THE ELEMENTS
OP
ELECTEOCHEMISTEY
c
^
- THE ELEMENTS
OF
ELECTEOCHEMISTEY
BY \
5\x^.v\ 3 < S I^OM^S
MAX.LE BLANC
PROFESSOR OF CHEMISTBW IN THF, UNIVERSITY OF LEIPZIG
TRANSLATED BY
W. R. WHITNEY
INSTRUCTOR OF CHEMISTRY IN THE MASSACHUSETTS INSTITUTE OF
TECHNOLOGY OF BOSTON, U.S.A.
ILontron
MACMILLAN AND CO., LTD.
NEW YORK: THE MACMILLAN CO.
1896
All rights reserved
TEANSLATOR'S PREFACE
WITH the exception of a few alterations, either sug-
gested or accepted by Professor Le Blanc, the present
work is as nearly as practicable a literal translation.
The rapid advance of the subject within the past
few years has rendered treatises which adequately
present it scarce, therefore I hope to have satisfied a
want, and to have increased the facility of study for
the English reader in this field.
It is with pleasure that I express here my great
indebtedness to Mr. J. A. Craw of Glasgow, Scotland,
for the aid he kindly gave me in the translation,
and to Professor A. A. Noyes of the Massachusetts
Institute of Technology, Boston, U.S.A., for correcting
the proofs.
W. E. WHITNEY.
AUTHOR'S PREFACE
THE greater part of the present work was written
during the winter term 1894-95 in connection with
a course of lectures which I was then delivering. It
is intended for students of science and those who,
having studied the subject, are already in practice, as
well as for those interested in electrochemistry. I
have endeavoured to write as clearly and simply as
possible, but for those whose previous knowledge of
the subject is very slight, a careful study of the book
is necessary before its maximum utility can be reached.
There are certain methods of conception used in
modern electrochemistry which the student must make
his own, and this process does not take place without
study.
The book presents a view of the present state of
the subject, and may contain some new ideas. The
references to the literature are limited to the most
important articles. It would scarcely have been
possible for me to write the book without personal
viii ELECTROCHEMISTRY
contact with Prof. Ostwald and access to his papers
on electrochemistry. The dedication of the book to
him is an expression of my gratitude.
Finally, I must not neglect to thank Dr. A. Dalims,
Dr. M. Trautscholdt, and Dr. J. Wagner for their kind
aid in reading the proofs.
M. LE BLANC.
LEIPZIG, end of September 1895.
CONTENTS
CHAPTER I
PAGE
INTRODUCTION : FUNDAMENTAL PRINCIPLES OF ELECTRICITY . 1
CHAPTEE II
DEVELOPMENT OF ELECTROCHEMISTRY UP TO THE PRESENT
TIME . 28
CHAPTEE III
THE ARRHENIUS THEORY OF DISSOCIATION .... 52
CHAPTEE IV
THE MIGRATION OF THE IONS ....... 62
CHAPTEE V
THE CONDUCTIVITY OF ELECTROLYTES 79
CHAPTEE VI
ELECTROMOTIVE FORCE 124
ELECTROCHEMISTRY
CHAPTER VII
PAGE
POLARISATION . ... 243
CHAPTER VIII
THE ORDINARY GALVANIC ELEMENTS AND ACCUMULATORS . 268
SUBJECT INDEX 279
LIST OF AUTHORS' NAMES 283
CHAPTEE I
INTRODUCTION : FUNDAMENTAL PRINCIPLES OF
ELECTRICITY
Energy. A clear conception of the fundamental
principles of energy is essential to a successful study
of electrochemistry, consequently we shall first con-
sider the different forms of energy and their relations
to each other.
The important role which energy plays in human
affairs is well known. If we buy coal or an article
of food, the important point to be taken into con-
sideration is, in reality, the quantity of energy we are
obtaining. The same holds true if the purchased sub-
stance is the electric current. The quantity of electrical
energy which the electric current gives us, determines
its cost.
We recognise five distinct kinds of energy, as
follows :
1. Mechanical Energy.
2. Heat Energy.
3. Electrical Energy.
4. Chemical Energy.
5. Eadiant Energy.
These different forms of energy are capable of
changing, one into another. For some of them arbitrary
B
2 ELECTROCHEMISTRY CHAP.
units have long been accepted. In the case of mechani-
cal energy, for instance, the unit commonly employed
in technical applications is that quantity of energy
which is expended in raising a gram- weight one centi-
meter high.
For the scientific measurement and expression of
quantities of mechanical energy, the centimeter-gram-
second system is in common use. According to this
system the unit of work, the erg, is the work which is
expended in moving the unit of mass (the mass of a
gram), the unit distance (the centimeter), against the
unit of force (the dyne).
The dyne or unit of force has been chosen as that
force which, in one second, produces in the mass of
one gram an acceleration of one centimeter. Gravita-
tion acts upon the gram-mass, producing an accelera-
tion of 980*6 centimeters, consequently the force of
gravity acting upon that mass amounts to 980*6 dynes.
The difference between the mass of a gram and the
weight of a gram must be kept in mind. The former
is invariable, and its unit is the mass of a cube of
water one centimeter on each edge when at 4 C.
The mass of any body, which, acted upon by the same
force, received the same acceleration as the above mass
of water, could serve as the unit of mass. 1
The weight of any body, on the contrary, depends
on its position, and, in general, becomes greater or less
as the body is moved nearer to or farther from the
earth, although the mass of the body does not change.
The gram -weight represents, then, that force with
which the gram-mass is attracted towards the earth,
1 As a matter of fact, a certain piece of platinum preserved in
Paris, which is about a thousand times as great as the above-described
unit, serves as unit of mass.
i FUNDAMENTAL PRINCIPLES OF ELECTRICITY 3
and since this is capable of imparting to a body a
mean acceleration of 980*6 cm. per second, we say that
the gram -weight is equal to 980'6 dynes, and the
technical unit of work 1 gm. cm. = 980*6 dynes cm.
= 980*6 ergs. Possessing such a system of units, we
can express the quantities of mechanical energy in
given cases, and can compare them with one another.
The unit of quantity which has been chosen for heat
energy is the hundredth part of the heat which is
necessary in order to raise the temperature of one gram
of water from zero to one hundred degrees centigrade.
After having chosen units for two kinds of energy,
we are able, aided by the law of the conservation of
energy, to determine how many units of the one kind
are equivalent to one of the other. By experiment, it
has been learned that 43280 gm. cm. = 42440 x 10 3
ergs, changed into heat, produce the heat-unit mentioned
above, which has received the name calorie. Conse-
quently, this quantity is called the mechanical equivalent
of heat. We might proceed in a similar manner with all
the five kinds of energy, but practically, the electrical
energy is the only other one for which units have as
yet been established. It is possible then to determine,
besides a mechanical equivalent of heat, an electrical
equivalent of heat and a mechanical-electrical equivalent.
We shall learn more about these values later.
We are satisfied at present to accept the fact of
the changes of energy from one form to another without
raising the question as to the circumstances under
which these changes take place, or as to the conditions
of equilibrium.
We will first study the case where two systems
possessing different amounts of the same kind of
energy are so arranged that the energy of one may
4 ELECTROCHEMISTRY CHAP.
pass into the other. Let us apply this consideration
to the volume -energy of two gases; volume -energy
being a kind of mechanical energy, we may measure
it in the above-described mechanical units.
If we have a mass of gas in a closed vessel, we
say that the gas possesses a certain amount of volume-
energy, because in expanding it is capable
of performing work. 1 Imagine a vessel
having the form given in the cut standing
in a vacuum and containing a movable
piston, A, weighing 100 grams ; if now,
by the expansion of the gas, the piston be
raised from a to I, the distance being 50
cm., then by means of the volume-energy
of the gas 100 grams have been raised 50 cm., that
is, 100 times 50 or 5000 units of work have been
produced ; consequently, the volume-energy of the gas
has been decreased by this amount. If the piston had
an area of 1 sq. cm., the unit of its area would weigh
one gram, and we should say that the piston exerted a
pressure p of one gram. The volume v by which the
gas has been increased in this movement of the piston
is 5000 cc., the product pv, expressed in grams and
cubic centimeters, is also 5000, or the product pv gives
us the number of units of work which were produced.
Imagine a horizontal vessel, as in Fig. 2, arranged
1 It may remove a source of error to add here that the work which
can be produced by the expansion of a gas is not derived from the
internal energy of the gas. The gas is only the medium or agent
which changes heat from the surroundings into work. If we say that
a gas has a certain amount of volume-energy, we mean simply that the
gas is capable of producing an equivalent amount of mechanical energy
at the expense of the heat of its surroundings. Keeping this in mind,
we may consider, for simplicity, that the volume-energy is possessed
by the gas itself.
i FUNDAMENTAL PRINCIPLES OF ELECTRICITY 5
with a movable piston C, containing hydrogen on the
left and nitrogen on the right of the piston. If the
gases exerted equal pressure
upon the piston it would re-
main at rest. There would
he no passage of energy from
one of the gases to the
other. The transference of energy is thus independ-
ent of the absolute quantities of energy which come
into contact, since the gas filling the larger space
has a greater quantity of volume -energy than the
other. This difference in quantity may be made
as great as desired by a proper choice of relative
volumes ; but if we change the density of one of the
gases and consequently its pressure, the piston is
set in motion, the volume of the denser gas increases,
the gas loses volume-energy, while the volume of the
other gas is diminished and its volume-energy increased.
Equilibrium will again exist when the pressure exerted
upon the. piston by both gases has become the same.
Eepresenting energy in general by E, the volume-
energy of any body is expressed by the equation
E=w. To the factor p belongs, as we have seen,
the important property of determining the equilibrium,
and we call this the intensity-factor. The other quan-
tity v is then simply equal to =- '-. It determines
the amount of energy which, at a given intensity, exists
in a system, and is called the capacity-factor. It is
in this case evidently the volume.
It has been possible to decompose several of the
forms of energy into two such factors capacity- or
quantity- and intensity-factors, and this greatly aids
in an understanding of energy phenomena.
6 ELECTROCHEMISTRY CHAP.
Electromotive Force, Current-Strength, Resist-
ance. Electrical energy is to be considered as the
product of the two factors : electromotive force (poten-
tial or tension), (TT), and quantity of electricity (e).
(Here the distinction between quantity of electricity
(e) and the en3rgy (E) is evident.) The former quan-
tity represents the intensity-factor, and the latter the
capacity-factor. This will be made clearer in the
following pages.
On account of our limited sense of perception of
electrical phenomena, we are not in position to
comprehend them to the extent possible in the case
of mechanical energy. The action and effects of
electrical energy must first be experimentally studied.
The imagination would not be able to grasp the idea
of the unit of work, or, let us say, of a meter, if the
action of the unit of work had not first been learned,
or if the length, which is represented by a meter,
had not been observed.
If we take a vessel which is divided into two parts
by a porous plate, as one made of unglazed porcelain,
and pour into one part a solution of copper sulphate,
and into the other a zinc sulphate solution, then put a
strip of copper into the copper and a strip of zinc into
the zinc solution, we have an arrangement called a
galvanic element.
If we connect the zinc and copper strips (the two
poles of the element) by means of a wire, the wire
becomes heated. If we bring a magnetic needle near
it, the needle is turned from its natural position.
Finally, if we cut the wire, fasten a piece of plati-
num foil to each of the two ends, and dip these pieces
of foil into a copper sulphate solution in such a manner
that they are not in contact with each other, we observe
i FUNDAMENTAL PRINCIPLES OF ELECTRICITY 7
that metallic copper separates upon one of the pieces
of platinum.
From these observations we must conclude that in
this connecting wire some process takes place, for we
have observed effects which were not observable before
we united the zinc and copper with the wire. When
such effects are produced as here observed, we say that
an electric current is passing through the wire. It is
conceivable that we might have a case in which the
wire would affect the magnetic needle, but would not
be heated, or would not possess all the properties
peculiar to the electric current. This was formerly
supposed by many to be true, but, as a matter of fact,
such is not the case. We know from long experience
that if a wire exhibits one of the above three pheno-
mena, it also exhibits the other two, as well as a
number of others which are not of interest here. That
many of the phenomena may be made to disappear
under the conditions of the observations does not
contradict the above statement. We are now able by
proper arrangements to ascertain the properties of the
electric current.
If in a galvanic element, as previously arranged, we
simply change the end connections so that the end which
was formerly joined to the zinc is now joined to the
copper, and the other end now joined to the zinc, we
observe the same phenomena, with the simple difference
that the magnetic needle is influenced so as to move
in the opposite direction and that the copper is precipi-
tated upon the other piece of platinum ; consequently
we may properly speak of the direction of the electric
current.
Naturally, the next thing to observe is whether the
deflection of the magnetic needle or the amount of
8 ELECTROCHEMISTRY CHAP.
copper separating out in a given time always remains
the same, and upon what the variation depends, if there
is any. To this end we lengthen the connecting wire,
and observe that the rate of the precipitation of copper
is decreased, while by shortening the wire the rate
becomes greater. We therefore conclude that the
electric current has a strength dependent on circum-
stances, and we obtain an idea of current -strength.
The current-strength has been decreased by increasing
the length of the wire, and increased by shortening ;
therefore the wire hinders, to a certain extent, the
passage of the current, i.e. the wire possesses a
certain resistance. We have found that the greater
the resistance, the less is the current-strength. Now
the question arises : Is it possible to change the
current - strength without altering the resistance ?
Experiment answers, Yes. If, instead of using one
electrical element, we use two, the zinc of one con-
nected with the copper of the other, we obtain a much
greater current-strength, although the resistance of the
circuit has been increased by the introduction of the
second element. Here the effect is as if the pressure
under which the electric current is driven through the
wire had been increased, and consequently we come
to speak of the electromotive force.
We may now assume that the words current-
strength, resistance, and electromotive force are not
meaningless terms to the reader, but that their use
is understood. We must now proceed to study the
units of these quantities, and in doing so we shall
follow a simpler way than that by which these units
were established. The electromotive force of the
previously described element (named, from its dis-
coverer, the Daniell element), the concentrations of
i FUNDAMENTAL PRINCIPLES OF ELECTRICITY 9
the two solutions being alike, we place at 1*10 unit,
and give to the unit the name volt. For the unit of
resistance we use that resistance possessed by a
column of mercury 106'3 cm. long, and of one sq.
mm. cross-section at zero degrees. This unit is called
an ohm. By the unit of current-strength we mean
that current by which 0'328 mg. of copper are pre-
cipitated in a second. This is called an ampere. 1
Why just these quantities have been accepted as
units need not occupy our attention here ; it is a
question belonging more to the history of the subject.
We already know that the current -strength is
dependent upon the electromotive force on the one
hand, and upon the resistance on the other. Ohm
made the assumption that the current-strength is
directly proportional to the electromotive force, and
inversely proportional to the resistance. This as-
sumption has been proved correct. We may write
electromotive force
current-strength = r k,
resistance
where Jc is a ratio-factor dependent upon the chosen
units, but we have here chosen the units, so that if
there exists in a circuit whose resistance is one ohm
an electromotive force of one volt, the current-strength
is exactly one ampere. Accordingly
volt
ampere = ,
ohm
the factor k in this case being 1. If we had chosen
1 These terms, as well as the coulomb and farad (explained later),
have been derived from the names Volta, Ohm, Ampere, Coulomb,
and Faraday, men whom we may call the pioneers of the science of
electricity.
10 ELECTROCHEMISTRY CHAP.
a unit ten times as great for current-strength, k would
have been O'l.
We are now in a position to see how unknown
electromotive forces and resistances are determined.
It is evident that to determine the current-strength it
is only necessary to ascertain the number of milligrams
of copper precipitated in a second, and divide this
number by 0'328 ; the quotient is the current-
strength in amperes. If we wish to determine the re-
sistance of the circuit, we may take a Daniell element
possessing an electromotive force of 1*10 volt, and
measure the current-strength which it produces in the
circuit. Let us say that we obtain O'OOl ampere, then
according to Ohm's law the resistance must be 1100
ohms.
1-10
o-ooi
7T
= 1100 ohms
( C = = ; C = current - strength ; TT = electromotive
7T\
force ; R = resistance ; consequently R = ^ J.
If now we connect into the same circuit, instead of
the Daniell, an unknown electromotive force (TT), and
do not alter the resistance, we can easily learn the
value of TT in volts by measuring the new current-
strength. Let us say, for example, that we have here
a current-strength of - ampere, then the electro-
motive force is 7r== T^- 1100 = 11'0 volts.
In order to obtain still clearer ideas of the electric
current, let us consider its analogy to a stream of
water. Electromotive force corresponds to the
pressure of the water, the electrical resistance to the
friction -resistance, and the strength of the electric
i FUNDAMENTAL PRINCIPLES OF ELECTRICITY 11
current to the current-strength or rate of flow of the
stream of water. "When we say that a stream
possesses a certain current, we mean that in a unit of
time a certain quantity of water passes through a
cross-section. A unit for current of water has not
been established for scientific use. We might con-
sider as a unit the current by which one cubic meter
passes in a second.
Just as we speak of the quantity of water in
the stream, we may also speak of the quantity of
electricity in the electric current, without necessarily
imagining the electricity to be of a material nature.
When the current-strength or current is an ampere,
we say that the unit of quantity of electricity passes
in a second ; this unit of quantity is called the
coulomb. The total amount of electricity which has
passed through a cross -section of a conductor is
obtained by multiplication of the current-strength by
the time during which the current has passed.
It is common in the science of electricity to
distinguish between electromotive force and potential
or tension (potential-difference or tension-difference).
The name electromotive force applies to that potential
of the element depending upon its chemical composition,
and this remains unaltered as long as the element
remains constant. It may be compared with the pres-
sure which forces a quantity of water through a pipe.
The potential or tension is that electric pressure which
we may find at different places along the conductor.
In most courses in physics the following experi-
ment is performed. Water under a certain pressure is
driven through a narrow horizontal tube, upon which
are a number of perpendicular tubes or water gauges
(see Fig. 3).
12
ELECTROCHEMISTRY
CHAP.
The height of the water in any of the perpendicular
tubes is a measure of the pressure with which the
water is driven through the horizontal tube at that
point. If we con-
sider the part of
the tube from a to
I, the pressure has
fallen from H to
h, and with the
latter pressure, A,
it makes its exit
* from the tube.
