.4
IO.I
12.5
9.58
21.91
30.66
Evidently the electrolyte was not saturated with cuprous salt, in spite
of its week's contact with the amalgam. Considering the small concentra-
tion in the amalgam and the fact that it can act upon the electrolyte only
at the surface in mercury, this is perhaps not surprising.
In the light of these experiments, let us turn back for a moment to the
results of Meyer and Spencer. The latter's are wholly comprehensible.
His first cell alone was dilute enough to be beyond the limit of saturation,
and that gave a result like ours. The other more concentrated amalgams
must have contained traces of solid, and if he had waited until they reached
equilibrium, his cell III must have reached zero potential. His figures are
just what one would have expected.
Meyer's figures are harder to explain. How he could have attained his
results from amalgams containing a large excess of solid phase will
"See for example, Richards, Collins, and Heimrod, Proc. Am. Acad., 35, 125
(1899); Zeit. phys. Chem., 32, 324 (1900).
54 ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS
always remain a mystery. Perhaps the compensating effects of rate of
solution and degree of saturation may have combined to give the results
he observed, or perhaps his potentials came not from copper at all, but
rather from some impurity.
It would have been particularly interesting to have obtained good
results in the case of this amalgam, for the electrolytic solution pressure
of copper is of the same order of magnitude as that of mercury, and it
might be expected that a balanced action would be established between
the passage of mercury into the electrolyte and of copper into the amal-
gam. This idea, which has been followed up by Hulett and De Lury in
another way since the beginning of our work, was one of the secondary
objects of the present research. A balanced action, indeed, may be in
part the cause of the lack of constancy of the potentials observed, as one
would be led to expect from this cause a gradual fall in potential. It is
possible that if the electrolyte were wholly saturated with cuprous sul-
phate, satisfactory measurements might be obtained, and one of us hopes
to return to the problem in the future.
IRON AMALGAM.
J. P. Joule " seems to have been the first person to study iron amalgams.
He records that an amalgam containing I per cent of iron is fluid, and 3
per cent is semi-fluid.
An amalgam containing I per cent of iron was therefore made, by elec-
trolysis. This amalgam on filtration through soft leather proved to be a
suspension. The amalgam was filtered twice more, and finally the mercury
in a weighed amount of the amalgam was evaporated, and the remaining
ferric oxide was weighed. The same process was repeated with a fresh
amalgam similarly prepared. In the first instance, 65.0 grams of amalgam
gave 0.0013 gram of Fe 2 O 4 ; solubility 0.00135 per cent. In the second,
143.0 grams gave 0.0027 grams of Fe 2 O s ; solubility 0.00133 per cent
Thus the solubility of iron in mercury can not greatly exceed I milli-
gram in i oo grams. There is no proof that even this small trace might
not have percolated in the solid state through the leather. As the solu-
bility is so small, the investigation of the potential of iron amalgams was
not pursued further.
a Journ. Chem. Soc., 16, 378 (1863).
OF ZINC, CADMIUM, LEAD, COPPER, AND LITHIUM 55
LITHIUM AMALGAMS.
Up to the beginning of last year but little accurate work had been done
on the amalgams of the alkali-metals from the standpoint of potential
measurements. The very recent discovery by Lewis and Kraus of a
satisfactory method of measuring these metals against an aqueous solution
of their hydroxides was not known to us at the time of our work, hence
its assistance was not available. 4 * The first step in the present quest was
obviously a repetition of the earlier work in the hope of discovering its
validity. If this promised well, more accurate determinations were to be
attempted.
Meyer and Cady, in their publications already cited, have furnished the
chief figures concerning the electrochemistry of the amalgams of the
alkali-metals. Meyer recorded the results on sodium amalgam, but, as
he spoke of using an aqueous electrolyte apparently without suitable pre-
cautions, his data have little significance. Cady, working under Bancroft's
direction, made measurements upon amalgams of the three most plentiful
alkali-metals, using pyridine as the solvent for the electrolyte. This work
shows the effects of great haste ; the figures in his tables are not wholly
consistent with themselves and are evidently vitiated by serious errors,
both of experiment and of proof-reading. Therefore it was thought
advisable to repeat his work. We employed at first as the electrolyte a
solution of lithium chloride in pyridine. The specimen of salt employed
was a very pure sample which was being used for work on atomic weights
in this laboratory. We are greatly indebted to Mr. H. H. Willard for his
kindness in providing it. As a solvent the best pyridine, supplied by Kahl-
baum, was redistilled with a fractionating column, giving as boiling-point
H5.2o.i at 760 mm. It was always protected from moisture during
distillation, and was subsequently kept in a potash desiccator. The con-
ductivity of lithium chloride " in pyridine is very small, hence the electro-
lyte was made very nearly saturated.
The amalgams were made by placing mercury and lithium in the lower
of the two bulbs in the usual apparatus shown in fig. I, page 9, sealing
everything into its place, and finally melting the lithium after the whole
apparatus had been filled with hydrogen. After cooling, the amalgam was
driven by the pressure of hydrogen into the upper pipette, from which a
sample was taken for alkalimetric analysis by means of digestion with a
standard acid solution. Two amalgams made in this way, which were
expected to give concentrations of about o.i and 0.5 per cent, were found
to contain 0.037 P er cen ^ an< ^ -36 per cent respectively ; and in both
"This method has not yet been published. In the near future it will be applied
either by Lewis and Kraus or at the Harvard Laboratory to a series of measure-
ments like those discussed in the present paper.
a Lasezynski and Gorski, Zeitschr. f. Electrochem., 4, 290.
56 ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS
cases solid amalgams could be seen floating on the liquid amalgam in the
pipettes. Hence it was evident that the solubility of lithium in mercury is
about 0.036 per cent. This agrees well with the observation of Kerp and
Bottger, 46 who obtained a solid amalgam containing 0.69 per cent to 0.72
per cent (having approximately the formula LiHg g ) from a mother-liquor
containing 0.04 per cent of lithium. In view of these facts it is evident
that Cady was much in error in his supposition that his amalgam contained
1.8 per cent of lithium far more than corresponds even to the solid
amalgam. In answer to our personal enquiry, Professor Cady states that
the cause of this error was a defective method of analysis, which multiplied
by 50 the absolute amount of lithium in each amalgam, but did not affect
the ratio of the two concentrations.
The saturated liquid amalgam, whose preparation is described above,
we diluted to form two less concentrated amalgams, and these were driven
into the pipettes under hydrogen in the usual manner. Analysis showed
them to contain 0.0255 P er cent an< 3 0.0144 per cent of lithium respectively.
With these amalgams a cell was set up, two cups being filled with each.
No constant readings could be obtained, but the value 0.0169 with a pos-
sible error of 0.0002 volt was indicated. The electromotive force deduced
from the simple concentration law equation is 0.0159; hence it appears
that, as had been expected, lithium ranks with lead, thallium, and indium
rather than with zinc and tin. It is pleasant to note that this result agrees
qualitatively with the outcome of Cady's experiments, in spite of their
inconsistency of detail.
The cell on standing rapidly changed in potential, and in a few hours a
number of small crystals were observed in the electrolyte, which itself
had assumed a dark-brown color. Hoping to establish a constant con-
dition in a fresh portion of the electrolyte, in order to obtain better results
upon refilling the cell, we allowed the solution of the chloride in pyridine
to stand over metallic lithium. In a few days the pyridine had become of
a dark-blue hue, which upon opening the bottle disappeared in a very few
moments. In a similar bottle containing pyridine and lithium, but no
lithium chloride, no blue color was formed, but nevertheless the lithium
attacked the solvent in another way, and a brown powder was deposited.
It thus appears that dry lithium attacks dry pyridine, and the hope of
obtaining really satisfactory results in this way was dispelled.
Several other series of potential measurements were tried, in some of
which lithium sulphate took the place of the chloride in the electrolyte;
but the series recorded above was the most satisfactory. More dilute
amalgams gave more erratic potentials. In some cases a potential of over
one volt was observed for several minutes, in the case of a cell where
about 0.02 volt was the value which theoretical considerations would give.
"Ze.it anorg. Chem., 25, i (1900).
OF ZINC, CADMIUM, LEAD, COPPER, AND LITHIUM 57
In view of these highly unsatisfactory results, and the rapidly approach-
ing conclusion of the academic year, it was decided to abandon for the
present the attempt to obtain accurate data concerning the alkali-metals,
and confine the theoretical treatment to the six metals which had given
unimpeachable results, namely, cadmium, zinc, thallium, indium, tin, and
lead. The theoretical discussion of these more satisfactory data follows.
APPLICATION OF THE EQUATION OF CADY.
It has already been pointed out in the preceding paper" that if the
electromotive force of a cell as depicted by the equation of Helmholtz is
made equal to that demanded by the equation of Cady, the term involving
the heat of reaction is eliminated, and we obtain the expression :
This equation was found as a matter of fact to hold approximately true
as regards thallium, indium, and tin, and it becomes a matter of interest
as applied also to zinc and lead. The average values for the zinc cells
Mi-M3and Ni-N3 are given on p. 45. The value of wa s ^^ =9-15
C n O.OQQo
Thus
3?
Difference = 0.000020
This small difference, not much exceeding 2 per cent, seems at first
sight inconsistent with the wide discrepancy found by the earlier investi-
gation as regards cells containing zinc amalgams. There are two causes
for this difference of verdict: the first and most important is not a real
inconsistency, but appears only because of the different mode of presenta-
tion ; the second subordinate cause of difference is due to the doubtful
character of the result for the heat of dilution previously employed a
datum wholly eliminated from the present calculation. This latter circum-
stance will be considered in the subsequent heading concerning the equa-
tion of Helmholtz ; the former is worthy of a further word of explanation
here.