The amount of
work which may be obtained when a quantity of
water, M, under the pressure p (per sq. cm.), passes
through the tube is Mp. The quantity of water,
M, in moving from a to 5 has had its efficiency
lowered from MH to M.h. The quantity of energy,
M (H h), has therefore been used to overcome the
resistance in the tube, that is, this energy has been
changed into heat which has been absorbed by the
surroundings and consequently lost to us. There
remains only the quantity of work MA, which is still
available, and may be applied in some way, as, for
instance, in moving a turbine. It is evident how
much depends upon the size of the conducting tube ;
the greater this is chosen the less will be the resistance,
and consequently the greater will be the amount of
available work at the exit.
Similar relations exist in the case of the electric
current. Let the wire, AB (Fig. 4), representing a com-
plete electric circuit, be drawn as a straight line. Just
as we measured the pressure of the water in the
tube by its height in the gauge tubes, we may here
FUNDAMENTAL PRINCIPLES OF ELECTRICITY
13
measure the tension or potential by an electrometer
(to be explained later).
We find at A the potential (here electromotive force)
TT, at B the potential 0, if B is attached to the earth by
a 'conductor. Furthermore, just as previously, when we
allow a quantity of electricity (e) to flow through the
circuit, we have at A the electrical energy ?re, and at
B, 0. The total energy Tre has been changed into
heat between A and B, and has disappeared.
If now we cause work to be done, as, for example,
in the decomposition of a solution at some point of the
circuit, we may use almost the whole of the electrical
7T
A
FIG. 4.
FIG.' 5.
energy in the work ; and moreover, it is immaterial at
what point of the circuit we have the work done.
Only a very small part of the energy is lost as heat,
this amount depending upon the material of the
circuit, its sectional area, etc. If we place the
solution to be decomposed at c (Fig. 5), an electro-
meter would show us the above depicted fall of
potential at this point, if the quantity of energy ire
were almost entirely used for decomposing the solution.
Fig. 6 represents the fall of potential in the case
where the energy used in doing work is only half
of the amount ire.
It is possible to use almost all of that energy
14
ELECTROCHEMISTRY
which in our analogy with the water was represented
by M (H A), and which was there entirely lost as heat.
If we close the tube at I, the pressure rises immedi-
ately from h to H, and we obtain at this point
the quantity of energy MH, which we may employ as
desired. The stream of water differs from the electric
current in that the former may leave its conductor
while still in possession of a certain amount of kinetic
energy, while this property is not possessed by the
latter.
We may picture the fall of potential throughout
,7T
FIG.
FIG. 7.
any galvanic circuit by the method just employed. At
a certain point the potential has its greatest value, and
it falls regularly to throughout the circuit when
the resistance of the circuit is the same in every part.
If work is to be performed requiring a certain amount
of electrical energy, and consequently a certain poten-
tial, the latter falls by a definite amount at the point
where this work is done. If this fall be = p, the
remaining potential IT p falls regularly throughout
the whole circuit. If the circuit does not possess the
same resistance in every part, the fall of the potential
takes place in the different parts in proportion to their
i FUNDAMENTAL PRINCIPLES OF ELECTRICITY 15
resistance. For example, in Fig. 7, if the resistance of
AB is twice as great as that of BC and four times as
great as that of CE, the fall of the potential takes
place as represented, TT being the electromotive force
in the circuit. This result follows of necessity from
Ohm's law (C = =), which serves as well for the whole
circuit as for each part. The value of TT for any
portion of the circuit is the difference of potential
between the two ends of that part, and E is the
resistance of the part. For the case illustrated by
Fig. 7 the following equations are true, since, as also in
the case of the stream of water, the current-strength
is the same throughout the circuit, independent of the
arrangement of the resistances of the parts.
r\
=
In consequence of this fact, the potential differ-
ences between the single points must be proportional
to the corresponding resistances. Whether the re-
sistance in the circuit is that of a metallic or of a
liquid conductor, or of both together, this statement
is true.
In a galvanic element whose poles are simply con-
nected by a wire, the resistance of the circuit consists
of that of the wire, called the external resistance, and
that of the liquids which are in the element, its inter-
nal resistance. If the external resistance is 1000 ohms,
and the internal 100 ohms, while the electromotive
force of the element is 1*10 volt, the fall of potential in
the external resistance is 1 volt, and in the internal
resistance O'lO. Thus we see that there is a difference
between the electromotive force of an element and
16 ELECTROCHEMISTRY CHAP.
the potential - fall which may exist in the circuit
outside of the element, and it is evident that the
greater the external resistance, the nearer the potential-
fall through that resistance approaches the electro-
motive force of the element. The potential-fall in the
circuit is always less than the electromotive force of
the element, but approaches the latter as the external
resistance approaches infinity, or the internal resistance
zero.
We have previously assumed from analogy that the
expression ire represents the electrical energy, it being
the product of the quantity of the electricity, into its
intensity or potential. Could another expression as
7T6 2 .express this energy? This we can determine
experimentally. Let us assume that there exists
in a circuit an electromotive force, TT, expressed in
volts, or in other words, the total fall of potential in
the circuit is from IT to 0. It may be here mentioned
that the beginner is inclined to fall into error through
the above expression by assuming that the value of TT
remains the same throughout the circuit, which, as we
have seen, is not the case. Let us also assume that in
the unit of time the quantity of electricity e expressed
in coulombs passes through the cross-section of the
conductor, or, as we may also say, since the quantity of
electricity in the unit of time is the current-strength,
that the current is e expressed in amperes. Imagine
the whole circuit placed in a calorimeter. The entire
electrical energy is here changed into heat through the
resistance of the circuit, and in the unit of time that
quantity of heat should be generated which is equiva-
lent to the product TTC, if this product properly ex-
presses the electrical energy.
If now we employ another circuit in which the
i FUNDAMENTAL PRINCIPLES OF ELECTRICITY 17
electromotive force is - and the current-strength 2?r,
the amount of heat generated in the unit of time would
be the same as in the former case, since - . 2e = TTC. In
2
fact, for any values of TT and e which give this pro-
duct, the heat generated in the time-unit would be the
same. From experiment we know that such is actually
the case. Moreover, if e is kept constant and the
electronic tive force is made 2?r, twice as much heat
would be developed as above, and so forth. Conse-
quently it is proven that the product Tre is an expres-
sion for the electrical energy.
The calculation of the electrical equivalent of heat
is now very simple. The unit of electrical energy is
naturally the product of 1 volt by 1 coulomb. It is
only necessary to measure the heat generated when a
coulomb of electricity passes through a circuit whose
electromotive force is 1 volt; or expressed differently,
when a coulomb experiences a fall of potential of 1
volt, independent of the resistance, since the latter
only determines the time in which the fall takes place,
while the energy is independent of the time.
If this amount of heat is K calories, ^ is the
electrical equivalent of heat, and represents the number
of units of electrical energy which are equivalent to
the unit of heat. It has been found that volt x coulomb
= 0*236 cal., or 4'24 x volt x coulomb = 1 cal. More-
over, since in mechanical energy 43280 gm. cm. = 1
cal., we have volt x coulomb = 10210 gm. cm. for the
mechanical-electrical equivalent.
?re represents the electrical energy which has
passed through a wire between whose ends there was
a potential difference, TT, and through which the quantity
c
18 ELECTROCHEMISTRY CHAP.
of electricity e flowed. If we allow this energy to
change completely into heat, we may write the equa-
tion Tre = JcA., where A is the total heat set free, and
Jc a factor depending only upon the ratio existing
between the units used in expressing the two kinds
of energy. If we represent the current-strength by
C, we have TrC = ka, where a is the heat generated in
the unit -time. According to Ohm's law 7r = & / CK,
and substituting this, we get C 2 R = &'X R represent-
ing here resistance, and k' and k" factors of proportion
depending upon chosen units. This last equation may
be put into the following words : The heat generated in
the whole or a part of a circuit in the unit of time is
proportional to the resistance and to the square of the
current -strength. This is known as Joule's law, and
was discovered by him in 1841. Its experimental
proof is a demonstration of the validity of Ohm's
law.
If we choose as units for a, R, and C, the calorie,
the ohm and the ampere, then the number of calories
generated in the unit of time becomes 0'236 X ampere 2
X ohm, 1 for volt x ampere = ampere 2 x ohm represents
the electrical energy available in the unit of time. One
such unit, transformed into heat, gives 0'236xcal.
^ units =0*2 3 6 % cal. The number of units (^)
present is expressed by the product ampere 2 X ohm.
Capacity. It may be well at this point to explain
the term electrical capacity, although it has more to do
with statical electricity than with our present subject.
It is to be especially noted that this so-called electrical
1 The following may be of interest. A volt-coulomb, called also a
joule, is equal to 10 7 ergs, 1 volt-ampere, also called a watt, is equal
to ~ second-kilogram eter =^ horse-power =10 7 second-ergs, the erg
I FUNDAMENTAL PRINCIPLES OF ELECTRICITY 19
capacity is quite distinct from the capacity-factor of
electrical energy, or the quantity of electricity.
By electrical capacity we understand the ability a
body possesses of taking up or holding electricity. This
evidently depends upon the nature of the body and
also upon the pressure or potential under which the
electricity exists. At the same pressure of electric
charge the capacities of different bodies are in the
same proportion as the quantities of electricity taken
up by them. The capacities of bodies upon which
equal quantities of electricity are present, under
different pressures or potentials, are inversely pro-
portional to those pressures. In general c = -, c being
the capacity. The unit of capacity is called the farad,
and is that of a condenser upon which the quantity of
electricity 1 coulomb produces a potential of 1 volt.
Positive and Negative Electricity. Thus far we
have considered the electric current in its analogy to
the stream of water, and this is an aid at first to
an understanding of the phenomena. The- analogy
is not however a perfect one, and care must be taken
to prevent misguidance. In the case of the electric
current we are dealing with something more compli-
cated than a stream of water.
If we introduce a solution of copper chloride into a
circuit as previously described, we observe that while
copper is separating at one of the pieces of platinum,
chlorine is separating at the other ; if we imagine the
copper to be transported by the electric current to the
one electrode, we must also picture to ourselves the
chlorine as carried in the opposite direction to the
other electrode. We are obliged then, from this motion
of ponderable material in two directions, to ascribe to
20 ELECTROCHEMISTRY CHAP.
the electric current, unlike the stream of water, two
oppositely directed motions. But we know from the
elements of statical electricity, that we have to deal
with two kinds of electricity, distinguished by the
names positive and negative; hence the conclusion
follows that the electric current consists of simultan-
eous motions of positive electricity in one direction
and negative in the other; a conclusion which is
supported by electrometric experiments later to be
described. The particles of copper always move in
the direction of the positive, the chlorine in the
direction of the negative electricity.
The conditions found in the case of the factors of
electrical energy differ somewhat from those of mechan-
ical energy, as will here be shown. The product
volume X pressure represents a quantity of mechanical
energy. We know that the capacity-factor, here the
volume, is always a positive quantity for we recognise
but one kind of volume, but in the electrical energy
we have two kinds of capacity-factors, + e and e.
For these factors we have the law that the amount
+ e combined with the amount e always gives the
amount 0. A quantity of positive electricity cannot
exist without the existence of the corresponding amount
of negative electricity, and the two on coming together
neutralise each other. We must accustom ourselves
to think of something abstract and cannot expect
electrical energy to represent anything as tangible as
matter itself. By careful consideration we find, more-
over, that if the word substance seems intelligible,
we have no reason to consider the expression quantity
of electricity, or electricity, unintelligible. Let us be
clear first as to what we understand by substance.
We speak of substance when we recognise a certain
i FUNDAMENTAL PRINCIPLES OF ELECTRICITY 21
number of properties at a single place ; one of the
properties is, for instance, the occupying of space,
that is, the presence of a certain amount of volume-
energy. If we compress the substance we diminish
its volume, and an amount of work is done which is
the equivalent of this compression.
In a similar manner, we learn to speak of electrical
energy at a point where we recognise the presence of
a number of definite properties or qualities. These
properties are not, however, the same as those possessed
by matter. A volume-energy cannot be ascribed to
electricity, and we cannot grasp it with the hand. It
is frequently asked : What are we to understand by a
quantity of electricity, or of what nature is electricity?
but one seldom inquires of what nature is matter. The
former question is really as idle as the latter. The
words matter and electricity are nothing more than
expressions for a number of definite properties.
We may transform mechanical work into electrical
energy, as, for instance, by rubbing a stick of sealing-
wax with a woollen cloth, but we always find that the
cloth as well as the wax has become electrically
charged by the process ; the one with positive, and
the other with negative electricity. It is a well-
known law of nature that whenever electrical energy
is produced it always appears in two separate places,
though they may lie exceedingly close to each other.
We usually speak of a quantity of electricity (e) as
passing through the cross-section of a conductor, and
also consider it as moving in that direction in which
the particles of copper move in the electrolysis; but,
as a matter of fact, we must recognise that the
quantity + - only is moving in this direction, while
22 ELECTROCHEMISTRY CHAP.
- always moves in the opposite direction. 1 The
a
movement of positive electricity in one direction is
equal to that of the negative in the opposite direction,
and we are really therefore justified in considering it
as a motion of the two quantities as of one sign, say
positive, in the one direction, that of the particles of
copper. This is done for simplicity, and we must
always bear in mind that it does not represent the
exact truth, otherwise we should not be able to under-
stand, for example, the treatment of the following
electrometric measurements.
Electrometric Measurements. In measurements
of any kind it is necessary to establish a zero or
starting - point. For the intensity - factor of heat -
energy, the temperature, we know the absolute zero-
point to be -273 C. For the in tensity -factor of
volume -energy, the pressure, we have a zero -point
from which we begin to measure pressures, viz. the
pressure zero existing in a vacuum. In the case of
speed of motion we do not have such an absolute
zero-point, but must always speak of relative motion.
In this case we usually consider the motion of the
earth as zero, and when we say that a body possesses a
speed of v f we actually mean that this is the difference
between its absolute rate of motion and that of the
earth. We reason very similarly in the case of the
intensity -factor of electrical energy, the potential,
which only appears in the form of differences, and we
know no absolute zero-point from which it may be
measured. We take arbitrarily for zero the potential
or tension which exists on the earth's surface. If we
wish to bring the potential of any point of an electric
1 Exceptions to this rule will be treated under the heading Shares
of Transport, or Transference Numbers.
i FUNDAMENTAL PRINCIPLES OF ELECTRICITY 23
circuit to the potential 0, we simply connect this
point with the earth by a good conductor.
Electric potentials are commonly measured by
electrometers, of which there are many forms, most
of which need not be considered here. The principle
is the same in all, and may be understood from
a description of one of the simplest forms, the well-
known gold leaf electrometer. The two strips of
gold leaf hanging together are first connected with
the earth, and have then the potential zero. If now,
after disconnecting from the earth, we bring into con-
tact with this electrometer a point whose electric
potential is to be measured, positive or negative elec-
tricity passes from this point to the strips of gold leaf,
and these separate, flying farther apart the greater the
charge or quantity of electricity given them. This
quantity is dependent upon the pressure of the
electricity or the potential, and consequently the
electrometer is a measure of this potential. The
electrometer can be so gauged that the potential, in
volts, may be read from a scale attached to it.
Let us now consider for a few moments an electric
circuit, the resistance of which is the same in all parts,
with a source of electrical energy having a potential
of 2 volts at the point AB, Fig. 8. We apply the
electrometer to different parts of the circuit, connecting
other points with the earth, and thus learn much con-
cerning the nature of the potential in the circuit.
If we connect the middle point of the circuit (C)
with the earth, and bring the electrometer in contact
with the circuit at A, the source of the positive elec-
tricity of the circuit, the electrometer shows us that
there is here a potential of one volt, and the electricity
may be shown to be positive.
24
ELECTROCHEMISTRY
CHAP.
If the electrometer be placed at B, the source of
negative electricity, a potential of one volt is also
shown, but of negative electricity ; at the point C the
electrometer shows no potential. Between A and C,
and B and C, we find all possible potentials between
and 1 volt, the fall of potential being always propor-
tional to the resistance ; the only difference being that
between A and C the charge given the electrometer is
always of positive electricity, while between B and C
it is negative. This same arrangement of potential is
A B
FIG. 9.
present if no point of the circuit be connected with
the earth, that is, when the circuit is isolated.
If now the circuit be connected with the earth at
B, the electrometer shows positive electricity through-
out the circuit. At A the potential is 2 volts, at C,
1 volt, and at B, ; between these points the gradual
fall is proportional to the resistance.
By connecting A with the earth instead of B, we
find only negative electricity in the circuit, 2 volts at
B, 1 volt at C, and none at A. The conditions are
then comparatively simple, but may be made still more
evident by a graphical representation as follows :
Imagine the circuit unrolled and arranged so that the
FUNDAMENTAL PRINCIPLES OF ELECTRICITY 25
line AB is the axis of abscissae of a co-ordinate system.
At separate points throughout the circuit the potential
may be represented by ordinates drawn at those points,
the potential zero being at the line AB ; potentials of
positive electricity may then be drawn above, and of
negative below this line.
According to this arrangement, Figs. 9, 10, and
11 represent the three cases just considered.
Moreover, we can represent the conditions existing
when any point of the circuit is connected with the
earth, the potential at that point being zero. We need
A
c
FIG. 10.
FIG. 11.
only to draw through the ordinate of that point, in one
of the above figures, a line parallel to the old to serve
as a new axis, remove the former, and we have the
potentials of positive electricity as before above, and
those of negative below the zero line. From Fig. 10,
for example, we obtain Fig. 9 by drawing through C 1
a line parallel to AB, and likewise Fig. 1 1 by draw-
ing the parallel through A 1 . In the former case the
arrangement is that obtained when C is connected
with the earth, C 1 becoming then ; in the latter case
A is connected with the earth, and A 1 becomes 0.
If work is done by the current, and in conse-
quence at a certain point there is a sudden fall in
26 ELECTROCHEMISTRY CHAP.
potential, the above method of graphical representation
is still as simple as before.
Another property of electrical energy is to be
mentioned : If we have two sources of such energy,
as, for instance, two Daniell elements having equal
electromotive forces, and we combine the source of
negative electricity of each, its negative pole, with the
positive pole of the other, the resulting combination
has an electromotive force equal to the sum of the
forces of the two elements, or 2 '20 volts. If they
were connected between like poles there would be no
current through the circuit. Here we have entirely
different relations from those existing in the case of
temperature. We cannot add the intensity-factors of
heat-energy in this way. If we have two pieces of
metal, each having a temperature of C. at one end,
while the temperature of the other end is 100, they
can in no way be so combined as to produce a tem-
perature of 200.
With electrical energy, when a potential differ-
ence exists between two points, this difference is not
altered through a change involving simply an increase
in the absolute potential of those points ; and because
of this law, we are able to produce an electromotive
force of any desired magnitude. If the negative pole
of a Daniell element be connected with the earth, the
positive pole shows a potential of -f- 1*10 volt; if now
we connect to this positive pole the negative pole of
a second Daniell element, we find a potential of + 2*20
volts at the positive pole of the latter, for its negative
pole has now the potential of the positive pole of the
first element, and the difference between its two poles
is I'lO volt. This arrangement of elements into
batteries is commonly called single series or tandem.
i FUNDAMENTAL PRINCIPLES OF ELECTRICITY 27
Another method, useful for certain purposes, con-
sists in connecting like poles of different elements in
groups, and then connecting by a conductor one of
these groups of like electrodes to the other. In this
way, although no increase in the electromotive force
over that of. a Dingle element is obtained, the internal
resistance of the battery thus formed is less than that
of the single element. This is called a parallel arrange-
ment of elements.
No attempt will be made here to give an explana-
tion of the production of the electricity, with its
current in two directions, or of the real cause of the
potential produced at any point. It is sufficient to
comprehend the relations described. To some, how-
ever, it is often an aid to consider the analogy of
electrical phenomena to some simpler mechanical
phenomena. The danger of overtaxing the elasticity
of the analogy seems to us to justify an omission of
such simplifying methods.
Having laid the foundations for an understanding
of the electric current, we may now turn towards the
special subject of electrochemistry, and as an intro-
duction to this branch of electrical science, we shall
briefly outline the most important part of the history
of electricity in general. Those desiring fuller know-
ledge we refer to Ostwald's Mectrochemie, Ihre
Gesckichte und I/ehre, and to Wiedemann's I/ehre von
der Electrizitat.
CHAPTEE II
DEVELOPMENT OF ELECTROCHEMISTRY UP TO THE
PRESENT TIME
A LITTLE more than two thousand years ago the first
electrical experiment recorded was performed by Thales,
who observed that under certain conditions amber
(rfXe/crpov) possessed the power of attracting light
bodies, as pieces of paper, feathers, etc. Later, it was
discovered that this property was not confined to
amber alone. It was called 77 / Xe/eT/>oz>-like, which
later was contracted to the word electric.
The phenomena of atmospheric electricity, as dis-
played in lightning, St. Elmo's fire, aurora borealis,
etc., have always been known, but their consideration
as electrical phenomena is of comparatively recent
date.
Up to the beginning of the seventeenth century our
knowledge of electricity was most limited ; at that
time it was somewhat augmented by the work of
William Gilbert. He showed that a great many sub-
stances became electric upon being rubbed, but that
none of the metals possess this property. He was the
first to declare necessary the rubbing of the material
to the production of the electricity.
From this time on, much more interest was taken
CHAP, ii DEVELOPMENT OF ELECTROCHEMISTRY 29
in electrical phenomena, and means were soon found
for the production of greater electrical effects than
were possible through the rubbing of such substances
as amber.
In 1733 Dufay first gave expression to the im-
portant fact that there are two kinds of electricity,
which he distinguished as that produced iipon glass,
vitreous, and that upon wax, resinous.
At the end of the eighteenth century five different
sources of electricity were known. Up to the time
of Franklin, friction had been the only source. He
observed that the atmosphere was a second source,
and a third was found by Wilke in the solidifying of
fused substances. This he named " electricitas spon-
tanea." The warming of tourmaline became the fourth
source, while the living animal organism offered the
fifth when the power of certain fish to produce elec-
tric shocks was recognised, as shown by the gymnotus,
torpedo, and silurus.
The great electrical discovery of the eighteenth cen-
tury, the one which attracted the attention of the best
investigators of that time, and which has proved to be
the discovery of a much more productive source of
electricity than was previously known, we owe to the
wife, of Aloisius Galvani. Galvani was then Professor
of Medicine at the University of Bologna. On one
occasion he had the freshly-prepared hind legs of a
frog lying upon a table, beside which stood an electric
machine which was being used. His wife noticed that
the frog's legs, which were touching a scalpel, moved
as if alive while the sparks were passing from the
electric machine. She called Galvani's attention to it,
and in a short time he was deeply involved in the
study of the phenomenon, considering it a good proof
30 ELECTROCHEMISTRY CHAP.
of his theory that the animal organism, in general, was
in possession of electricity.
In carrying on his experiments he was accustomed
to place the preparations of frogs' legs upon an iron
railing in the open air, and he often noticed the con-
tractions taking place in them there, and conceived
that it might be due to atmospheric electricity. He
found that when lightning was discharged, or storm
clouds approached, contraction in the frog's legs was
most often produced.
Eepeating this experiment during a series of
calm, clear days, and observing no effect upon the
frog's legs, he twisted the wire which was hooked
through the back of the frog, about the iron railing
upon which the preparation had been placed, thinking
thus more easily to discharge any atmospheric electricity
which might have accumulated in the preparation.
He observed muscular contractions, which he then
concluded were at least not entirely produced by
atmospheric electricity. Later experiments carried on
in a room showed him conclusively that these same
contractions in 'the frog preparations could be produced
without assuming an action of atmospheric electricity,
it being only necessary to bring the wire which was
hooked through the frog's back into contact with the
iron plate upon which the preparation was lying.
The tremendous expansion which the principle
involved in this simple discovery received was
remarkable. The contractions of the muscles of the
frog's legs were recognised as produced by electricity,
and the first question arising was as to the source
of this electricity.
Galvani declared that the electricity existed in
the preparation, which he compared to a charged
ii DEVELOPMENT OF ELECTROCHEMISTRY 31
Leyden jar. The muscles and nerves replace the
coatings of the Leyden jar, and the wire simply serves
as the discharging rod. He believed that every animal
organism was a source of electricity, this being most
evident in the case of the electric eel and certain
fishes. He hoped through this discovery to be able
to penetrate farther into the mysteries of life in
general.
Galvani's opinions were at first pretty commonly
accepted by physicists, many of whom repeated the
experiments. Even Volta at first was inclined to these
views, but later observed that the effects produced were
very marked when the material connecting the back of
the frog or the nerve with the leg or muscle consisted
of two different metals, while the effect was very
weak, or entirely wanting, when only a single metal
was used. He therefore began to doubt Galvani's
explanation, and soon reached the conclusion that the
source of the electricity was either in the point of
contact of the two different metals forming the "dis-
charging rod," or else at the point of contact between
the metal and the liquid (the frog's legs being moist).
The preparation itself he considered as nothing more
than a delicate electroscope. Volta finally concluded
that the principal seat of the electricity was the contact
point between the two metals. He believed the action
brought about at the point of contact of a metal with
a liquid to be of secondary importance. This theory
of Volta's has been the commonly accepted theory
regarding the source of this electricity until within
very recent years.
Volta originally separated conductors into a first
and second class the first comprising the metals,
carbon, and certain other good conducting substances
32 ELECTROCHEMISTRY CHAP.
occurring in nature, such as the metallic sulphides ;
the second consisting of all conducting solutions. This
distinction is still retained. We describe conductors
of the first class as those in which the electric current
moves without a simultaneous motion of matter, while
conductors of the second class are those in which the
transportation of electricity requires a corresponding
motion of ponderable material.
Volta soon arranged the conductors of the first
class in what was called the electromotive series
that is, he arranged them in such order that if two of
them are combined with a conductor of the second
class, and also directly with each other, the electric
current always passes from the one higher in the
series through the liquid to the other. Moreover, the
current is greater the farther apart the two chosen
metals stand in the series.
After the establishment of this order of electro-
motive forces of the conductors of the first class, J. W.
Eitter made the discovery, entirely unappreciated at
the time, that the order is the same as that according
to which the metals precipitate one another from
solution. Zinc, copper, silver is the order of these
three metals in the electromotive series, and zinc pre-
cipitates metallic copper from solutions of its salts, and
zinc and copper both precipitate silver from its solu-
tions. A connection between electricity and chemistry
had thus been practically shown.
A little later Volta stated his law of electromotive
forces. This declared that the same potential always
exists between two given metals, whether they are
directly in contact with each other or form part of a
connected series. It explains the impossibility of
obtaining an electric current from a circuit made up
ii DEVELOPMENT OF ELECTROCHEMISTRY 33
entirely of metals, for all the electromotive forces
which might exist in such a circuit would always
give a sum of zero.
The above law, according to Volta, does not hold
good for conductors of the second class, because two
metals could be connected by a conductor of that class
with scarcely any change in the potential from one
metal to the other through the solution, since, as he
believed, only very slight potential differences were
produced at the surface between liquid and metal.
Accordingly, the electricity flowing in the circuit
Zinc Copper
/ \ would have nearly the same poten-
Conducting liquid
tial as that between zinc and copper.
As long as the attention of investigators was
employed with frictional electricity, scarcely any
attention was paid to relations which might exist
between chemical and electrical processes. Moreover,
the quantities of electricity which were produced by
the friction methods were too small to bring about
any considerable chemical effect. A few experiments
were known as early as the middle of the previous
century, pointing to relations between these two forms
of energy. It was known that by means of the electric
spark certain of the metals could be obtained from
their oxides; that air, other gases, and water were
affected by the passage of the spark had also been
observed. The chemical effect of the electric current
was first studied on a large scale after Volta had con-
structed his so-called " electric pile." The latter con-
sisted of pieces of zinc, pieces of pasteboard moistened
with a salt solution, and pieces of silver, these being
piled in a column in the order given ; instead of zinc
and silver, other metals could be used. The strength
D
34 ELECTROCHEMISTRY CHAP.
of the pile varied with the choice of the metals and
depended upon the number of the pieces from which
it was made. Almost every one who was in a position
to do so built such a pile, and the scientific papers at
the beginning of this century were filled with descrip-
tions of experiments in which the pile was used.
It is worthy of notice that Volta himself says
nothing of the chemical action of his pile, in spite of
the fact that in his experiments he must have observed
the decomposition of water. He evidently could not
understand the significance of this phenomenon. The
discovery that the voltaic pile could decompose water
thus became the work of others.
In the year 1800 Nicholson and Carlisle showed
that on conducting the electric current through water,
gases appeared at the ends of the conducting wire
dipping in the water, one of the gases being hydrogen
and the other oxygen, and that except when the
wire was of noble metal, it was oxidised. The fact
was also not overlooked that the liquid about the
wire at which hydrogen was evolved became alkaline,
while that about the other wire became acid.
It is surprising that as early as 1802 detailed
measurements of potentials of the voltaic pile, which
are still accepted as correct, were published by Ermann.
Some of the results we have already considered in the
introduction; others will now be given. Ermann
inserted a silver tube filled with water into the circuit ;
the ends of the tube were of glass, and through these
the wires of a battery were brought in contact with
the water. By connecting an electroscope to any
desired point of the silver tube, the presence of elec-
tricity was shown, and Ermann established the im-
portant fact that the column of water between the two
ii DEVELOPMENT OF ELECTROCHEMISTRY 35
ends of the battery wire actually contains electricity
during the passage of the galvanic current. The fall
of the electroscopic potential, when the column of
liquid forms part of the circuit, takes place as we
have learned on page 13. In such a case as this,
sudden falls of the potential occur at the two poles
because of the work performed there.
Ermann also placed wires between the two poles
in the tube, as shown in Fig. 12, and observed that
gas was evolved at all of the wire ends ; in each case
U /)~ ilf ^ U
Jfg l/i NZ
z H*
2 H g
o,
FIG. 12.
an end at which hydrogen appeared was adjacent to
one giving off oxygen, as shown in the figure. The
conduction of the current occurred in part through
the water, and in part through the wires. In this
case also the electroscopic potential showed the same
arrangement throughout the circuit as before. By
properly connecting the circuit with the earth, it
is possible to have positive or negative electricity
alone in the column of water and the wires ; or finally,
one part of the pile may be made to exhibit positive,
while the rest shows negative electricity. 1
1 The discovery first made by Ermann, that when a piece of metal
is placed in a liquid through which an electric current is passed, a
part of the current goes through the metal, and decomposition of the
water takes place at its two ends, has lately received practical applica-
tion in causing metals to melt under water.
The greater part of the current passing through the metal causes it
to become very highly heated, while the water is only moderately
heated because of the existence of the well - known Leidenfrost's
phenomenon.
36 ELECTROCHEMISTRY CHAP.
The evolution of the gases, hydrogen and oxygen,
and the production of alkali and acid at the ends of
the wire in the water, was a phenomenon the com-
prehension of which gave the investigators great trouble.
Are these substances produced by the action of elec-
tricity upon water ? The law of the conservation of
matter was at that time not commonly accepted, so
that such a supposition could not of itself be declared
absurd, but must first be subjected to experimental
proof. Sir Humphry Davy undertook this work, and
showed, by very careful investigations, that pure
water was decomposed into hydrogen and oxygen by
the electric current, but that the formation of acid
and alkali was due to impurities. Furthermore, he
performed an experiment of the greatest importance
upon the migration of acid and alkali to the two
poles, for which a satisfactory explanation was not
found until after the establishment of the theories of
the past few years. This experiment is here briefly
described because it relates to phenomena of interest
to us. It will be more thoroughly understood after
the next chapter has been read. When the reader
has become acquainted with the modern theories of
electricity, we advise him to attempt to discover an
explanation of this experiment. It ought not to be
difficult, and he will thereby recognise the advantages
of the new conceptions.
If we connect two platinum wires to the poles of a
voltaic pile, placing one of the free ends into a vessel
filled with pure water, and the other into one con-
taining potassic sulphate solution, the two vessels
being connected by means of a tube filled with water,
acid is formed at the positive pole (the end of that
wire which is attached to the positive pole of the
ii DEVELOPMENT OF ELECTROCHEMISTRY 37
voltaic pile), and alkali accumulates at the negative
pole. The same result is obtained if three connected
vessels are used instead of two, the electrodes dipping
into the end vessels which contain water, while the
middle vessel contains the potassic sulphate solution.
It looks just as if the positive pole possesses an attrac-
tion for the acid, the negative for the alkali, a,nd that
in consequence the salt is decomposed.
Davy was seized with the desire to learn more
about this motion of the acid and alkali, and by the
use of litmus paper he found, much to his astonish-
ment, that the first appearance of acid or alkali was
not in the water at the point where it came in con-
tact with the salt solution, but, on the contrary, at the
electrodes, whence it gradually spread throughout the
liquid. If acid and alkali could pass through the water
in going to the poles without affecting the litmus on the
way, Davy questioned whether it was not also pos-
sible that they might pass through substances for
which they had a great affinity without acting upon
them, and he found that an interposed acid did not in
any way hinder the passage of the alkali to its pole,
nor did an interposed alkali solution offer any apparent
obstacle to the migration of the acid. There was
found, however, in the interposed acid and alkali
solutions some of the corresponding salt, just as though
the chemical affinity had caused some of the passing
compound to be retained. If, when employing potas-
sium sulphate solution, barium chloride solution was
used to intercept the sulphuric acid, barium sulphate
was formed, and no acid was to be found at the posi-
tive pole. Here, thought Davy, the chemical affinity
had completely overcome the electrical attraction.
A little later, Davy crowned his experimental work
38 ELECTROCHEMISTRY CHAP.
with the separation of the alkali metals from their
solid hydrates by means of the electric current, and
afterwards advanced what we may call the first electro-
chemical theory. This was based upon the atomic
hypothesis of Dalton. Experiment had shown that
when, for example, copper and sulphur are in contact,
the copper becomes positively electric, and the sulphur
negatively. It seemed possible, from this fact, that the
atoms of two substances when in contact might also in
like manner take to themselves charges of electricity.
If the electric charges in the atoms were great
enough, the differently charged atoms would leave
their former positions and come closer together ; in
other words, a chemical compound would be formed.
A decomposition or rearrangement of the atoms
would take place if a new atom coming into contact
with the previous compound, could assume a charge
greater than that already existing on that atom pos-
sessing the same kind of electricity ; the new atom would
attract the atom of opposite sign from its union with
the weaker atom, and a new compound would be formed.
In agreement also with Berthollet's law of the effect of
mass in reaction, he conceived that a large number of
atoms with small electric charges might be of greater
effect than fewer atoms possessing greater charges.
Davy's theory was not commonly accepted. Ber-
zelius was at that time just beginning his work, and
in one of his first investigations, which he under-
took with Hisinger, he studied the action of the
electric current upon solutions of different inorganic
substances, the result of this investigation being the
establishment of an electrochemical theory which has
been of the greatest importance to chemistry through-
out the century.
ii DEVELOPMENT OF ELECTROCHEMISTRY 39
According to this theory, each atom when in con-
tact with another possesses two poles, one electro-
positive, and one electro-negative. When the atoms
are in contact one of these poles is usually much
stronger than the other, so that the atom acts as if
unipolar that is, electro-positive or electro-negative.
The chemical affinity of an element depends upon the
amount of the electric charge of its atoms ; positively
charged atoms react with negatively charged, and the
two kinds of electricity partially neutralise each other,
the resulting compound being electro-positive or nega-
tive, according as the excess of electricity is positive
or negative. In this manner the formation of a
compound from its elements was explained, as well as
the union of two compounds to form a new substance.
The existing electric charges of these compounds were
thus partially or almost completely neutralised.
An example may make this point clearer. Accord-
ing to the old atomic weights, a positively charged
potassium atom combining with a negatively charged
oxygen atom resulted in a compound, KO, still
possessing a certain charge of positive electricity,
as the potassium possessed more positive electricity
than the oxygen did negative. A negative sulphur
atom combines with three negative oxygen atoms to
form the compound SOg, 1 which is itself negatively
charged, because a negative residue results from the
union; furthermore, KO and S0 3 combine to form
KOS0 3 , which still possesses some positive elec-
tricity. It was supposed that sulphate of alumina,
1 Berzelius explained the fact of the energetic action between these
two negative substances by assuming that the sulphur possessed a
comparatively great positive charge as well as its predominant nega-
tive charge, and that the negative charge of the oxygen neutralised
the former.
40 ELECTROCHEMISTRY CHAP.
Al O a (SO Q ) a , was formed in a similar manner, but
i O v O 7 O
that it was slightly negative ; and the formation of
the double salt, KOS0 3 + A1 2 3 (S0 3 ) 3 , was therefore
explained as the union of the two differently elec-
trical components, sulphate of potassa and sulphate of
alumina.