In the paper by Richards and Forbes, the equation of Cady was trans-
posed thus :
RT d U
This monograph, p. 31.
58 ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS
and the two members were calculated separately and compared. Thus
all the errors, both of theory and observation, were heaped upon the
smallest term involved f^K-l and naturally formed a much larger per-
centage of this smallest term than they would when applied, as in the
present paper, to the much larger term =- i n -- . Cady's equation thus
vr Ci
failed as applied to the calculation by difference of the smallest term ; but
the present method of presentation shows that the equation may be of
use in calculating approximately the temperature coefficient of an amalgam
cell. I
As the amalgams become more dilute, the fulfilment of the equation of
course becomes more exact, because the concentration ratio gives more
and more nearly an exact measure of the osmotic work, and all the other
irregularities probably decrease. Thus for the cell M3-M4 (or N3-N4),
(pages 45 and 46), where ^ = 0.01395 volt, An- for 29.96 =0.001541 volt,
and the ratio of the concentrations is 3.305: I, the following results are
calculated :
Temperature coefficient calculated from concentrations.. 0.0000515
Actually observed temperature coefficient ............... 0.0000514
The difference is only 0.2 per cent, an amount distinctly less than the
experimental error.
Similar calculations for lead give similar results ; for example, let us
take the cell Pi-P2, having a concentration ratio equal to 2.53. Then
Difference = 0.0000008
In the more dilute cell Qi-Q2 where the concentration ratio = 6.21, we
have
Temperature coefficient calculated from concentrations = 0.0000786
Temperature coefficient actually observed ............. = 0.0000793
With this more dilute amalgam the difference is less than i per cent
instead of being 2 per cent as in the case of the more concentrated lead
cell.
Turning back, now, to cadmium, investigated by Richards and Forbes,
we find that the results recorded there give somewhat similar indications,
when compared according to the present method. Thus the cell 1-5 **
(made from an amalgam containing 2.955 P er cen ^ of cadmium and
another amalgam obtained by diluting 12.226 grams of this amalgam with
** Carnegie Institution of Washington Publication No. 56, 46 (1906).
OF ZINC, CADMIUM, LEAD, COPPER, AND LITHIUM
59
12.762 grams of mercury) gave a potential of 0.009405 volt at 23.03, and
must have had a value for the function ^^,=0.003655.*'
From these facts the following results may be calculated :
.,-&_ 8.316
,0.703.
=0.0000303
f = 0.003655^0 = 0.003655 TM -23 . ....=0.0000318
Difference .............................. =0.0000015
Thus the discrepancy, which (according to the previous method of cal-
culation, already explained in the case of zinc) had seemed very large
when heaped upon the smallest term, does not exceed 5 per cent when
applied to the larger terms.
Thus all the six metals, thallium, indium, tin, lead, zinc, and cadmium,
show an approximate agreement with the Cady equation, when tested in
this way. The discrepancy never exceeds 5 per cent, and usually is little
greater than 2 per cent. The deviations are sometimes in one direction,
and sometimes in another, and in some cases are no greater than the errors
of experimentation. For the sake of convenient reference, it is worth
while to present in a single table all these results concerning the equation
Although by no means giving all the results which may be calculated
from the measurements, table 17 presents a typical example of each metal,
as well as of the effect of increasing dilution.
TABLE ij.The Application of the Equation Derived from that of Cady.
Designation
Per cent of
solid metal in
Temperatur
e coefficient.
of cell.
concentrated
amalgams.
Observed.
Calculated.
Thallium
Cl-C2
1.84
O.OOOI08
O.OOOIO8
Do
B2-B3
o. 172
o 000104
o 000106
Indium
Ei-E2
1 .92
o 000044
o 000046
Tin
Ji-T 2
O.2I
o 000052
o 000053
Zinc
Mi-M3
o 91
o 000093
o 000095
Do
M3-M4
O IO
o 000051
o 000051
Lead
Pl-P2
I O2
o 000073
o 000075
Do
Qi-Q2
IO
o 000079
0.000079
R & F 1-5
2 Q5
o 000032
0.000030
The theoretical significance of the close agreements shown in this table
is worth further attention.
40 Carnegie Institution of Washington, Publication No. 56, p. 50.
6o
ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS
The outcome may be stated as follows : The temperature coefficient of
the electromotive force of a cell made from liquid amalgams is as a matter
of fact approximately equal to the ideal potential of the cell (calculated
from the relative concentrations of the amalgams) divided by the absolute
temperature. The result is independent of the temperature: the increase
of potential is a linear function. This has already been shown experi-
mentally. 50
One may well inquire concerning 1 the ultimate significance of this
phenomenon ; and the following suggestion is offered as a tentative
explanation.
In these cells, the change of heat capacity during the reaction is very
small. Hence according to the theorem recently advanced by one of the
present authors, 51 the free energy output of the chemical part of the change
may be expected to be equal to the total energy output, and both would
be expected to remain invariable with the temperature. Thus the part of
the electromotive force due to the chemical change would have no tem-
perature coefficient, and all the change of potential with temperature must
be ascribed to the change in the osmotic work. This would be expected
to be linear, and directly dependent upon the concentrations as it is actually
found to be, at least approximately. The rule would be expected to hold
only when no change of heat capacity occurs in the reaction. Thus these
troublesome and time-consuming measurements have shed new light upon
the mechanism of the galvanic cell, and have justified the labor expended
upon them.
TABLE 18. Calculation of E. M. F., by Cady's Equation.
Metals.
Designation
of cell.
Observed
potential
atO.
Potential
according to
Cady*
Difference,
error of Cady
equation.
Error of
simple
concentration
equation.
Thallium. .
Cl-C2
Yolt.
o 03390
Volt.
O 01102
Millivolt.
+0 02
4 41
Do
C2-C3
o 02048
o 02060
+O 12
I O2
Indium
Tin
Ei-E2
Jl-J 2
0.01445
o 01361
0.01493
o 01415
+0.48
-hO 54
-1.86
+0 QO
Zinc
Mi-M2
o 02424
o 02477
+ *S\
+ 1 28
Cadmium
Lead. . .
R&Fi-s
PI-P2
0.00867*
o 00896
0.00830*
o 00914
-0.37
_l_o 18
-0.34
-hi 0^
Do
P2-P4
o 01626
o 01663
+O 17
+o 68
Do
Qi-Ql
o 03138
o 0112^
IS
+o 24
These are reduced to o from the observations at 23.
'* This conclusion may be drawn from the table on p. 22.
81 Richards, Proc. Am. Acad., 36, 300 (1002); Zeitschr, phys. Chem., 42, 138
(1902). This theorem has been elaborated by Nernst in a very interesting way.
(See Nernst's Silliman Lectures.) "Thermodynamics and Chemistry," page 56,
New York, 1907.
OF ZINC, CADMIUM, LEAD, COPPER, AND LITHIUM
6 1
The equation of Cady may also be used to calculate the electromotive
force from the heat of reaction and the concentration effect, supposing
these to be known. Indeed, this corresponds to Cady's first method of
expressing the results. In a subsequent section the heats of reaction are
calculated with the help of the temperature coefficient and the equation
of Helmholtz. Using the values for U there given and the values of the
concentration ratios already presented in this section, the given results
in table 18 are obtained from the Cady equation
On comparing these results in the fifth column with those in the sixth,
it is evident that Cady's equation is a much closer approximation to the
truth than von Turin's. The average deviation shown by Cady's equation
is only about 0.3 millivolt, whereas the average deviation shown by the
simpler equation is about 1.3 millivolt. In other words the departure of
the potential from the simple values indicated by the gas law may be
ascribed chiefly to the heat of reaction. Clearly, however, the differences,
although much smaller than before, are still probably in most cases beyond
the limit of error of the experimentation. It will be noticed that in the
case of the concentrated thallium cell the Cady equation is almost exactly
right ; in the cases of tin, zinc, and the concentrated lead cells the correc-
tion afforded by the heat of reaction is not enough to explain the deviation
from the simple concentration law ; in the cases of the indium cells and the
dilute thallium and lead cells, the heat of dilution supplies too large a cor-
rection, and in the case of cadmium the correction is in the wrong
direction.
It is interesting to observe that, assuming U to be constant at different
temperatures, Cady's equation predicts that the difference between the
observed values and those calculated from the concentrations alone by
the simpler equation should be independent of the temperature also. By
reference to the tables this will be seen to be the case with considerable
approximation with all the metals concerned in these tables.
The figures for thallium and lead (table 19), taken from foregoing
tables 2 and u, may serve as examples:
TABLE 19. Difference between Observed Values and Concentration Values,
in Millivolts.
Tempera-
ture.
(C.).
Cell
Cl-C2.
Cell
C*-C 3 .
Cell
C3-C4.
Cell
Pl-P2.
Cell
Pa-P 4 .
Cell
Q-Q 3 .
4.364
1. 014
0080
0.266
o 263
1-935
0.983
0.258
30
4-357
1. 000
0.266
1-957
1.022
0.242
62 ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS
This approximate constancy of the value of TT obs. TT calc. at different
temperatures had already been observed by Cady, 62 and was recognized by
him as proving the heat of dilution of the cell was constant over the range
of temperature used. His confirmation was far less exact than ours,
however. The relation is not only of theoretical interest, but is also
useful practically, as it offers a means of checking the potentiometer
measurements.