Chemical and electrical processes were closely
associated by the above method of reasoning, and
the dualistic theory was introduced into inorganic chem-
istry, or chemistry, since at that time the two were
practically synonymous. Every compound was con-
sidered as composed of two parts, which might them-
selves be composed of two other parts. If this theory
assumed much that was arbitrary, it performed a
great service because of its systematising influence.
From this time no very great advance was made in
electrochemistry until Faraday's important discoveries
about 1835. Faraday first convinced himself that
there was only one kind of positive and negative
electricity ; that is, whether it was produced by friction
or in the voltaic pile, the action was always the same.
He then attempted to discover a relation between
the quantity of electricity passing through a circuit
and the chemical and magnetic effects which it could
produce. He found the three proportional to one another.
By the comparison of the quantities of different
substances which were decomposed by the same
quantities of electricity, Faraday discovered a second
law, which is proved in the following simple manner.
Different electrolytes which are to be investigated
are connected into the same circuit in series, so that
the same quantity of electricity passes in a given time
through each solution. The discovery which he made
may be stated as follows: The quantities of the sul-
ii DEVELOPMENT OF ELECTROCHEMISTEY 41
stances, separating at the electrodes in the same time,
are in the proportion of their equivalent or combining
weights.
If by using platinum poles we connect an acid
solution, a solution of a mercurous salt, and one of
mercuric salt into the same circuit, and measure the
quantity of hydrogen and of mercury, which have
separated after a certain time, we find that for every
gram of hydrogen liberated in the first solution, 200
grams of mercury are set free in the second and 100
grams in the third. These quantities of mercury are
in the ratio of 2:1, and correspond to its different
valencies in the solutions.
These laws of Faraday have been proved to hold ;
both that in regard to the proportionality between the
quantities of electricity and of decomposed substance,
and that concerning the chemical equivalents of the
separated substances. It may be stated here that in
order to decompose an exact gram-equivalent of any
conducting compound, it is necessary to send 96540
coulombs of electricity through the circuit; conse-
quently this number represents the electrochemical
unit of electricity; 96540 coulombs will decompose
169*98 grams of silver nitrate. The quantity of
silver separated in this case amounts to 10 7 '9 3 8
grams. By one coulomb or one ampere in a second,
1 07'Q^S
= 0*001118 gram of silver are precipitated.
We see from these figures that the transportation of
very considerable quantities of electricity is brought
about by very small quantities of matter.
Faraday's law at first met with great opposition,
due principally to the fact that its meaning was not
clearly understood. Trouble arose through the mis-
42 ELECTROCHEMISTRY CHAP.
conception of the electrical energy factors ; in other
words, quantity of electricity and quantity of electrical
energy were confounded. The law refers simply to
quantity of electricity, and asserts the separation of
chemical equivalents of substances in the passage of
equal quantities of electricity without referring at
all to the quantity of electrical energy necessary.
Among those who made this mistake was Berzelius,
who thought that the law required the decomposition
of chemical equivalents of all the different electro-
lytes by the use of equal amounts of energy. This
made the law seem absurd, because the chemical
affinity or cohesion overcome by the electric current
in the decomposition of different compounds is not
the same. This mistake and method of reasoning is
not entirely of the past, but is still often made.
We have also to thank Faraday for much of our
electrochemical nomenclature. Motion of ponderable
matter in a solution through which the electric
current is passing was assumed to take place in order
to explain the observed phenomena. The particles
of matter thus moving with the electric current
Faraday called ions, and gave the name cathions to
those which move in the same direction as the positive
electricity, and the name anions to those moving in the
opposite direction. Conductors of the second class, or
substances which conduct electricity with such an
internal motion, he called electrolytes, and to the pro-
cess gave the name electrolysis. The name electrode he
gave to the surface of contact between conductors of
the first and second classes. That surface to which
the cathions move is the cathode, that to which anions
move is the anode. Although some investigators
unfortunately use the word anode to indicate that
ii DEVELOPMENT OF ELECTROCHEMISTRY 43
electrode to which the cathions move, and call the
pole to which the anions move the cathode, the
terms will be used in this book as they were intended
by Faraday.
The Electrolytic Process. Those who first recog-
nised the decomposition of water by an electric cur-
rent sought an explanation for the appearance of
hydrogen and oxygen at the two electrodes. In the
year 1805 Grotthus gave the first complete theory of
the phenomenon. According to this theory, in the
presence of an electric current, one of the electrodes
is positively and the other negatively charged with
electricity. The molecule of water (then represented
FIG. 13.
by HO) becomes polar that is, the H is positively
electrified and the negatively. The electrodes attract
(and repel) the H and because of these charges, and
the molecules of water between the electrodes arrange
themselves as shown in the figure, the positive H being
turned towards the negative electrode, the towards
the positive.
If the electromotive force or charges of the
electrodes are great enough, the extreme atoms of
hydrogen and oxygen are simultaneously liberated.
Their electric charges go to neutralise the electricity
of the electrodes, and the electrically neutral substances
are evolved as gases. The oxygen and hydrogen of
these extreme molecules, which are left behind by the
44 ELECTROCHEMISTRY CHAP.
liberated hydrogen and oxygen respectively, immedi-
ately combine with the hydrogen and oxygen of the
adjacent molecules, and this successive decomposition
and combination passes on throughout the space
between the electrodes. The new molecules then all
turn about and again take positions as in the figure,
the process proceeding as before. This explanation
satisfied the scientific world for many years.
Another point was soon investigated. It was
desired to know which really conducts the electricity,
the water or the dissolved substance. For a long
time this was an open question. One spoke then of
" water which by the addition of sulphuric acid, for
example, becomes a good conductor," without having
apparently conceived any explanation of the fact.
There was also considerable disagreement as to
what constituted the positive and what the negative
ions of the dissolved substances. Berzelius had brought
forward the opinion, at first generally accepted, that
for example, in sodium sulphate, which he wrote
NaOS0 3 , NaO was the positive ion and S0 3 the
negative, and that these moved to the electrodes, where,
by taking up water, they became alkali and acid.
Some time later views were expressed to the effect
that Na constitutes one ion and S0 4 the other.
These questions were answered by an experiment
of Darnell's, which, however, must be considered as
decisive only in view of the conceptions then held.
He electrolysed sodium sulphate and sulphuric acid
solutions separately but simultaneously, in the same
circuit, and found that the amounts of hydrogen and
oxygen separated were the same for each of the two
solutions. He also found that the quantities of base
and acid formed in the salt solution were equivalent
ii DEVELOPMENT OF ELECTROCHEMISTRY 45
to the hydrogen and oxygen liberated there ; con-
sequently the Berzelius conception must be wrong.
According to the latter, by the electrolysis of the
salt into base and acid, and the simultaneous libera-
tion of an equivalent amount of hydrogen and oxygen,
a double electrical action must have been effected,
which is contradicted by the law of Faraday. In
agreement with this law Daniell declared that the Na
must be the positive ion, and the S0 4 tLe negative;
that they give up their electricity at the electrodes,
and then act upon the water to produce alkali and
acid, and that in this secondary action the hydrogen
and oxygen are set free. The amounts of alkali and
acid formed must then be equivalent to those of
hydrogen and oxygen set free in the solution, and
these quantities must also be equal to those of the
gases generated from the simple acid solution, as was
found to be the case. The salt alone must have con-
ducted the electricity in its solution. The hydrogen
and oxygen there evolved are, as shown, the result of
a secondary action, otherwise, if the water conducted
a part of the electricity, the separated quantities of
the gases could not be the equivalent of the acid and
alkali produced. In such a case the amount of acid
and alkali would be less.
Later experiments of Hittorf and Kohlrausch con-
firmed Daniell's conclusion ; accordingly, the metals
and metallic radicles, as H, Na, K, Ag, Hg, Hg n , Fe 11 ,
Fe m , NH 4 , NH 3 CH 3 , etc., are positive ions, and the
remaining atoms or groups of the conducting sub-
stances, as OH, N0 8 , 01, Br, I, S0 4 n , FeCy 6 m , FeCy 6 IV , '
etc., form the negative ions. We see here that there
are isomeric ions of different valencies, as well among
the negative as the positive ions. The trivalent
46 ELECTROCHEMISTRY CHAP.
FeCy 6 m is the negative ion of potassium ferricyanide.
The tetravalent isomer FeCy 6 IV is the corresponding
ion of potassium ferrocyanide. The electrical con-
ductivity is a property of the dissolved substance,
and not of the solvent.
As the science gradually advanced, the insufficiency
of the Grotthus theory began to be perceived. Accord-
ing to this theory, decomposition, and consequently
conduction of electricity, could not take place until
the electromotive force reached a certain value, below
which the affinity or the cohesion of the compounds
would not be overcome. But it was found that, with
suitable arrangement, the passage of the current took
place even when the electromotive force was extremely
low. For example, if two silver electrodes be dipped
into a silver nitrate solution, a decomposition of the
salt can be shown to have taken place, even when
the amount of energy used is extremely small. Silver
is precipitated upon one electrode, and dissolved from
the other, the whole action consisting merely in the
passage of silver from one electrode to the other.
According to the Grotthus theory we must imagine
the molecule of silver nitrate decomposed at one
electrode, and the N0 3 of this molecule recombining
with Ag of the next molecule, and so forth to the
other electrode, where the last silver atom is oxidised
to AgN0 3 by the N0 3 set free there. Thus equal
numbers of molecules are formed and decomposed.
There is here no contradiction of the first law of
energetics, but there is of the second law, which
may be expressed as follows : Energy in a condition
of rest cannot of itself become active. To illustrate :
a stone lying on the ground cannot of itself rise
to a certain height and then fall back again ; although
ii DEVELOPMENT OF ELECTROCHEMISTRY 47
such an action would not contradict the first law
or that of the conservation of energy, it is contrary
to the second. If a stone is to be raised, work must
be done upon it from without. The amount of work
so employed might be recovered by the fall of the
stone back to its original position, but without external
aid the stone cannot be raised at the expense of the
work to be recovered later.
The Grotthus theory would present us with an
exactly similar case. Here the decomposition of the
molecules must be brought about by that energy
which is recovered when the recombination takes
place, and it is this fact that the second law of
energetics will not allow. The Grotthus theory
requires that the electromotive force shall be above a
definite amount before decomposition can take place,
which is also, as already explained, contrary to fact.
It was Clausius who first showed the disagreement
of the theory with the facts. Basing his conclusions
upon the experimental material above mentioned,
he declared every supposition to be inadmissible
which requires the natural condition of the solution
of an electrolyte to be one of equilibrium, in which
every positive ion is firmly combined with its negative
ion, and which at the same time necessitates the
action of a definite amount of energy, in order to
change this condition of equilibrium into another,
differing from it only in the fact that some of the
positive ions have combined with other negative ions
than those to which they were formerly attached.
The necessary conclusion, frorn a knowledge of the
facts and a consideration of Clausius's statement, is that
the individual ions must exist uncombined and free
to move in the solution. Clausius was himself pre-
48 ELECTROCHEMISTRY CHAP.
vented from drawing this conclusion by the condition
of the chemical theories of his time. In keeping with
these views, he attempted an explanation which
approaches the present theory. He imagined the
positive and negative parts of the molecules in inde-
pendent motion or vibration, but kept together by
their chemical attraction. The latter, he thought, is
often overcome by the extreme vibrations, and when
the positive part of one molecule comes into a
favourable position with respect to the negative of
another, these two unite, while their previous com-
panions, momentarily free, come into convenient posi-
tions for union with parts of other molecules, and so
forth.. In other words, he imagined a continual
exchange between the positive and negative parts of
the various molecules. When an electric current
acts upon a solution, the molecule -parts no longer
vibrate and exchange with entire irregularity as before,
for decompositions taking place in such a way that
they are aided by the electric current, that is, those
in which the molecule-parts can follow the direction
of the electrical force, become much more frequent
than other decompositions. Considering a cross-
section at right angles to the direction of the electric
current, it is evident that more positive ions would
move in the direction of the positive electricity than
in the negative direction, and more negative in
the negative than in the positive direction. As a
result of these different motions, a certain quantity of
positive ions passes in one direction, and a quantity of
negative ions in the opposite direction. This motion
of the two parts of the molecules in the solution
causes the conduction of the electricity. According
to this theory of Clausius, the current does not cause
ii DEVELOPMENT OF ELECTROCHEMISTRY 49
any decomposition of molecules, but only guides those
molecule -parts which are momentarily free, so that
their motion is in the direction of one of the oppositely
charged electrodes. This theory was very commonly
accepted, and has been almost until the present time.
At about the same time that Clausius brought
forward his ideas, Hittorf began his work upon the
migration of the ions, and a little later Kohlrausch
commenced his experiments upon the conductivity
of solutions. Through these investigators a great
advance was made, and from their acquisitions,
Arrhenius in 1887 replaced the Clausius theory by
the theory of free ions.
Relation between Chemical and Electrical
Energy. Before closing this brief historical account
it is necessary to state that, soon after the establish-
ment of the law of the conservation of energy, attempts
were made to answer the question : Does the chemical
energy of the process taking place in a voltaic element,
as measured by the heat generated, change completely
into electrical energy ?
The Daniell element consists of zinc, zinc sulphate,
copper sulphate, and copper, and when in action, zinc
goes into solution while copper separates out. The
generation of heat corresponding to this reaction is
known from thermochemical measurements; for the
gram-equivalent of the two substances it amounts to
25050 cal.
CuS0 4 + Zn = ZnS0 4 + Cu + 25050 cal.
If this reaction yielded only electrical energy, the
electrical equivalent of 25050 cal. would be pro-
duced. On the other hand, the amount of electrical
energy actually obtained from the element may be
E
50 ELECTROCHEMISTRY CHAP.
easily calculated. The above reaction represents the
case when one gram-equivalent of copper has separated,
consequently 96540 coulombs of electricity have passed
through the circuit. For it follows from Faraday's law
that this amount of electricity always passes through
the circuit when the electric deposition or solution of
a gram- equivalent of any substance takes place.
The electromotive force TT of the element can be
measured, and it is known that volt x coulomb = 0'236
cal. ; consequently in order to express the electric units
volt x coulomb in calories, it is necessary to multiply
their number by 0'236.
The electrical energy expressed in calories is there-
fore
0-236 x 96540 x TT cal.
The chemical energy in heat-units is 25050 cal. If
they are equal in this case,
0-236 X 96540 x TT cal = 25050
and
25050
22784
= 1-10 volt.
This calculated value 1-10 volt is also the electro-
motive force of the Daniell element experimentally
found, and it was concluded from the agreement in
this case that the chemical energy of a reaction is
changed completely into electrical when that reaction
is the source of the electric current from an element.
Later experiments with other elements gave re-
sults not entirely agreeing with this conclusion. The
question was finally answered by the theoretical
and experimental investigations of Willard Gibbs,
J\ Braun, and H. von Helmholtz, who showed that
n DEVELOPMENT OF ELECTROCHEMISTRY 51
there is usually a difference in the amounts of chemi-
cal energy transformed in an element and electrical
energy obtained therefrom. This difference is mani-
fested by a generation or absorption of heat in the
element when it is in action.
CHAPTER III
THE ARRHENIUS THEORY OF DISSOCIATION
ELECTRICAL investigation received a great impetus
from the theory of Arrhenius 1 in 1887. Well-known
facts- whose relation to one another was previously
unknown became connected by this theory, and it was
a great impetus to new discovery. The scientific
electrochemistry of to-day has this theory for its
foundation. We shall consider in detail its develop-
ment, and shall then ascertain the present position of
electrochemistry as it appears in the light of this new
conception.
In 1887 J. H. van't Hoff published an article in
the first volume of the Zeitschrift fur physikalische
Ghemie upon the role of osmotic pressure in the
analogy between solutions and gases. He had
established theoretically and experimentally the
following very important generalisation of Avogadro's
law.
" At the same osmotic pressure and temperature, equal
volumes of all solutions contain the same number of
molecules, and, in fact, that number which under the
same pressure and at the same temperature exists in
the same volume of a gas."
1 Zeitschr. physik. Chem. i. 631, 1887.
CH. in THE ARRHENIUS THEORY OF DISSOCIATION 53
It was likewise shown that the gas laws of Boyle
and Gay-Lussac applied also to dilute solutions.
What is to be understood by osmotic pressure may
be made clear by the following experiment. A vessel
is filled with water, and in it a vertical tube, closed
at its lower end by a semi-permeable membrane and
open at the upper end, is placed. A quantity of some
solution, for example, of sugar, is poured into the tube
until the heights of the liquids outside and inside are
the same. The semi-permeable membrane here used
is of such a nature that the water may pass through it
while the dissolved sugar is prevented from doing so ;
such membranes are not difficult to prepare. It is
observed in this experiment that the column of liquid
in the tube begins to rise, water entering from the
outer vessel through the membrane. A certain press-
ure must be exerted upon the liquid in the tube in
order to prevent its rising. That pressure, which will
just hold the level of the liquid in the tube in its
original position, is the equivalent of the osmotic
pressure. This osmotic pressure of dissolved sub-
stances corresponds to the pressure of gases.
It is known that the equation pv = ET expresses
Avogadro's, Boyle's, and Gay-Lussac's laws regarding
gases, v being the volume in cubic centimeters of
a gram -molecule of the gas under the pressure p
expressed in grams per square centimeter, T the
absolute temperature, and E a constant. The expres-
sion Y has a constant value for a perfect gas, indepen-
dent of its nature and condition of dilution. This value
is represented by E. The expression is the result of
experimentally discovered facts, though not obtained
in a direct manner. Whenever the molecular volume
54 ELECTROCHEMISTRY CHAP.
of a gas is multiplied by its pressure and the product
divided by its absolute temperature the constant E
is obtained, which, when the units are those above
described, is 84700.
This gas equation also holds good for dissolved
substances. Pfeffer found the osmotic pressure of
a 1 per cent sugar solution at 6*8 9 C. to be equal
to 5 0'5 cm. of mercury or 50'5 x 13*59 gms. There
being nearly one gram of sugar in 100 cubic centi-
meters of the solution, the molecular weight in grams
(342) is contained in 34200 cubic centimeters, and
this is then the value of v or the molecular volume.
T was in this case 2 7 9 '8. Consequently for this
sugar solution
pv 50-5x13-59x34200
Tg' 2?9 . 8 - = 83900 (approximately).
This value of E only differs from the value for gases
by the possible errors of experiment. Evidently then
the osmotic pressure of the sugar solution is the same
pressure as the sugar would exert if it existed in the
gaseous state and occupied the same volume.
Because of the prominence of osmotic pressure in
the considerations of the following pages, it is well
at this point to obtain an idea as to how it is
produced. If the lower end of the tube in which
the sugar solution is placed be entirely closed, we
of course observe none of the evidences of this press-
ure. At the limiting surfaces of a solution there
exists a pressure the internal pressure acting in-
ward at right angles to the surface and amounting
to over a thousand atmospheres. 1 In a 1 per cent
1 We are obliged to recognise the existence of such a pressure by
certain experimental facts which cannot be here described.
in THE ARRHENIUS THEORY OF DISSOCIATION 55
sugar solution there is an osmotic pressure of only
about one atmosphere directed against this enormous
internal pressure. This pressure is due to the sugar,
which acts in the water just as it would if it were in
the gaseous state and confined in the same space.
Even with very concentrated solutions the internal
pressure is still hundreds of atmospheres greater than
the opposite or osmotic pressure exerted by the dis-
solved substance. It is on this account that the vessel
containing a solution is not broken by the osmotic
pressure exerted against its walls. Besides the weight
of the solution itself there is no pressure acting upon
the containing vessels.
By employment of the semi-permeable membrane
we are enabled to observe the effect of the osmotic
pressure. When the tube is closed at its lower end
by this membrane, and placed in water, the water
enters through the membrane. In the solution, at
all" surfaces, the internal pressure A of the water
is exerted inward and the osmotic pressure & of
the dissolved sugar outward, while in pure water
only the pressure A exists. Upon the membrane
only the pressure ~b is exerted, because the membrane
is permeable to the water. There being at the mem-
brane no liquid surface, there is consequently no
manifestation of internal pressure. Leaving out of
account the internal pressure of the water, there is
exerted upon the surfaces of the solution and the
membrane the pressure due to the dissolved sugar,
which of course disappears when pure water is used to
replace the solution. The solution therefore tends to
expand when in contact with the water of the outer
vessel, and can do so at the expense of this water,
which enters through the membrane.
56 ELECTROCHEMISTRY CHAP.
It is evident that the membrane enables us to
observe the existence of osmotic pressure, and this
may be defined as the pressure exerted on the mem-
brane. The rising of the water in the tube may be
more easily understood by calling to mind an experi-
ment with the air-pump. If water be placed in the
tube with the permeable wall and in the outer vessel
as well, it could be made to rise in the tube by
diminishing the atmospheric pressure acting upon it
there. In this way we diminish the external pressure
which is acting inward. By dissolving sugar in the
water, a pressure is created inside the solution directed
outward. The result will evidently be the same,
whether the former be the case or the latter. The
liquid must rise in the tube, as it actually does. In
order then to explain the osmotic pressure, we evidently
need not make any assumption as to an attraction
existing between the solvent and the solution, but
only the assumption that the substance in solution
acts as it would in the gaseous state.
Van't Hoff has, in fact, proved the existence of
far-reaching analogies between dilute solutions and
gases, and has also been able to deduce laws for phe-
nomena not apparently related to osmotic pressure,
from the laws of osmotic pressure itself. Among such
phenomena may be mentioned the influence of a dis-
solved substance upon the vapour pressure and upon
the freezing point of the solvent. These laws had
already been discovered, principally by Eaoult, and
were thus expressed : the lowering of the freezing point
and vapour pressure of a solvent ly a dissolved substance
is proportional to the concentration, and is the same for
equi-molecular solutions that is, such as have, in equal
amounts of the solvent, quantities of the dissolved
in THE ARRHENIUS THEORY OF DISSOCIATION 57
substances proportional to their molecular weights.
These discoveries furnished an opportunity of making
great advances in our knowledge of the conditions
of matter, and especially gave us a simple method of
determining the molecular weights of all soluble sub-
stances, while this could previously be done only for
those which are volatile.
One great difficulty presented itself, and cast a dark
shadow upon the otherwise bright theory of solutions.
Almost all acids, bases, and salts which were soluble
in water gave agreeing results for molecular weights
by the methods of the osmotic pressure, freezing point,
and vapour pressure lowering, which were much lower
than those obtained by the vapour density method,
and were less than expected from the chemical proper-
ties of the substances. In other words, assuming the
normal molecular weights, these showed too great
osmotic pressures and freezing point depressions.
Not very long before, the molecular theory had
been in a very similar position, because of the devia-
tions of many vapour densities from the requirements
of the theory. It was only with considerable hesitancy
that the explanation was admitted that there was a
dissociation of the molecules of these gases. At the
present time this hypothesis is accepted. It seemed
natural to expect a similar dissociation in solutions,
and this assumption was first made by Planck, 1 who
based his reasoning upon thermodynamical considera-
tions. This explanation of the difficulty was not then
accepted by chemists. Such a supposition seemed
absurd, for it required that substances like potassium
chloride, in which the attraction holding the atoms
together was considered very great, should decompose
1 Zeitschr. physik. Chem. i. 577, 1887.
58 ELECTROCHEMISTRY CHAP.
into potassium and chlorine, and that these should
exist as such in the solution, in spite of the fact that
potassium reacts so energetically with water. The
supposition also seemed to be contradicted by the law
of the conservation of energy, for the assumption im-
plied that substances which combined so energetically
that much heat was generated, should separate again,
apparently of themselves.
Before such an essential change could be made
in the opinions held regarding solutions the apparent
contradictions had to be removed. This was done by
Arrhenius, who was able not only to do away with
the seeming contradiction, but also to produce clear
evidence for the truth of Planck's hypothesis. In an
early investigation of the electric conductivity of solu-
tions, Arrhenius had recognised two kinds of molecules,
and had concluded that only one of these kinds, the
active molecule, caused the conductivity and that the
other kind was inactive. He also expressed the opinion
that all inactive molecules changed into active in
solutions of extreme dilution. He recognised an
activity coefficient of a solution, this being the rela-
tion between the number of active molecules and the
sum of active and inactive molecules therein, and
that at infinite dilution this coefficient would be equal
to unity. For other dilutions it was less than unity,
and expressed the relation between the existing molecu-
lar conductivity, of which we shall soon learn more,
and its limiting value, or the molecular conductivity
at infinite dilution. It was unknown in what respects
the active molecules differed from the inactive. As
soon, however, as the above-mentioned work of van't
Hoff appeared, Arrhenius was able, by comparing the
effects of the electrolytes in depression of the freezing
in THE ARRHENIUS THEORY OF DISSOCIATION 59
point of water with their electrical conductivity in
solution, to adduce perfectly convincing proof of
electrolytic dissociation. This proof was published in
the article previously referred to, and entitled, " Uber
die Dissociation der im Wasser gelosten Stoffe."
As already remarked, there is a class of compounds,
such as sodium chloride, which give too great a
reduction of the freezing point. A gram-molecule of
sugar dissolved in ten liters of water produces a re-
duction of the freezing point of about 0*186, while
a gram-molecule of sodium chloride gives nearly twice
that reduction. It is evident, if we accept van't
Hoffs assumption applied to this case, and consider
the molecules of salt as dissociated into sodium and
chlorine atoms, the extent of this dissociation may be
calculated from a knowledge of the deviation of the
freezing point depression from the value for the
undissociated substance. If i represents the ratio
between the actual depression of the freezing point
and the depression which the substance would give if
normal or undissociated, and k is the number of
parts into which each molecule divides (2 in the case
of NaCl, for MgCl 2 3, etc.), while a stands for the
degree of dissociation, that is, the number of dis-
sociated molecules, divided by the total number of
molecules, then :
i=
and
This degree of dissociation represented by a, called
by Arrhenius the affinity coefficient, was calculated by
him for a great many substances from their known
freezing point depressions, and it was found that these
60 ELECTROCHEMISTRY CHAP.
results agreed with the dissociation values which the
electrical conductivity had given. Only those sub-
stances conduct which are at least partly dissociated,
and therefore the conductivity is due to the dissociated
parts; to the latter, which were called by him the
"ions," Arrhenius ascribed electric charges. He did
not fail to call attention also at that time to the fact
that many other physical and chemical phenomena
receive a great deal of light from this recognition of
the free ions.
Evidently we have here a dissociation differing
from that which ammonium chloride undergoes when
heated. The parts resulting from the decomposition
are electrically charged, and contain equivalent amounts
of positive and negative electricity. It is natural to
ask : Whence come these sudden charges of electricity ?
They seem to be produced from nothing. An answer
which seems satisfactory is not difficult to give. It
is known that metallic potassium and iodine combine
to form potassium iodide. In this combination heat
is generated, which shows that the two have entered a
state in which they contain less energy than before.
A certain amount of chemical energy doubtless still
remains in the compound, and when the salt is dissolved
in water, the greater part of this chemical energy is
changed into electrical, through the influence of the
solvent. This is the energy seated in the charges of the
ions. The potassium ion is positively, and the chlorine
negatively electric. By aid of the electric current, it
is possible to add to these ions the energy in the form
of electricity necessary to give them the energy they
originally possessed as elements. In such a case they
separate in the ordinary molecular forms at the
electrodes.
in THE ARRHENIUS THEORY OF DISSOCIATION 61
From this consideration the difference between ions
and atoms, or molecules of an element, is made clear.
They contain usually very different quantities of
energy. Elements in their natural or molecular
state differ so widely from the ions in all their
properties, that we may say they have nothing to do
with each other further than that one may change
into the other.
Although the theory of dissociation in solution
encountered a great many opponents in its early
years, it has nevertheless successfully advanced, and
to-day there are few who openly oppose it. The
benefits being constantly derived from it are very great,
and we shall be continually reminded of its value and
utility.
CHAPTEE IV
THE MIGRATION OF THE IONS
IN the aqueous solution of an electrolyte we recognise
the existence of free ions, each possessing a definite
electrical charge. For example, in the solution of
hydrochloric acid there are the hydrogen ions charged
with positive and the chlorine ions charged with
negative electricity. We can now express Faraday's
law by saying first that conduction of electricity
through a solution is only brought about by the
movement of those ponderable particles which are
charged with electricity, in this case the hydrogen
and chlorine ions, and secondly, that chemically
equivalent quantities of the substances are charged
with equal amounts of electricity.
A galvanic or an electric current may be produced
in an electrolyte by dipping into it two electrodes,
which are connected, one with the positive and the
other with the negative pole of a source of electricity.
In consequence of the difference of potential thus
produced, motion of the ions is brought about, and an
electric current passes through the solution. Under
such circumstances a decomposition of the electrolyte
always takes place, even though this may not be
manifest. With hydrochloric acid, gaseous hydrogen
fcffApfiv THE MIGRATION OF THE IONS 63
and chlorine separate in unelectric form at the
electrodes. An electric current can also be produced
by induction without the use of electrodes, in which
case no transformation of the conducting particles from
the electric (or ionic) into the unelectric or molecular
state takes place.
When an electric current is conducted through
a solution, a certain number of positive ions pass
through a cross -section of the solution in one direc-
tion, and simultaneously a certain number of negative
ions in the opposite direction ; and it was previously
believed that when the two were of the same valency
this rate of motion of the positive and negative ions
was the same for both, undoubtedly because of the fact
that equivalent quantities separate at the electrodes
in a given time. We know now, however, that these
rates of motion are seldom the same for different
ions, for the phenomena of electrical conduction
and precipitation are not so closely connected as
at first seemed probable. Their relation, and the
general division of the work of conductivity among
the different possible ions, were discovered by Hittorf. 1
This knowledge was obtained by a careful study of
the changes in concentration taking place about
electrodes when the electric current is being passed
through solutions.
It will now be seen how it is possible to learn from
these concentration - changes the relative rates of
migration or motion of the ions.
Migration of the ions takes place whenever a solu-
tion of an electrolyte conducts electricity, and the ions
separate at the electrodes in the molecular condition.
1 Pogg. Ann. 89, 98, 103, 106 (1853-1859). Collected in Ostwald's
Klassiker d. exakt. Wiss. Nos. 21 and 23.
64 ELECTROCHEMISTRY CHAP.
Since now there are always present in the electrolyte
equivalent amounts of positive and negative ions, it
follows that, if at the positive electrode a negative ion
separated without the simultaneous removal from the
solution of a positive ion at the other electrode, the
solution would contain more positive than negative
ions. In other words, it would be charged with
positive electricity, and because of the great quantity
of electricity which characterises an ion, the charge
would be strong. If still another negative ion were
to separate alone, a greater amount of work would be
necessary than before, because the solution, being
positively charged, would now have a greater attraction
for the negative ion, and resist its separation. On the
other hand, the separation of a positive ion at its
electrode would become easier than before, because of
the repelling force of the positive electricity of the
solution. Since this electrostatic force, compared to
the others coming into play, is very great, the decom-
position of the electrolyte must take place in such a
manner that the positive and negative ions always
leave the solution at such rates that the solution
itself remains electrically neutral.
Besides this fact of the simultaneous separation of
equivalent positive and negative ions, it is also known
that the current-strength, or the quantity of electricity
passing through a cross-section of the electrolyte in
the unit time, is the same at all points of the circuit.
Now the total quantity of electricity in motion is evi-
dently the sum of the two oppositely-directed quanti-
ties of positive and negative ; but there is no reason
why, if in one part of the circuit the quantity of
electricity 1 consists of J positive and J negative, it
may not at another point be composed of J positive
iv THE MIGRATION OF THE IONS 65
and J negative electricity ; for the motion of the one
kind of electricity in one direction is equivalent to
the motion of the other kind in the opposite direction.
Consequently we are justified in considering the current
as a motion of the one kind of electricity in a single
direction. As a matter of fact, any portion of the whole
electricity in motion may move in one direction, while
the remainder is oppositely directed. In consequence
of these statements there is no necessity for assuming
equal rates of speed for the different ions. This would
only be the case when there was a motion of equal
quantities of positive and negative electricity at the
same rate in opposite directions.
In metallic conductors, or conductors of the first
class, equal quantities of positive and negative electri-
city flow in the same time, but this is seldom true of
the conductors of the second class, the electrolytes.
This arises from the different degrees of mobility
possessed by the ions ; the mobility of the chlorine
ion, for example, differs very much from that of the
hydrogen ion. When they are subjected to the same
force, as in the electrolysis of a solution of hydro-
chloric acid, the hydrogen moves, in fact, about five
times as fast as the chlorine. It will presently be
seen that a number of facts concerning conductivity
in solutions may be explained by the assumption of
different rates of motion for the different ions, but it
must always be remembered that the same quantity
of positive electricity in cathions must be present in
any part of a solution as there is negative in anions
there.
The motion of the different ions may be illustrated
by comparing them to two companies of cavalry going
in opposite directions. Suppose one company walking,
F
66
ELECTROCHEMISTRY
CHAP.
the other galloping, and imagine a ditch in the way,
which they all cross. If the second company moved
five times as fast as the first, five horsemen would cross
the ditch in one direction, while one was crossing in
the other, or, of the six crossing the ditch in a given
time, five belong to the second, and one to the first
company. If each of the horsemen carried a sixth
of a bushel of oats with him, one bushel would cross
the ditch in the unit time, though |- of it go in one
direction and -^ in the other. The oats here represent
the electricity.
When a solution of hydrochloric acid forms part
of an electric circuit, the conduction of a quantity of
electricity through the solution takes place in such a
manner that % of it, as positive electricity, moves in
one direction with the hydrogen ions, and ^ in the
other with the chlorine.
The effect of these different rates of migration
upon the composition or concentration of the different
parts of the solution may
be easily calculated: Sup-
pose a solution of hydro-
chloric acid containing 30
gram- equivalents be placed
in a vessel between the
electrodes A and B (Fig.
14). In each third of
the vessel there are then
10 gram -equivalents. If
96540 coulombs be conducted through the solution,
one gram-equivalent of hydrogen and one of chlorine
will separate at the electrodes A and B, and we may
imagine these gases removed from the solution. The
amount of electricity, 96540 coulombs, must have
FIG. 14.
iv THE MIGRATION OF THE IONS 67
passed through every cross -section of the solution,
therefore through C and D.
If both ions migrate with the same speed, one
half of a gram- equivalent of H ions, carrying 482*70
coulombs, has passed from BD through DC to AC, and
half a gram-equivalent of Cl, also carrying 48270
coulombs, has moved through DC from AC to DB, or
one gram - equivalent of ions has passed the cross-
sections C and D. One gram-equivalent of hydrogen
has been removed from AC as gas, while, according
to the supposition, one half a gram -equivalent has
come in from DC, therefore AC now contains 9|-
gr am -equivalents of H ions. Since one half of a
gram -equivalent of Cl has passed from AC, there
are also 9j gram-equivalents of Cl there. Similarly
DB contains 9|- gram -equivalents of H and Cl. It
follows, then, that when the rates of migration of
the ions are the same, the relation of the concen-
tration in AC and BD remains unchanged. The
solution in the middle division, DC, has the same con-
centration as originally, that is, 1 equivalents, because
the same number of ions have entered this portion as
have left it.
The hydrogen ions really migrate about five times
as fast as the chlorine, and the above consideration
must be altered accordingly. There have actually
|- gram-equivalents of H ions with |-. 96540 coulombs
passed from BD through DC to AC, while -g- gram-
equivalent of Cl ions with -J-. 96540 coulombs have
passed from DB to AC, or, in all, one gram-equivalent
with 96540 coulombs has passed through the sections
C and D. The composition of the middle portion
remains unchanged as before ; AC and BD have under-
gone the following changes : one gram-equivalent of H
68 ELECTROCHEMISTRY CHAP.
ions has left the solution in AC, being evolved as gas,
|- of an equivalent have entered AC, so there are now
here 9|^ gram-equivalents of H ions ; there is also the
same number of Cl ions in this portion of the solution,
because only ^ gram-equivalent of Cl has left it. In
BD there are left only 9-^ gram-equivalents of H ions,
since |- have passed from this portion to AC, and
there are also 9^- gram-equivalents of Cl here, for one
equivalent has been evolved as gas at the electrode,
and only ^ equivalent has entered from CD. There
are then 9|^ gram-equivalents of hydrochloric acid in
AC, and only 9^- in BD, or AC has suffered a loss of
|-, while BD has lost - equivalents.