The deviations from the exact fulfilment of Cady's equation must be
ascribed, as they were in the previous paper, to the inexactness of the
expression In , as a means of estimating the free energy of the osmotic
C-L
effect. As was said before, these irregularities can hardly be traced with
exactness until precise measurements of the osmotic pressures of the amal-
gams have been made; and such are not yet available. The paper of
Richards and Forbes, already so often quoted, amplifies the obvious fact
that the formation of hydrargyrates in solution will tend to increase the
observed potential, while the polymerization of the dissolved metal will
tend to diminish it. This paper disclosed also the fact that if in the case
of cadmium allowance is made for the space occupied by the dissolved
cadmium, a large part of the difference between the theoretical and
observed values is eliminated. According to a previously made similar
observation of Morse and Frazer, 58 the excessive osmotic pressure of
sugar solutions is to be corrected in a similar way.
Very recently Lewis " has pointed out in an interesting paper that a
more generally accurate method of expressing osmotic effect is found in
the generalization expressed essentially as follows : " The activity of a
substance is proportional to its mol-fraction." Thus instead of expressing
the electrically manifested osmotic effect of a concentration cell by the
equation it ^~ In one may express it as TT= ^~ In / - -=
vb c<i vr n + NI I n + NI
where n signifies the numbers of gram-molecules of dissolved substance
and N l and N 2 those of the solvent in the two amalgams respectively.
This is essentially an application of the equation of Raoult to electro-
motive force. On the same pattern the equation of Cady would become
x _ U , RT la n + N*
vF * V F '* + &
Neither of these equations is given in just this form by Lewis in his
paper, but each is an immediate outcome of his reasoning.
M Journ. Phys. Chem., 2, page 562.
58 Am. Chem. J., 34, i (1905) ; 37, 324, 425, 558; 38, 175 (1907).
M G. N. Lewis; J. Am. Chem. Soc., 30, 668 (1908). See also Lewis, Zeit. phys.
Chem., 61, 163 (1907). In connection with this latter article, read Journ. phys.
Chem., 4, 389 (1900).
OF ZINC, CADMIUM, LEAD, COPPER, AND LITHIUM
It is easy to see that neither of these equations will give very different
results from the concentration-equations in the present cases. Indeed, if
the atomic volume of the substance in solution is the same as that of
mercury, the two roads lead to exactly the same numerical goal, as is
seen from the following logic.
It is obvious that in general N ^, where N equals the number
M A
of gram-molecules, W the total weight of substance, V the total volume of
substance and M and A the atomic weight and atomic volume, respectively.
Using capital letters to denote the solvent and small letters to denote the
dissolved substance, we have the following expression :
if a is taken to mean the atomic volume of the dissolved substance in its
dissolved state, that is to say, the increased volume which a gram-atom
causes in the mercury, and v the similar volume of the amount of the
substance under consideration. In this equation when A a both cancel,
and the last member of the equation takes a form identical with the
preceding and gives like results, but with V and v in place of N and n.
This consequence might not be perceived at first sight from Lewis's paper.
On the other hand, when A~>a, the Raoult law will give a lower theo-
retical value than the concentration law; and when A<a, the opposite is
true. The metals concerned at present have so nearly the same atomic
volumes that the deviations are very slight, as is shown in the following
table (all the cells were at oC.) :
TABLE 20. Comparison of Raoulfs Equation with Concentration Equation.
Metals.
Cell.
*At. volume
of dissolved
metal.
Comparison of
at. volume.
Calculated by
Raoult
equation.
Calculated by
concentration
equation.
Thallium
Indium
CI-C2
Ei-E2
I 7 .6
15.5
A<a
A<a
Millivolts.
29-59
12. 60
Millivolts.
29-53
12.59
Cadmium
Pure mercury. . .
R&Fi-s
II. 9
14.8
A>a
8.28
8.33
* These values are calculated from the densities of amalgams on page 13.
On comparing the last two columns, the differences are seen to be
small, and with more dilute amalgams they are yet smaller.
It will be observed that in cases of this kind both of these equations
give results very different indeed from the mode of calculation which
64 ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS
takes account only of the space occupied by the solvent, where
7r=^r In . The latter method will evidently, as has been found by
Richards and Forbes, give a much higher value. For the cadmium cell
this was found to be 8.56 millivolts at o C, instead of about 8.3 given by
the equations above, the actually observed value being 8.67 at o. 55
In any case, it is clear that the new method of calculating the results
from the equation of Raoult throws no light upon the major deviations
of the cells from the equation of Cady, for these deviations are far too
great to be explained by such insignificant alterations in the numbers
predicted by theory, and some of the changes are in the wrong direction.
On this account, it was thought unnecessary to recalculate the new theo-
retical values for each case.
As an outcome of these considerations, one may say that while the
equation of Cady in one or other of its forms affords a fairly satisfactory
means of calculating the temperature coefficient of an amalgam cell (and
probably also of other cells in which there is but little change of heat
capacity), and the best available means of finding the potential without
electrical measurement, it does not afford a good method of determining
the heat of dilution. This latter quantity is to be much more accurately
found with the help of the equation of Helmholtz, to which the reader's
attention is now directed.
EQUATION OF HELMHOLTZ.