From these two examples the rule is derived that
the loss at the cathode (in AC) stands in the same
ratio to the loss at the anode (BD) as the rate of
migration of the anion (Cl) to that of the cathion (H)
(1:5 in this case).
It was in the manner just indicated that Hittorf
was able to determine the relative rates of migration
of the different ions from the changes taking place in
the concentration of the solution near the electrodes.
His conclusions, though they at first met with some
opposition, are now generally accepted.
From a superficial consideration of the question,
one is inclined to believe that when one of the ions
migrates faster than the other, positive ions must
accumulate in one part of the solution, and negative in
another. That this is not the case has, however,
already been observed. If, for example, x be the
amount of positive ions separated from the solution,
and y the amount which has come to AC from BD
through CD, then AC has x y less positive ions than
before the passage of the current. The same amount
iv THE MIGRATION OF THE IONS 69
x yoi negative ions must in this case have gone to
BD, for if x ions have separated at the electrode, x
ions must also have passed the sections C and D, and
y have gone from BD to AC. Similar considerations
apply to BD. In order that the law of electricity
that the current-strength shall be the same in all parts
of the circuit may obtain, the relations must be as
here described.
A second question which might naturally present
itself is : How can one gram-equivalent of chlorine
separate at the electrode B, when only -J- gram-equiva-
lent has passed through any section of the solution ?
To explain this it is assumed that there is always a
large excess of ions in the immediate vicinity of the
electrode, so that in any given time more may
separate at the electrode than migrate towards it.
The phenomenon of ordinary diffusion assists in this
case.
The determination of the ratio of the rates of migra-
tion of two ions is as simple as it appears from the
above. It is only necessary to divide the solution,
whose concentration is known, into three parts, and,
after the passage of a known quantity of electricity, to
measure the concentration -changes which have taken
place. The middle portion must always remain un-
altered. This being the case, the material which has
been concentrating at the electrode has not diffused
from that portion of the solution, and thus destroyed
the value of the results.
"We will represent by 1, expressed in gram-equiva-
lents, the amount of cathion or anion (since the two
quantities are always alike) separated at the electrodes,
and by n that portion of a gram-equivalent of cathion
which has passed from the anode to the cathode ; then
70 ELECTROCHEMISTRY CHAP.
1 __ n gram-equivalents of anion must have migrated
from the cathode to the anode. These quantities, n
and 1 n, are called the shares of transport or trans-
ference numbers of the cathion and anion respectively,
and their ratio gives us, as above described, the ratio
of the velocities of migration.
n u loss at the anode
I -n v loss at the cathode '
where u represents the velocity of migration of the
cathion, and v that of the anion. Finally, the relative
rate of migration of an ion is the quotient obtained
by dividing the distance over which it has gone by the
sum of the distances both ions have covered. For the
cathion this would evidently be represented by n, and
for the anion by I n, since the distances are pro-
portional to the transported amounts.
As is evident, the relative rates of migration of the
ions can be experimentally determined, but their actual
velocities expressed in a definite unit of measurement
cannot be learned in this way.
The following example illustrating the method
employed is taken from Hittorf s work. It will make
the point still clearer, and show how the calculation is
easiest made.
A solution of silver nitrate was electrolysed for
some time, and the quantity of precipitated silver deter-
mined. This amounted to 1*2591 gram. A certain
volume of the solution about the cathode gave 17 '46 2 4
grams of AgCl before, and 16-6*796 after the electro-
lysis. It had lost 0*7828 gram of AgCl, or 0'5893
gram Ag. If no silver had come into this portion of
the solution, its loss would have been the silver pre-
cipitated on the electrode, but being found only 0*5893
iv THE MIGRATION OF THE IONS 71
gram poorer in silver, 1-2591 0'5893 or 0'6698
gram of silver must have migrated into it. If as
much silver had migrated as was precipitated (1*2591
gram), the share of transport for silver would have
been = 1, and the N0 3 ion would not have taken part
in the migration. But only 0*6698 gram of silver
actually migrated, so the share of transport for silver is
^^5 =0-532. For the NO, ion it is 1 0-532 =
1*2591
0*468. The solution about the anode might have been
analysed to serve as a check for the above. A loss of
0*6698 gram of silver would have been recognised at
that point.
When it is preferable from an analytical standpoint,
the analysis may, of course, be carried out for the
anion instead of the cathion, if, for the sake of greater
certainty, both anion and cathion are not investigated.
An example of this is found in the determination
of the shares of transport for cadmium and chlorine.
In this case the anode consisted of amalgamated
cadmium, which formed cadmium chloride with the
chlorine liberated. From the loss in weight of the
anode the quantity of chlorine separated was deter-
mined. The original concentration of chlorine at the
anode was known, and after the electrolysis it was
again determined. All of the cadmium chloride formed
remained in this portion of the solution, and the cor-
responding amount of chlorine was subtracted from
the total amount found here. This remainder, when
subtracted from the original amount present, gave the
" loss," from which, as before, the transported quantity
of chlorine was calculated. This is the difference
between the amount of chlorine which combined with
cadmium and the above " loss."
72
ELECTROCHEMISTRY
CHAP.
There are a great many forms of apparatus which
have been used for the measurement of these quanti-
ties. In order to give an idea
of the essential features of
such an apparatus, one used
by Nernst and Loeb for deter-
mining the shares of transport
for silver salts is represented
by the cut (Fig. 15). The
two electrodes are silver.
Upon the cathode a quantity
of silver was precipitated,
which was in each case a
measure of the quantity of
electricity which had passed.
The same amount of silver
was simultaneously dissolved
from the anode. The appar-
atus resembles the Gay-Lussac
burette in form. In order to
do away with the disturbance caused by the falling of
silver from the cathode, this was placed in the side
tube, being introduced through the small tube B into
the bulb at its bottom. This electrode consisted of a
cylindrical piece of silver foil attached to a silver wire.
The anode, which was a silver wire twisted at its
lower end into a spiral, was introduced through A, and
reached to the bottom of the longer tube. The straight
portion of this electrode was encased in a glass capil-
lary. At A and B were corks, each pierced by a short
piece of small glass tubing. The piece in A simply
allowed of the passage of the electrode wire, while that
at B had a piece of platinum wire fused into its side,
upon which the electrode could be hung. With this
FIG. 15.
iv THE MIGRATION OF THE IONS 73
arrangement it was possible to remove portions of the
solution from the apparatus without disturbing the
electrodes, by drawing or forcing the liquid through
the rubber tubes which are shown connected to the
glass tubes at A and B.
In performing an experiment with such an appar-
atus the electrodes and corks were weighed. When
the apparatus had been put together, the opening at A
was closed, the opening of the tube C was placed in
the solution to be used, and by sucking at B, the whole
was filled to a point above the side tube. The tubes
usually held from 40 to 60 cubic centimeters of solu-
tion. The exit tube was then closed with a rubber
cap, and the whole placed in an upright position in an
Ostwald thermostat. After the temperature was properly
adjusted the current was conducted through the solution.
Immediately after disconnecting the current the exit
tube was opened, and by blowing at the opening B, the
desired quantity of solution removed into a properly
tared vessel. It was then weighed and analysed.
The amount of solution remaining in the tubes was
determined by weighing the whole and subtracting
the weight of the apparatus. In case no considerable
motion had taken place within the solution, as through
diffusion or convection currents, the altered portion of
the solution about the anode was removed in the first
small portion, and there was sufficient of the unaltered
middle portion to serve for washing out from the
electrode the solution of changed concentration. The
following portions of solution were then unaltered in
concentration, while that part of the solution which
was about the cathode remained in the apparatus. A
test of the accuracy of the experiment was found in
the unaltered condition of the middle portions of the
74 ELECTROCHEMISTRY CHAP.
solution, as well as in the fact that the solution about
the cathode had lost as much silver as that at the
anode had gained.
Hittorf asked himself at the beginning of his work,
Are these shares of transport constant, or are they
variable under varied conditions ? and, if they are
variable, upon what do the variations depend ?
He recognised three points to be taken into con-
sideration the influence of the current- strength, that
of the concentration, and that of the temperature. He
found that the velocities of migration of the ions were
independent of the current -strength, but dependent
upon the concentration.
As solutions more and more dilute were examined, he
found, however, that a point was finally reached beyond
which further dilution caused no change in the relative
rates of migration. This is not difficult to understand.
In the concentrated solutions there is a considerable
quantity of undissociated molecules, and these mole-
cules offer resistance to the motion of the ions among
them, which resistance must be dependent upon the
nature of the ions, the molecules, etc. As the dilution
becomes greater the molecules disappear, until the
point is reached where the dissociation is complete, or
their effect not to be observed.
Hittorf did not discover any effect produced by the
moderate changes of temperature to which his solutions
were subjected. Later and more extended investiga-
tions, however, have proved that the relative rates of
migration of the ions are slightly affected by changes
in the temperature, and that these changes lie in
such a direction that with increased temperature the
velocities of the different ions seem to tend toward
a common value.
iv THE MIGRATION OF THE IONS 75
If other solvents than water be used, as, for instance,
methyl or ethyl alcohol, in which dissociation also
takes place, the values found for aqueous solutions
are no longer applicable.
Thus far only univalent ions have been considered.
In the case of ions of other valencies, the method
for determination of the shares of transport is the
same as given. If one bivalent is combined with
two univalent atoms, as in BaCl 2 , the charged ions
are Ba 11 and Cl, Cl, and, in the above notation,
M
- represents the ratio existing between the rates of
migration of the barium ions Ba 11 and that of the
two Cl ions.
Still another advance was possible through Hittorf s
study of the concentration - changes at the electrode ;
namely, the compositions of the ions resulting from the
dissociation of the compounds were discovered. Cyanide
of silver, for example, dissolves in a solution of potassium
cyanide, but the exact nature of the compound formed,
and the composition of the ions into which it dissociates,
cannot be determined from this fact alone. When Hit-
torf conducted the electric current through this solution,
silver was precipitated at the cathode. Upon analysis
of the solution at the cathode after the electrolysis he
found that the quantity of potassium had increased
by an amount equivalent to the separated silver, and
also equivalent to the quantity of electricity passed
through the circuit as measured in a silver voltameter.
This result he interpreted in the following manner :
K is the positive and Ag(CN) 2 the negative ion. Leav-
ing out of account the precipitated substance, the
positive and negative ions must always be present in
equivalent amounts, which evidently requires the silver
76 ELECTROCHEMISTRY CHAP.
and potassium to be present here in equivalent quanti-
ties. The potassium must have separated at the
cathode, and then have acted upon the solution, pre-
cipitating silver and entering the solution itself. This
explains the presence of an excess of potassium in this
part of the solution exactly equivalent to the separated
silver or to the electricity which has passed. The
precipitation of the silver then becomes, in this case, a
secondary reaction ; the potassium equivalent to the
electricity has precipitated the equivalent of silver.
In a similar manner he found that sodium platinic
chloride dissociates into two sodium cathions and the
bivalent anion PtCl 6 , sodium gold chloride into one
sodium ion and the univalent ion AuCl 4 , ferro-cyanide
of potassium into four potassium ions and the quadri-
valent ion FeCy g , ferri-cyanide of potassium into three
potassium ions and the trivalent ion FeCy 6 , etc.
These conclusions of Hittorf, which, when first
published, met with great opposition, are now known
to be perfectly correct, and have been proved in
many ways, for instance, by the method of the
determination of freezing point reduction. Another
experiment which Hittorf also made may well be
considered at this point. He found in his study of
potassium chloride and iodide solutions that the chlorine
and iodine ions have nearly the same velocity of migra-
tion. With our present knowledge we can safely
predict that through the electrolysis of a mixture of
these salts the ratio of the concentrations of chlorine
and iodine will remain unchanged in all parts of the
solution, since these two take part equally in the
conduction. This was found to be the case. At that
time this point caused some trouble, because the iodine
alone separates at the electrode, and the difference
iv THE MIGRATION OF THE IONS 77
between the phenomena of electrical conduction and
precipitation was not understood. Since the iodine
alone separated, it was concluded that possibly this
alone, belonging to the easier decomposed body, con-
ducted the electricity. The fact that iodine alone
separates at the electrode in this case is no evidence
as to what ions conduct the electricity through the
solution.
F. Kohlrausch l has lately arranged the relative
rates of migration of the ions of the most important
and best - investigated electrolytes in tabular form,
and this table is here given. The values are the
transference numbers, and represent the ratio of the
velocity of migration of the anion to the sum of
the velocities of the anion and cathion. The con-
centrations of the solutions (m) are given in gram-
equivalents per liter.
1 Wied. Ann. Iv. 287, 1893.
[TABLE
HIM?
1 1 1
1 i 1 1 ! I? 1 1
1 1 1 1 1 I
1 1
S 1
1 1 lt=
1 i 1 1 1 1? 1
O
1 1
1 1
1? 1 l<p
1 1 1 II 1 IS
M M???
o o o
??l
? l?l 1 1
O
1 1
??l iS
00 000
1? 1
? 1
n COCO t-
cp t- | | | ^
00000
1 1 1 IP 1
00
S|| M H?
00
IP 1
10 | o i- | o 1*7*
b bo b bb
1 1 1
I
* 99^
000
CO i O
*- 1
b bbbbbbb
>o co o o o *
bbbbbb
bb
1? 1? l
000
t- 00 OS
co * in
bob
. 1 ? 1 1 1
000
1 i 1 1
00
1 I
1 1 1
1 1
1 i 1
00
1 1
1 1 1 1 1 1 1
Pi 1
1 1
1 1 1 1 1 1 1 i
1 i 1 1
CHAPTEE V
THE CONDUCTIVITY OF ELECTROLYTES
Specific and Molecular or Equivalent Conduct-
ivity. We have already learned something of the
nature of conductors of the first class. The resistance
of such conductors is dependent upon the nature of
the material, its form and the temperature.
Eepresenting the resistance of a cylinder one
meter long, and of one square millimeter cross-
section, by k, the resistance of a similarly formed
piece of the substance at the same temperature is
* - , where I is the length in meters and q the area of
the transverse section in square millimeters. The factor
k represents the specific resistance of the substance.
The resistance of a cylinder of mercury one meter
long and one square millimeter in section at has
been chosen as the unit of resistance, so that all re-
sistances referred to this unit are easily comparable.
In using this unit it may also be said that the value k
for any substance is that number by which the resist-
ance of a certain amount of mercury of a definite form
at must be multiplied to give as product the re-
sistance of the substance itself when possessing exactly
the same volume and form.
80 ELECTROCHEMISTRY CHAP.
Besides the mercury, or the so-called Siemens unit,
the ohm is also used as unit. This is the resistance
of that length of a conductor in which the potential
falls one volt when the current-strength is one ampere.
The specific resistance expressed in ohms is evidently
that of a cylinder of the substance in question, which
is one meter long, and whose cross-section is one square
millimeter in area. The Siemens unit stands to the
ohm in the ratio 1 : 1*063, so that in order to express
Siemens units in ohms, it is necessary to divide the
former by TO 6 3. Conversely the product 1*063 x
ohms gives us the value of the ohms in Siemens units.
Kecently the centimeter has come somewhat into use
in the unit of specific resistance instead of the meter
and millimeter. This specific resistance is then
that of a cube whose edge is one centimeter long,
and is evidently ten thousand times as small as the
former.
The greater the resistance, the less is the con-
ductivity, and as the conductivity increases, the
resistance decreases. That is, resistance (R) and con-
ductivity (L) are reciprocal values, or
The word conductivity is used mainly with reference
to solutions, and will be here so used. The word
resistance is applied more especially to conductors of
the first class. It seems at first natural to express
the conductivity of solutions in reciprocal Siemens
units or ohms, but this has not proved a satisfactory
method of expressing these solution -conductivities.
The conductivity depending in this case almost
entirely upon the dissolved substances, it has been
v THE CONDUCTIVITY OF ELECTROLYTES 81
found advantageous to base the comparisons upon
the contents of the solutions, the conductivities of
solutions being compared which contain one gram-
molecule of the electrolyte. This is called the
molecular conductivity, and is commonly expressed
by fj,. If v be the volume in cubic centimeters in
which one gram -molecule of an electrolyte is dis-
solved, then the molecular conductivity p = vx specific
conductivity, and may be deduced as follows. Between
two parallel electrodes exactly one centimeter apart
for instance, two opposite walls of a vessel one liter
of a solution containing one gram -molecule of the
electrolyte is placed. The value of v the volume for
the solution is then 1000, the cross-section of this
liquid conductor is 1000 sq. cm., and its conductivity
is called the molecular conductivity //, for the electro-
lyte. This value is evidently 1000 times as great
as the specific conductivity I of a cube whose edge
is one centimeter long, consequently //, = vl. With a
half normal solution (t/=2000) two liters of the
solution must be placed between the electrodes to
introduce one gram -molecule, and the cross -section
of the circuit has an area of 2000 sq. cm. The
molecular conductivity // is then 2000 times as great
as its specific conductivity I' or // = i/l'.
The specific conductivities naturally change when
the concentration of the solution is changed, as do also
the molecular conductivities. In other words, p the
molecular conductivity is equal to the product vl or
10000 vl l} where I represents the specific conductivity
of the solution in the form of a cube whose edge is one
centimeter long, and ^ is the specific conductivity of the
column of liquid one meter long, whose area of cross-
section is one square millimeter. If the number of
G
82 ELECTROCHEMISTRY CHAP.
gram-molecules of substance which are contained in
one liter be represented by m, then
I 10 3 L - 10 7
Instead of the molecular conductivity p, the value
X is sometimes used as a basis to which conductivity
may be referred; it is called the "equivalent con-
ductivity"
1 ' 1Q3 * 1QT
when n is the number of equivalents which a liter of
the solution contains. For univalent compounds, as
those first to be considered, the values of //, and X are
identical.
General Laws. The first clear ideas to be
obtained concerning the conductivity of electrolytes
resulted from the experiments of Kohlrausch. The
work of discovery was then rapidly pushed forward by
Arrhenius, Ostwald, and others. It was found that
the equivalent conductivities of all electrolytes in-
creased with increasing dilution, reaching in many
cases a maximum which did not alter for further
dilution. In cases where this maximum value for the
equivalent conductivity is reached, the following law
of Kohlrausch 1 is true.
The equivalent conductivity of a binary electrolyte is
equal to the sum of two values, one of which depends only
upon the cathion, and, the other upon the anion.
This expresses the fact that the conductivity of an
electrolyte is an additive property ; in other words, it
is simply the sum of the conductivities of its ions.
1 Wied. Ann. vi. 1, 1879, and xxvi. 213, 1885.
THE CONDUCTIVITY OF ELECTROLYTES
This law is evident from the accompanying table
containing the equivalent conductivities of the com-
pounds of the metals in the vertical columns, with the
radicles in the horizontal. 1
K
Na
Li
NH 4
H
Ag
01
123
103
95
122
353
N0 3
OH
118
222
98
201
...
350
109
C10 3
115
103
C 2 H 3 2
94
73
...
...
...
83
The differences between corresponding values of the
vertical columns are approximately equal, as are also
those between corresponding values in horizontal lines.
This could only be explained by considering the con-
ductivities as the sums of two independent constants.
A great many other properties of dilute solutions of
electrolytes, which may be similarly expressed as the
sums of the properties due to the ions constituting the
electrolyte, are recognised. Ostwald has called them
additive properties ; among these may be mentioned
the colour and the index of refraction.
It is found that the dissociation theory offers a
perfect explanation of the above law of conductivity.
The conductivity of electricity through a solution
consists in a motion of the single ions. If in a solu-
tion of x ions in an electric circuit there are 100
ions passing the cross-section of the liquid conductor
in unit time, then 200 ions would pass if there were
1 t = l8 C. The numbers represent the equivalent conductivity at
extreme dilution, and are taken from Kohlrausch's tables ( Wied. Ann.
1. 406, 1893).
84 ELECTROCHEMISTRY CHAP.
2 x ions in the solution, providing other conditions
remained unaltered, that is, the conductivity would
be twice as great as before. The conductivity of a
solution depends primarily upon the number of ions
between the electrodes, but also upon the sum of the
velocities of migration of the two kinds of ions.
The equivalent conductivity of an electrolyte can
be measured directly by placing a solution of one
gram-equivalent of the electrolyte in question into a
vessel, two of whose opposite walls one centimeter
apart, serve as electrodes. Other dimensions of the
vessel than the distance between these wall- electrodes
need not be fixed. The measured conductivity is in
such a case also the equivalent conductivity. The
volume of the solution may evidently be of any
desired magnitude, so long as the quantity of the
dissolved substance is the same. If the substance is
completely dissociated there are in such a case two
gram-equivalents of ions between the electrodes, and
the conductivity will always be the same, no matter
how much of the solvent be present, while these ions
which alone carry the electricity are present between
the electrodes. The size of the electrodes need not be
taken into consideration, for it plays no part in the
conductivity, provided that the number of ions between
the electrodes is not changed. Consequently with
increasing dilution, a maximum for equivalent con-
ductivity is finally obtained which remains constant
for further dilution. It is also easy to understand
why the equivalent conductivity should be less for
concentrated solutions than for dilute, because in the
former the dissociation is less ; or, in other words, the
number of ions has been diminished. With increasing
dilution the degree of dissociation, and consequently
v THE CONDUCTIVITY OF ELECTROLYTES 85
the equivalent conductivity, also increases, until that
maximum value is reached which corresponds to
complete dissociation.
Through these facts we observe the superiority of
the new theory over that of Clausius. According to
the latter, the conductivity depends upon the frequency
of the changes between the parts of molecules, and it
would seem necessary to conclude that the more
concentrated the solution, the more often would these
changes take place ; the equivalent conductivity, in
consequence, would increase with increasing concen-
tration, which is contrary to fact.
Dilute equivalent solutions of neutral salts, strong
acids, and bases, since they are practically completely
dissociated, contain the same number of ions ; conse-
quently their equivalent conductivities stand in the
same ratio as the sums of the velocities of migration of
their respective ions. The velocity of migration of an
ion is a constant, because the ion moves independently
of other ions in the solution ; therefore X = K(u + v), K
being a factor of proportion dependent upon the chosen
units, and u and v representing the rates of migration of
the gram-equivalents of the positive and negative ions.
This is an expression for the law of Kohlrausch.
The maximum value of the equivalent conductivity
of an electrolyte is the sum of the velocities of
migration of its ions, and as we have already obtained
the relative values of these rates of migration from
Hittorfs work (see p. 70), we can now calculate the
single values.
u n
v I n
u ' K = nX.
86 ELECTROCHEMISTRY CHAP.
The proportionality factor K being unity, in other
words, expressing the rates of migration in the same
units as the conductivities, then
When the value of the rate of migration for a
single ion is known, that of the others may be obtained
from the shares of transport as well as from values for
the limits of conductivity ; the fact that the results
as obtained by the two methods agree, justifies the
interpretation of' the phenomena. Kohlrausch has
calculated and compared many of these velocities of
migration, and found that the two methods of deter-
mi$ation give the same results.
From the latest and most correct collection of
velocities of migration computed by Kohlrausch ( Wied.
Ann. 1. 385, 1893) the following mean values have
been selected (*=18 C.) :
K = 60, Na = 40, Li = 33, NH 4 = 60, H = 290, Ag=52;
01 = 62, 1 = 63, N0 3 = 58, C1Q 3 = 52, C10 4 =54,
C 2 H 3 2 = 31, OH =165.
The conductivity at great dilution, X, is = u + v.
If not all the molecules were dissociated, but only half
of them, the conductivity ~\f would only be half as
great, because it is proportional to the number of ions,
or
'
and in general \ = x(u + v\ where \ represents the
equivalent conductivity of an electrolyte, one gram-
equivalent of which is contained in the volume v, and
x is the portion which is dissociated, or the degree of
dissociation. Kepresenting the maximum value for the
v THE CONDUCTIVITY OF ELECTROLYTES 87
equivalent conductivity by X^ the following equations
may be written :
A^ = u + v
The degree of dissociation of a substance in a solution
is equal to the ratio of the equivalent conductivity of that
solution to its equivalent conductivity at infinite dilution.
As already seen (p. 59) Arrhenius had come to
this conclusion, and there was agreement between the
values for the degree of dissociation as obtained from
the conductivity and from the method of freezing
point depression.
The determination of the degree of dissociation of
different substances has led to very important results.
Ostwald found by experiment that the order in which
the acids act in the catalysis of methyl acetate, sugar,
etc., is also the order of their " affinities " for a base.
This latter could be determined by thermochemical or
volume-chemical measurements. From Ostwald's work
a measure for the chemical activity, " affinity," or
" strength " of an acid (or base) is obtained.
Arrhenius sought to discover the existence of a
connection between conductivity and the chemical
activity, determined as just mentioned, and found
that the two are in reality closely connected.
Having solutions of two acids, each containing one
gram-equivalent per liter, the "strengths" will evi-
dently not be the same if the degrees of dissocia-
tion differ. On diluting the two solutions the dis-
sociation increases, and finally the acids are wholly
dissociated. At this point the two " strengths " must
88 ELECTROCHEMISTRY CHAP.
be the same.. The relative "strengths" of acids and
bases change therefore with the conditions of concen-
tration. This was shown by Ostwald before the advent
of the Arrhenius theory of dissociation.
Determination of the Dissociation Constant by
Electrical Conductivity Kohlrausch Method.
Eecognising the dissociation theory, and the applica-
bility of the gas laws to dissolved substances, as
established by van't Hoff, an affinity constant for
binary electrolytes, or, in other words, a dissociation
constant which is independent of the dilution, may be
calculated. This was first shown by Ostwald. 1
According to the law concerning the effect of mass
in a reaction for a gas which decomposes into two
parts, the temperature being constant, the following
principle holds :
The product of the concentrations of the two parts,
divided ty the concentration of the undissociated part, is
a constant.
For example, the vapour of ammonium chloride at
high temperature decomposes partly into ammonia and
hydrochloric acid. When the temperature is constant
r> 2
the conditions may be represented by = K , where
p l is the pressure due to the ammonia (or acid), the
two being the same, because the substances are present
in equal molecular quantities, p represents the press-
ure due to the ammonium chloride. These values,
being evidently proportional to the concentrations,
may be used in place of them.
Compressing the gas, the values for the partial
pressures are increased, and increasing its volume, the
partial pressures diminish, but the value K' remains
1 Zeitschr. physiJc. Chem. ii. 270, 1888.
v THE CONDUCTIVITY OF ELECTROLYTES 89
constant. Moreover, if an excess of one of the com-
ponents is added, no change takes place in the constant.
If ammonia is added, its partial pressure or the ammonia
pressure is increased, and if no other change took
place, the value of K 7 would be greater than before ;
but, since this remains the same, either the numerator
o
of must decrease or the denominator increase, or
P
both changes take place. The latter happens. A part
of the ammonia and acid combine to form ammonium
chloride, this combination taking place to such an
extent, that the product of the partial pressures of
NH 3 and HC1, divided by the partial pressure of the
salt, assumes its previous value :
P NH 4 C1
Here, of course, p f and p" do not have the same value.
Since, according to van't Hoff's theory, substances in
dilute solution obey the laws governing gases, it is
natural to assume that such relations as are illustrated
by the ammonium chloride vapour would be found
in the case of a binary electrolyte, or one which
decomposes in solution into two ions. For example, a
dilute aqueous solution of acetic acid contains besides
undissociated CH 3 COOH also a quantity of the two
ions H and CH 3 COO, and it should consequently be
c 2
expected that the equation -^ = K for this solution
c
would be independent of the dilution, ^ representing
the concentration of each of the ions, and c that of the
undissociated molecule. Such is actually the case.
The presence of other substances in the solution does
not affect this constant. The magnitude of the dis-
90 ELECTROCHEMISTRY CHAP.
sociation constant K is a characteristic of every
compound, and its determination is therefore of great
importance.
In order to show the existence of this relation
for solutions, it is of course primarily necessary to
have a method for finding out the concentrations c
and c r For this purpose the determination of
electrical conductivity is most satisfactory, and it is
in consequence of this fact that the conductivity
measurements in general are of such value.
If in V liters one gram -molecule of a binary
electrolyte is dissolved, and x is the degree of dis-
sociation of the electrolyte, or that part of the gram-
35
motecule which has decomposed into ions, ^ will
then stand for the quantity of a gram -ion in one
liter, that is, for the concentration of each of the ions ;
1 x
therefore -=r- must be the concentration of undissociated
3.2
material, and finally - =. = K.
Hence for the determination of the dissociation
constant K of a given solution, only the degree of
dissociation need be known. But this dissociation x
is equal to the ratio of the molecular or equivalent
conductivity of the solution in question to the same
at infinite dilution, or & = and substituting this
QO
value of x in the above equation,
_
~
A knowledge of the molecular or equivalent con-
ductivity and the conductivity at infinite dilution
v THE CONDUCTIVITY OF ELECTROLYTES 91
suffice therefore for a determination of the dissociation
constant K.
Before considering the experimental proof of the
formula it is advisable to become acquainted with
the methods for determining the conductivity of a
solution.
Through the use of Ohm's law (C = j measure-
\ /
ment of the resistance of metallic conductors, or those
of the first class, is very simple, but in the case of
electrolytes this is no longer true. The gradual fall
of potential, TT, which exists in that portion of the
circuit occupied by a solution is more difficultly
determinable, because of the variable changes of the
potential at the electrodes due to the chemical pro-
cesses taking place there. Many methods have been
devised for overcoming this difficulty and measuring
the actual conductivity or resistance of solutions.
The one now commonly in use is the only one which
need be here described. This is the method of
Kohlrausch.
The method depends upon the application of
an alternating current. By its use the change of
potential at the electrode due to polarisation is practi-
cally removed, for the polarisation effect produced by
the current of one direction for a small fraction of a
second, may be considered as neutralised by the
current when its direction is reversed. The circuit is
then similar to one composed of conductors of the
first class only, and has practically only constant
electromotive forces at the electrodes. Under such
conditions, the resistance may be measured as in the
case of metallic conductors.
The apparatus employed is shown in Fig. 16, and
92 ELECTROCHEMISTRY CHAP.
is essentially the ordinary Wheatstone's bridge arrange-
ment. 1 At 5 is a galvanic element connected with an
induction coil (6) for
producing the alter-
nating current. At 7
is a telephone, a gal-
vanometer being, of
course, inapplicable to
alternating currents.
FIQ. 16. The four arms of the
bridge are represented
by a, b, c, and d. When the element at 5 is in
activity a tone is audible in the telephone, except
when the resistances of the four parts of the bridge
are in the relation expressed by r = -3 . When
such is the case, a clearly denned minimum, if not
entire absence of sound, is the result. At c there
is a resistance box usually measuring ohms or
Siemens units. The electrolyte whose resistance is
to be determined is placed in the vessel at d, which
is in a thermostat. The two parts of the bridge
a and I are most conveniently composed of a
uniform platinum wire, which is stretched over a
meter scale; upon this wire a movable contact con-
nected with the telephone is brought by changing the
position of which the tone-minimum may be found.
Kesistance of such an amount is introduced into the
branch c of the circuit, that the point of contact for
minimum tone is in the middle portion of the wire a,
~b. That portion of the wire from one end to the point
of contact leading to the telephone is a, and the other
portion &, and the lengths of these may be read to
1 Ostwald, Zeitschr. physik. Chem. ii. 561, 1888.
v THE CONDUCTIVITY OF ELECTROLYTES 93
tenth-millimeters directly from the scale. The actual
resistance of this wire does not enter into the calcu-
lation, as it is only the ratio a : b which is required.
The resistance of the other metallic conductors in
the circuit from the resistance box to the electrolyte,
etc., must be negligibly small. The desired resistance
of the electrolyte is then d and its conductivity
For a vessel in which to determine
the conductivity the one represented
in Fig. 17 is usually employed.
The electrodes may be separated
by the desired distances, and their
area made to suit the requirements
of most cases. Platinised platinum
electrodes are used to the best
advantage.
Expressing the distance between
the two electrodes in meters and their
surface -area in square millimeters, the specific con-
ductivity may be obtained as follows :
sq.mm.
meters '
cb
and also, according to
equivalent conductivity X = -
page 82, the molecular or
10 7
. The conductivity
is thus expressed either in reciprocal ohms (mhos) or
in Siemens' units.
In order to obviate the necessity of measuring the
space between the electrodes, mercury may be placed
in the vessel and its resistance measured at 0,
expressed in any desired units. Now measuring
94 ELECTROCHEMISTRY CHAP.
the resistance of an electrolyte in the same vessel,
the two resistances found will stand in the same
ratio as the specific resistances of the mercury and
electrolyte. The specific resistance of mercury (re-
ferred to one meter length with one square millimeter
sectional area) is one Siemens unit ; therefore the
relation of the desired resistance to that of the mercury
(or the specific resistance of the electrolyte) is expressed
in Siemens units. The resistance of the mercury in
the vessel at is called the resistance -capacity of
the vessel, and, as stated, may be measured in any
desired units, as the final result is only a ratio. The
units chosen must, however, be retained in measuring
the resistance of the electrolyte. The resistance-
capacity is then represented by that number by which
the resistances measured in the vessel must be divided
in order to obtain the specific resistance, or it is the
number with which the conductivity corresponding to
the measured resistance must be multiplied in order to
obtain the specific conductivity.
In practice this method is not always applicable,
because the resistance offered by the mercury between
the electrodes is so small that it cannot be measured
with sufficient accuracy. This is true in the case of
the vessel above depicted, which is in most common
use. To obtain the resistance - capacity of such a
vessel, a solution possessing much greater specific
resistance than mercury is used, its specific resistance
being measured in turn, in a vessel of different form.
The solution best adapted for such a purpose is 0'02
normal potassium chloride. The relation which its
specific conductivity bears to the conductivity as
measured in the vessel, is the resistance -capacity of
the vessel.
v . THE CONDUCTIVITY OF ELECTROLYTES 95
The calculation is perhaps simplified when carried
out in the manner usually adopted, as follows. If c
be the resistance in the resistance box, and a and b the
lengths of the portions of the platinum wire as
determined by the movable contact when the mini-
mum tone is given by the telephone, the conductivity
of the electrolyte is then expressed by
Knowing the resistance-capacity of the vessel to
be K, the specific conductivity ^ of the electrolyte
would be, as previously explained,
I I = K reciprocal Siemens units.
uC
The equivalent conductivity would therefore be
represented by
A = K ^ 10 7 .
o c n
Instead of using - where n is the number of gram-
equivalents in a liter of solution, V may also be used
where V is the number of liters in which one
gram -molecule is dissolved, and using instead of
K - 10 7 , then
a - V
A = reciprocal Siemens units.
The value of f may be calculated, the equivalent
conductivity X of a 0*02 normal potassium chloride
solution being known, and the value 7 may be ex-
C
perimentally determined. V is here 50, and , being
96 ELECTROCHEMISTRY ^ CHAP.
the only unknown quantity in the equation, is deter-
mined. This ( is equal to the resistance K, of the
vessel multiplied by 10 7 .
Having once determined the value of f for the
vessel, one can proceed to measure the resistance of
any electrolyte at any known state of dilution, and
calculate its equivalent conductivity by means of the
above formula.
The specific conductivity of a 0*02 normal potassium
chloride solution (referred to a length of one meter
with one square millimeter section) is l^ = 2'244 10~ 7
reciprocal Siemens units at 18, or 2 '5 9 4 10~ 7 at
25. The corresponding equivalent conductivities
are.:
= 2-244 ID- 7 - 50 10 7 = 112-2 at 18,
= 2-594 10~ 7 . 50- 10 7 = 129-7 at 25.
The other specific conductivity I is = 2'244 10~ 3
and 2 *5 9 4 10~ 3 at these respective temperatures
from which naturally the same values for X result as
above :
A ( =2-244- ID- 3 - 50- 10 3 = 112-2 at 18,
( =2-594- 10- 3 -50. 10 3 = 129-7 at 25.
That the equivalent conductivities are very great
is shown by the above. A gram - equivalent of
potassium chloride in the 0*02 normal solution, when
placed between electrodes one centimeter apart, offers
at 25 a resistance to the electric current of only
129-7
Siemens units.
The equivalent conductivities of all binary electro-
lytes for infinite dilution are of about this order, and
vary between 50 and 500. This conductivity X, may
evidently have exceedingly small values when the
concentration of the solution is great.
v THE CONDUCTIVITY OF ELECTROLYTES 97
Besides the value of \ v it is necessary to know
the magnitude of X^, in order to calculate the dis-
sociation constant K of an electrolyte.
(A*) 2
ft- = \ r\
Having learned how \ v is determined, attention
will now be given to X M . In some cases this is
obtained in the course of determining \ in dilute
solutions, a maximum value for \, being obtained,
beyond which further dilution does not affect its value.