In the first part of this monograph the temperature coefficients of the
cells consisting of amalgams of thallium, indium, and tin were used for
computing the heat of dilution, according to the equation of Helmholtz.
The same calculation may now be applied to zinc, cadmium, and lead.
Turning first to the case of zinc, we may take the cell Mi-M3 where
TT O = 24.237 millivolts and ATT between o and 29.96 . = 2.799 millivolts."
Because the temperature coefficient has been shown to be very nearly if not
quite independent of the temperature, the value given may be used at o.
Then
*vp 4679.2 joules
ATT
v FT~/p 4926.0 joules
U -246.8 joules
This value for the heat of dilution, 246.8 joules, or 59.0 calories,
is considerably greater than the value 52 joules found by actual ther-
mochemical experiments. The difference is due in part to the fact that
"Richards and Forbes, Carnegie Institution of Washington, Publication 56, p.
62 (1906). The values there given are for 23.
* This paper, p. 45.
OF ZINC, CADMIUM, LEAD, COPPER, AND LITHIUM 65
the cell in the present calculation involved much further dilution than
that corresponding to the thermochemical experiment. In the present
case one amalgam was about nine times as dilute as the other, while in the
thermochemical experiment the dilution was only to double the bulk.
Nevertheless, even allowing for the heat which would be absorbed by the
further dilution of the amalgams, it is clear that the electrochemical
estimate of the cooling effect exceeds the actual thermochemical measure-
ment. This lack of coincidence was to have been expected from the
results already chronicled in the preceding section of the monograph,
concerning thallium, indium, and tin ; in each of these cases also the ther-
mochemical effect appeared to be too small, and in the case of lead, soon
to be discussed, the same discrepancy was observed. The lack of agree-
ment is undoubtedly due not to fault in the Helmholtz equation, but
rather to the inadequacy of the clockwork stirrer used in the thermo-
chemical work. Liquid amalgams, because of their great inertia, are hard
to mix ; but their ready conductivity quickly establishes a nearly equable
temperature throughout, even when they are not thoroughly mixed.
Hence it is easy to be deceived concerning the results.
In spite of the lack of exact agreement, the thermochemical result of
Richards and Forbes is nevertheless of value, for it shows that liquid zinc
amalgams really produce a large cooling effect upon dilution, and it thus
confirms, both as to sign and as to order of magnitude, the results of the
electrical measurements.
Turning to cadmium we find that the work of Richards and Forbes has
quantitative as well as qualitative significance. By reference to the origi-
nal data," it is seen that at o ^=30.826 millivolts and ~ =0.003655,
TT U j(
therefore
fvp ...................................... 5951 joules
S9S7 J ules
6 joules
This difference is no larger than the possible error of experiment, and its
sign is therefore somewhat uncertain ; but nevertheless it is supported by
the very small cooling effect which was at that time actually found. In
this case, the inadequacy of the mixing in the thermochemical experiment
would have very little significance, because the effect to be observed
formed so trifling a part of the whole phenomenon.
In this connection it may be noted that Carhart "* assumes on the basis
of his theory, without any published experimental justification, that the
"Carnegie Institution of Washington, Publication No. 56, pp. 50 and 57 (1906).
"Phys. Rev., 26, p. 216 (1908).
66 ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS
heat of dilution of cadmium amalgams is positive, not negative. In our
experience, this assumption is contrary to fact. With the help of Dr. H.
L. Frevert one of us has found that solid cadmium amalgams produce a
large cooling effect on dissolving in more mercury, and there is every
reason to believe that the dilution of liquid cadmium amalgams is like-
wise an endothermic reaction, although its thermal effect is so small as to
make accurate measurement difficult. The dilution of a 3 per cent
cadmium amalgam with an equal bulk of mercury would evolve over 30
joules of heat if Car hart's theory were correct, and this would have raised
the temperature of the calorimetric system by 0.02. So large a thermal
effect could not have escaped detection.
This example remains the most precise verification of the Helmholtz
equation which has ever been offered, coming within the experimental
error of about o. I per cent. The interesting measurements of Carhart "
show an average deviation of nearly 2 per cent.
Turning now to lead, we find results very like those of zinc and tin.
Let us take the cell Pi-P2, of which TT O = 0.008960 and ATT for 29.96 C.
=0.001175. Then
rvF 1730 joules
ATT
vFT 2^-= 2068 joules
U - 338 joules
The attempt was made to verify this value by actual thermochemical
experiment, using the same apparatus as in the other cases already men-
tioned in the previous papers. The apparatus was not suited for exact
quantitative work, but the test was enough to show a very decided cooling
effect (of 0.018 C.) in the apparatus, and to confirm in sign and in order
of magnitude the figure calculated from the electrical measurements.
Calculated in the same way from the electrical measurements of the
other lead cells, the values for the heat of dilution are found to decrease
as the dilution increases. Figures for three lead cells are given in table
21 to serve as typical examples of this phenomenon, which of course
appears in the measurements with other metals also, in so far as their
degrees of accuracy permit. It is interesting to note that the maximum
cooling effect of dilution has not been wholly reached in a solution contain-
ing only o.i per cent of lead (or I gram-atom in 15 liters) ; for an amal-
gam of this considerable dilution is still found to absorb 20 calories more
upon dilution to fourteen times its volume. This last exceedingly attenu-
ated material would probably absorb very little more on further dilution ;
hence the limiting value is probably not far off. According to these results,
"Carhart, Phys. Rev., March, 1908.
OF ZINC, CADMIUM, LEAD, COPPER, AND LITHIUM
6 7
then, a gram-atom of lead dissolved in a hundred gram-atoms of mercury
must absorb about 540 joules or 130 calories on infinite dilution; and of
this amount about two-thirds is absorbed when the amalgam is diluted
with twice its bulk of mercury.
With these figures are repeated also, in conveniently accessible form,
the other results obtained in this monograph by the application of the
equation of Helmholtz.
TABLE 21. Heat of Dilution of Amalgams Calculated from the Electrical
Measurements.
Metal.
Designation
of cell.
Range of dilution
(per cent of metal).
Heat of dilution per gram-atom
of solid metal.
Joules.
Gram calories.
Thallium
CI-C2
C2-C 3
Ei-Ea
Gi-Ga
Ji-Ja
MI-MS
R & F i-s
PI-P2
P2-P4
Qi-Q3
1.84 to 0.53
0.53 0.23
I.Q2 0.38
0.016 0.008
0.21 0.061
0.91 o.io
2.45 0.29
1.02 0.40
0.40 0.093
o.io 0.007
+427
+ 109
+677
^
I 24 ?
-338
-117
- 77
+ 102.3
+ 26.1
+ 161.9
- I.
- I6. 5
- 59-0
- 1.4
- 80.8
- 28.0
- 20.3
Do
Indium
Do
Tin
Zinc
Cadmium
Lead . .
Do
Do
Because the heat capacity of the reacting system is essentially constant,
these values are independent of the temperature, as far as our measure-
ments were concerned. Their chief uncertainty depends upon the diffi-
culty of measuring exactly the temperature coefficients of small electro-
motive forces; but they are accurate enough to serve as a fairly close
guide to the behavior of the respective amalgams. They are hardly close
enough to serve as the basis for a search after an exact mathematical law
governing the change of thermal effect with increasing dilution, although
such a search would be an interesting aspect of yet more precise measure-
ments.
68 ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS
COMPARISON OF DEVIATIONS FROM CONCENTRATION LAW.
As in the case of the previous paper, it is interesting to compare the
deviations of the potentials given by various amalgamated metals from
the requirement of the simple concentration law. In order to make the
understanding of this matter more vivid, there are given together in the
following diagram the several curves showing the deviations of the various
potentials from the concentration equation. These lines are all drawn
upon the same scale and are arranged so that for any ordinate the atomic
concentration is identical. If the equation of Cady represented a complete
correction, it would reduce all the lines to the horizontal straight line
marked O. As a matter of fact only about three-quarters of the devia-
tions, on the average, are to be explained in this way ; and only thallium
and lead are brought nearer to the horizontal line than the unconnected
curve for cadmium.
These curves, therefore, not only give an excellent collective picture of
the behavior of these amalgams, but they enable anyone with a compara-
tively small expenditure of time to compute the potential which would
actually exist between two amalgams of the same metal between these
limits of concentration. The divisions in the direction of abscissae mean
in each case the doubling of the volume. Suppose one wished to deter-
mine the potential between an amalgam of a given concentration and that
of one-fourth its concentration. The place of the more concentrated
amalgam is found upon the proper curve and the second one will be just
two divisions to the right. The difference between the ordinates corre-
sponding to these two points will give the deviation from the exact gas
law for that particular combination. Accordingly the potential is to be
computed according to the following equation :
in which ATT designates the difference between the ordinates just men-
tioned. If any dilution other than 2, 4, 8, 16 is desired the appropriate
point may easily be found from these and a table of logarithms, it being
borne in mind that each large division in the direction of abscissae signi-
fies 0.30103 for Briggs's logarithms or 0.6932 for natural logarithms. The
scale of the curves here depicted is rather small for an accurate determi-
nation. Obviously the potential could hardly be found more nearly than
perhaps within the fiftieth of a millivolt, because the large divisions in the
direction of ordinates represent millivolts ; but this same principle might
be employed on a larger scale and with more accurate data to within any
degree of precision desired.
It will be noticed that all the curves approach horizontality as the
deviation proceeds. It is clear that long before infinite dilution is reached
OF ZINC, CADMIUM, LEAD, COPPER, AND LITHIUM
the values will accord, within a limit of error of measurement, with either
the equation of von Turin or of Cady. This seemed to us so clear that
further prolongation of the curves to the right seemed to us hardly worth
-3
log 2 Iog4 log 8 log 16 log3Z log 64- loglZB Iog256 Iog5l2 log 1024
Fig. 12. The Approach of the Potentials of all the Amalgams to the Concentration Law.
Deviations, both positive and negative, are plotted in millivolts as ordinates;
logarithms of concentration ratios are plotted as abscissae. Thallium,
indium, and cadmium give potentials greater than those corresponding
to the equation it = -r ' ~^~ ', zinc, lead, and tin give potentials less
than the actual valu
sponds to 4.00 gram
extends to amalgam
per 256 liters). Th
almost if not quite
and
solu
bl 3 eat
excepting
s thus computed. The origin of abscissae corre-
toms of dissolved metal per liter, and the diagram
1024 times as dilute as this (i. e., i gram-atom
dotted lines are extrapolated. The curves ar;
ndependent of temperature, at least between o*
n the case of tin, which is only very slightly
7O ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS
the labor involved, especially as the chance of error increases greatly as
the amalgams become more dilute. The possible appearance of a balanced
reaction at great dilution we attempted to detect by using, not greater
dilutions, but rather metals with the least possible solution-tensions. The
interesting work of Hulett and De Lury, published after ours was com-
pleted, supplements our work by carrying the curve of one of the metals,
cadmium, much further to the right than we have done. Neither of our
curves shows any certain indication of the balanced reaction for which
Hulett and De Lury were independently seeking, although several of the
metals are distinctly less electropositive than cadmium.
In conclusion, we take pleasure in expressing our obligation to the
Carnegie Institution, of Washington, for generous pecuniary assistance.
ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS 7!
SUMMARY.
The results obtained in the foregoing papers may be summarized as
follows :
(1) The electromotive forces of various cells, containing amalgams of
thallium, indium, tin, zinc, lead, copper, and lithium, have been measured
at o and 30, with many precautions against experimental errors.
(2) The temperature coefficients of cells containing zinc amalgams
were also obtained by actually opposing cells at o against cells at 30.
(3) It is shown that in every case the more concentrated amalgams
deviate by appreciable amounts from the theoretical values calculated
from the simple concentration law, thallium and indium resembling cad-
mium in giving potentials higher than those demanded by the concentra-
tion law ; whereas lead and tin resemble zinc in giving potentials lower
than those demanded by the concentration law. Thallium showed the
greatest positive deviation, and tin and lead the greatest negative deviation.
(4) It is shown further that on the average about three quarters of
each of these deviations are to be explained by the heat of dilution of the
amalgam, according to the equation of Cady.
(5) The other quarter of the deviation, not explained by the equation
of Cady, must be ascribed either to experimental error or more probably
to the inexactness of the concentration law. Such inexactness would be
caused either by polymerization or by the formation of hydrargyrates,
according as the computed potential is greater or less respectively than
the observed potential.
(6) It is shown that the equation of Cady requires that the temperature
coefficient of a cell of this type should be equal to the total concentration
effect divided by the absolute temperature, and should be independent of
the temperature. The verification of these conclusions is shown to hold
approximately in all the cases studied, by comparison with the actual
values. This fact affords a simple method of computing with moderate
accuracy the temperature coefficient of the electromotive force of cell of
this type, without having recourse to electrical measurement.
(7) It is shown that the equation of Cady is not well adapted for com-
puting the heat of dilution, for in this case all the errors and deviations
accumulate upon the smallest term of the equation.
(8) The heats of dilution of these various amalgams are computed
with the help of the equation of Helmholtz ; and it is shown, as was to be
expected, that the heat of dilution decreases very rapidly as the dilution
progresses.
(9) The difficulties of actual thermochemical measurement of the heat
of dilution of amalgams are emphasized.
72 ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS
(10) It was found impossible to obtain satisfactory results with an
electrolyte containing tin in a quadrivalent condition, either as stannic
chloride or as sodium stannate. In this connection it was pointed out
that Cady must have had a two-phase amalgam in his tin cell, and that his
results with tin were illusory.
(n) The solubility of copper in mercury was found to be only 0.0024
per cent, and of iron 0.00134 per cent by weight, amounts too small to
give satisfactory electrochemical results. The results of Meyer upon
copper are shown to be without significance, because he imagined that he
used a much. more concentrated solution, which must have been a mere
suspension of copper in mercury.
(12) It is shown that since lithium is only soluble to the extent of
0.036 per cent by weight in mercury, the results of Cady upon lithium are
likewise questionable; but more dilute solutions of lithium are shown
to behave in a general way as Cady's equation requires. No exact deter-
minations were made, because of the difficulty of finding a suitable electro-
lyte.
(13) All the deviations from the simple concentration law were found
to decrease as dilution increases, so that upon reaching a concentration
of o.oi gram-atom per liter all the amalgams investigated behaved prac-
tically as ideal solutions.
( 14) The density of pure indium at 20 was found to be 7.28.
(15) The densities of various liquid amalgams of thallium, indium, tin,
and lead were determined.
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