This maximum is then X^. This is a method appli-
cable only to electrolytes whose tendency to dissociate
is great. The direct experimental determination of
X^ is not possible for compounds which dissociate but
little, because a condition of complete decomposition
would only be reached at such a great dilution that
the measurement of the resistance would be impossible.
It is therefore inapplicable, for instance, to solutions
of the organic acids and bases, where the knowledge
of the value of X^ is very important. Fortunately,
however, the alkali salts of all acids and the halogen-
acid salts of all bases, whether strong or weak, dis-
sociate to a high degree in moderately dilute solutions,
so that the value of X can be determined for these
00
compounds. But X^ represents the sum of the veloci-
ties of migration of the ions of the electrolyte, and
since the rate of migration of the alkali metal ion in
one case, and of the halogen ion in the other, is
known, that of the acid and basic ion respectively
may be obtained by subtraction of these quantities
from the values of X^. Having thus obtained the
velocities of the negative ion of the metal compound,
and of the positive ion belonging to the halogen
H
98 ELECTROCHEMISTRY CHAP.
compound, it is only necessary to add to the former
the rate of migration of the hydrogen ion, and to the
latter that of the hydroxyl ion, both of which are
easily determined experimentally, and the values of
X M for the desired ^compounds are determined.
Through the investigation of a great many feebly
dissociating acids and bases, under very varying
conditions of dilution, it has been found that there
exists for each a dissociation constant which is in-
dependent of the dilution, in conformity with the
theoretical predictions alluded to above.
As a consideration of the significance of this
constant belongs to the subject of chemical statics, it
will not be discussed in detail here, but it may well be
mentioned that the order of the magnitudes of these
constants for different compounds is also the order
of their degrees of dissociation, as they exist in
solutions of the same equivalent concentration.
Direct proportionality does not, however, exist between
the constants and the dissociation, for as the dilution
is made greater, the degrees of dissociation approach
a common value. Some of the results of the existence
of these constants as they were empirically established
by Ostwald before the dissociation theory was proposed
will now be considered.
1. With increasing magnitude of V in the formula
=VK
the value of the left-hand portion of the equation
must also increase and approach infinity. As \ v and X^
are always finite quantities, this can only occur when
\ v = x or with increasing dilution the equivalent con-
ductivity approaches the value X .
v THE CONDUCTIVITY OF ELECTROLYTES 99
2. In the case of weakly dissociating and, con-
sequently, badly conducting electrolytes, where \ is
very small as compared to \ w , the value of X^ X y
is only slightly changed by increasing dilution, so that
it may be practically considered as constant. As a
result
/\ 2
= constant.
That is, the equivalent conductivity increases with in-
creasing dilution in proportion to the square root of the
volume, or the square of the equivalent conductivity
increases in proportion to the volume.
3. If the formula for the dissociation be written as
follows :
the value of 1 x for slightly dissociating substances
differs but little from 1, and the equation approaches
the form
* 2 K
v = K *
4. When the volume V of two or more slightly
dissociating electrolytes is the same, then from the
above
(V) 2
)\ //\o = constant, and
X/, x lf K', and X/, x 2 , K" being the molecular con-
ductivities, degrees of dissociation, and dissociation
constants. X v = x - X , and in consequence, when the
maxima of conductivity of two electrolytes are
practically equal, which is the case with many acids
100 ELECTROCHEMISTRY CHAP.
because of the very great velocity of migration of the
hydrogen ions common to them, the equation
(V)
-, is true, or
the squares of the equivalent conductivities of different
electrolytes stand to one another in the same proportion
as the dissociation constants, when the degrees of dilution
are the same.
5. In the formula
\ v> in the case of highly dissociating electrolytes, may
be considered as nearly constant with changing
dilution, and as X is eo ipso constant,
eo *
: = constant.
The product of the difference between the maximum
of conductivity and the equivalent conductivity into the
volume is a constant.
6. The equation
may be considered as having the form
(T^)v = K
for highly dissociating electrolytes, for here x* is nearly
equal to 1.
The undissociated portion of the compound, multiplied
by the volume, is equal to the reciprocal value of the
dissociation constant.
v THE CONDUCTIVITY OF ELECTROLYTES 101
From this it is evident that, if the undissociated
portion amounts to 1% when V=500, it would
decrease to 1% for V= 1000.
7. If two or more electrolytes having great
tendencies to dissociate are compared under the same
condition of dilution,
A. ' X '
-T- 5 ^ r-^, = constant, and
A ~ A >
the latter may be verbally expressed as follows :
The undissociated portions of different electrolytes, at
the same degree of dilution, are inversely proportional to
the dissociation constants.
If the different maxima of conductivity are nearly
equal,
is approximately correct, or :
The differences between the maxima of conductivity
and the equivalent conductivities arc inversely pro-
portional to the corresponding dissociation constants
wJien the degrees of dilution are the same.
8. Finally, the following regularities for all electro-
lytes may also be deduced. With two electrolytes of
the same degree of dissociation, the left side of the
x 2
expression - = V K being the same for both, the
right side must also be the same, or V 7 K = V" K",
V K"
or ^ = --
V K
The dilutions at which different electrolytes possess
the same degree of dissociation (and also often nearly
102 ELECTROCHEMISTRY CHAP.
the same equivalent conductivity) are in a constant
ratio, and this is, in fact, the inverse ratio of the dis-
sociation constants.
The foregoing approximations may often be used
with advantage.
Relation between Dissociation Constants and
Chemical Constitution. Some very interesting re-
lations have been brought to light between the magni-
tudes of the dissociation constants and the chemical
constitution of the acids, as may be illustrated by
a few examples. The constants for acetic 'and the
three chloracetic acids at 2 5 are as follows :
Acetic acid . . . . 0-00180
Monocliloracetic acid . . 0'155
Dichloracetic acid . . . 5-14
Trichloracetic acid . . . 121*
Through displacement of hydrogen by chlorine, a
large increase in the value of the constant takes
place, the first chlorine atom increasing the constant
about 86 times. The second chlorine makes this new
constant about 3 3 '2 times greater, and the third 2 3 '5
greater still. We are forced then to conclude that
the introduction of chlorine, for example, into acetic
and monochloracetic acid does not produce like effects.
This is not surprising since a chlorine atom is already
present in the latter compound.
An increase in the value of the constant indicates
a greater degree of dissociation for the new compound,
that is, its acid character is more marked. Therefore
an influence in this direction must be ascribed to the
introduction of chlorine. The introduction of such
negative radicals as Br, Cy, SCy, OH, etc., also in-
creases the so-called acid properties like chlorine.
v THE CONDUCTIVITY OF ELECTROLYTES 103
The a and /3 substituted derivatives of acids
possess very different dissociation constants, and the
constitutive property of this constant is thus very
marked. The same thing applies to the isomeric
benzol derivatives, for example :
Benzole acid, C 6 H 5 COOH . . G'0060
o-Oxybenzoic acid, C ( .H 4 (OH)COOH -102
m-Oxybenzoic acid, C 6 H 4 (OH)COOH '0087
2>-Oxybenzoic acid, C 6 H 4 (OH)COOH '00286.
These examples show that a knowledge of the
dissociation constants is of aid in determining the
chemical constitution of compounds. By the intro-
duction of OH into benzoic acid ortho to the carboxyl
group, the value of the constant for this acid is
increased seventeen fold. When the OH enters into
the meta position instead of ortho, the change from
the benzoic acid value is very small but positive,
while an entrance into the para position causes a
considerable reduction of the constant. Consequently
it might be assumed that on starting with ortho-
oxybenzoic acid and substituting its different re-
placeable hydrogen atoms by hydroxyl, the values
for the dissociation constants of the resulting com-
pounds, though not the same as in the benzoic acids,
would still show similar relations. This is the case,
as may be observed from the following table :
Ortho-oxybenzoic (salicylic) acid . .0*102
Oxysalicylic acid, C 6 H 3 (OH) 2 COOH (2-3) 0'114
(2-5)0-108
a-Resorcylic (2-4) 0-052
P- (2-6)5-0
In the acid 2 -3 as also in the acid 2 -5 the new
is in the meta position to the carboxyl group,
104 ELECTROCHEMISTRY CHAP.
and consequently only a very slight increase in the
dissociation constant is to be expected. This agrees
with the experimental observation.
In the compound 2 '4 the new OH has the para
position, and again a new constant less than the
original one is the result. Finally, when the second
OH has taken the other ortho position, as in the acid
2 '6, a correspondingly great increase in the constant
results, the value being about fifty times as great as
before.
Velocity of Migration of Single Ions. Con-
ductivity measurements have served not only to
determine the dissociation constants of a great
many organic acids, but have also given us the
relative rates of migration of the organic anions and
cathions. It has already been stated that the alkali
salts of the acids and the chlorides or nitrates of the
bases are so highly dissociated in solution that the
value of \ m is experimentally determinable. By
subtraction of the known velocity of migration of the
metal ion or of the halogen (or N0 3 ) ion, we obtain
for remainder the velocity of the other ion of the
compound, as already explained on page 97.
Through the stochiometric comparison of the
numbers representing the migration velocities of the
individual ions, certain relations have been discovered,
of which a few at least will be mentioned here. These
are taken from Bredig's l work.
The velocity of migration of the elementary ions is
a function of the atomic weight, and in each series of
related elements the velocity increases with it. With
respect to these the rule holds that great differences
occur only with the first two or three members of
1 Zeitschr. physik. Chem. xiii. 191, 1894.
v THE CONDUCTIVITY OF ELECTROLYTES 105
each series. Similar or related elements with atomic
weights above 35 have about the same velocity of
migration. These points may be illustrated by the
following data (for 25) :
Fl 50-8 Li 39-8
Cl 70-2 Na 49-2
Br 73-0 K 70'6
J 72-0 Cs 73-6
For the complex ions the following principles have
been established :
Isomeric ions migrate at the same rate, e.g.
Butyric acid ion 30*7 Propylamrnonium ion 40'1
Isobutyric acid ion 30'9 Isopropyl ammonium ion 40 '0
Cinnamic acid ion 27'3 Chinolinmetliylium ion 36 '5
Atropic acid ion 27*1 Isochinolinmethylium ion 36 -6
Similar changes in the composition of analogous
ions produce alterations (da) in their velocities of
migration (a) which are of the same general order and
sign, but their magnitudes are less the lower the
migration rates themselves, instead of remaining
constant. In other words, the velocities of migration
of very complicated ions tend towards a common
limiting value when the number of atoms increases.
This minimum rate of motion for the univalent anions
and cathions lies between 17 and 20 reciprocal
Siemens units, e.g. :
a da for + CH 2
Ammonium ion, NH 4 . . 70*4
Dimethylammoniurn ion, C 2 H g N 50 '1 -2x10-2
Diethylammonium ion, C 4 H 12 N 36-1 -2x 7'0
Dipropylammonium ion, C 6 H 16 N 30*4 -2x 2-9
Dibutylammonium ion, C 8 H 20 N 26 -9 -2x 1'8
Diisoamylammonium ion, C 10 H 24 N 24 '2 - 2 x 1'4
In analogous series of anions and cathions of the
same valency, the rates of migration are diminished :
106 ELECTROCHEMISTRY CHAP.
By the addition of hydrogen, carbon, nitrogen,
chlorine, and bromine.
By the displacement of hydrogen by chlorine,
bromine, iodine, etc.
In general, the more complicated the ion, the
lower is its velocity of migration, and in accordance
therewith the polymeric ion moves slower than the
simple one. This additive nature of the velocities
is often obscured by considerable constitutive in-
fluences :
Metameric ions, for example, very often possess
different rates of migration because of their different
structures, the migration velocity increasing with
increasing symmetry, e.g. the velocity of migration
increases in passing from the primary form to the
secondary, the secondary to the tertiary, etc., as seen
in the following table :
Primary base, Xylidine ion, C g H 12 N = 30 '0
Secondary base, Ethylaniline ion, C 8 H 12 N = 30'5
rp ,. , f Dimethylaniline ion, C S H 19 N = 33'8
.tertiary bases < x, ,,.,. . ' -, 8 TT XT n * o
( Colhdme ion, C 8 H 12 N = 34-8
I Picolineethylium ion, C 8 H 19 N = 35 '1
Quaternary bases < T ,.,. Tr* 7 ,. . ' ^ 8 TT 12 XT
( Lutidmemethylmm ion, C 8 H 12 N = 35'2
Thus the additivity, particularly with cathions, is
often destroyed by the opposing influences of such
constitutional differences. Indeed, the sense of the
additive change may be reversed through over-
compensation, e.g. : >i(
Triethylammonium ion, NC 6 H 16 . 32 '6
Methyl-triethylammonium ion, NC 7 H 18 34-4
In spite of the increase CH 2 no retardation takes
place, but, on the contrary, an acceleration.
Empirical Rules. It is evident, from a considera-
THE CONDUCTIVITY OF ELECTROLYTES 107
A 2
tion of its derivation, that the formula
is only applicable in the case of binary electrolytes.
From the fact that other acids, the dibasic, tribasic,
etc., show agreement with this formula until they are
about 50 per cent dissociated, we conclude that at
first the dissociation taking place is simply the separa-
tion of one hydrogen atom as ion from the molecule,
the rest forming the negative ion. On continued
dilution further production of hydrogen ions takes
place, and at the same time the valency of the negative
radical increases. Experiments have not been made
for determining a dissociation constant for ternary
electrolytes ; moreover, as will be seen from the follow-
ing, these would not have much value.
The above dissociation formula does not represent
the exact truth for highly-dissociated binary electro-
lytes, as neutral salts, mineral acids, and inorganic
bases. An explanation of this fact is not certainly
known. Noyes and Abbot 1 have lately shown that the
law of mass - action, as applied to the dissociation
especially of neutral salts, cannot be considered
perfectly valid ; consequently we must only accept
the relations formerly deduced from the formula as
a first approximation. On the other hand, Ostwald 2
discovered an empirical rule governing the changes of
the equivalent conductivity of neutral salts with the
dilution, and by its aid we may calculate the basicity
of an acid as well as the value of its limiting conduct-
ivity X^. This is of great value for such salts as only
undergo complete [dissociation at very great dilutions.
It has been found that the equivalent conductivities
1 Zeitschr. physik. Chem. xvi. 125, 1895.
2 Ibid. i. 109, 529, 1887 ; ii. 901, 1888.
108 ELECTROCHEMISTRY CHAP.
of the sodium salts of all monobasic acids increase by
about 1 units between the concentrations V = 3 2
and V=1024, while for dibasic acids these values
increase by about 20, and for tribasic by 30 units.
Representing this increase by A, and by n the basicity
of the acid, n = . The following values have been
obtained for A :
A
Sodium salt of nicotic acid .... 10'4 = 1 x 10'4
chinoline acid . . . 19'8 = 2x 9'9
pyridine tricarbonic acid . 31'0 = 3 x 10*3
pyridine tetracarbonic acid . 40*4 = 4 xlO'l
pyridine pentacarbonic acid . 50'1 = 5 x 10*0
l?or strongly dissociating neutral salts generally, the
following relations have been shown to exist, when X v
is not very different from X^ :
A w - A, = n-^ x n 2 x C,
A^ = rtj x n z x C, 4- A e .
^ and n 2 represent the valency of the anion and
cathion, while C is a constant common to all electrolytes
and dependent upon the dilution. Having determined
the value of C at different dilutions once for all for a
single electrolyte, whose X^ is known, we are able to
calculate X^ for other electrolytes from a knowledge of
n v n 2 , and the equivalent conductivity for a concentra-
tion at which their C is also known. If we say that
n 1 xn 2 xC v = d v , then
The following table of Bredig (I.e.) contains values
of d v for the valency products and dilutions at 25,
which come into consideration :
THE CONDUCTIVITY OF ELECTROLYTES
109
Valency
KI ' %
^64
^128
^256
^512
^1024
1
11
8
6
4
3
2
21
16
12
8
6
3
30
23
17
12
8
4
42
31
23
16
10
5
53
39
29
21
13
6
(60)
48
36
25
16
It is well to note finally that in the calculation of
the value of X^ for complex anions or cathions, we
can use the previously indicated fact that their rates
of migration depend chiefly upon the number of atoms
contained in the complex ions. If it is known, for
example, that the anion of a certain acid contains 18
atoms, its value of X^ may be considered to be the
same as that of another anion of 18 atoms without
introducing any considerable error.
Conductivity and Degree of Dissociation of
Water. Thus far it has been assumed that the ob-
served conductivity of an aqueous solution was entirely
due to the material dissolved, and that the water itself
possessed no conductivity. Strictly taken, this assump-
tion is not true, for the water dissociates, though to
an extremely slight degree, into H and OH ions,
which take part in the conductivity. For ordinary
measurements in the conductivity of solutions, the
conductivity of the water is quite inappreciable. But
the presence of impurities in the water, such as traces
of salts, acids, and bases, which are extremely difficult
to remove, may cause a considerable error in the de-
irminations, especially when the conductivity of very
lilute solutions is being determined. In such cases it
110 ELECTROCHEMISTRY CHAP.
is necessary to determine the conductivity of the water
used and to apply a correction.
Kohlrausch has expended a great deal of effort
during the past few years in determining the actual
conductivity of perfectly pure water. For water which
was prepared with the greatest care, he found the values
of the specific conductivity in reciprocal Siemens units
to be: 1
= 0-01 4 x l(r 10 at
= 0-040 18
= 0-058 25
= 0-089 34
= 0-176 50
" One millimeter of this water at had a resistance
equivalent to that of forty million kilometers of copper
wire of the same sectional area an amount of wire
capable of encircling the earth a thousand times."
For reasons not necessary to give here, it is prob-
able that this experimentally-found value of Kohl-
rausch represents the actual conductivity of pure water.
On this basis we can easily determine the degree of
dissociation of the water. As the above table indicates,
the conductivity of a column of water one meter long
and of one square millimeter in section is equal to
0-040-1 0~ 10 reciprocal Siemens units at 1 8. The con-
ductivity of a liter of this water between electrodes one
centimeter apart would be 10 7 greater or 0*040 -10~ 3 .
If there were present in the water a gram-equivalent
of H and of OH ions, the conductivity would be equal
to 455 reciprocal Siemens units, for we know from
our previous considerations that a gram-equivalent of
hydrogen ions between two electrodes one centimeter
apart would show a conductivity of 290, while for a
1 Zeitschr. physik. Chem. xiv. 317, 1894.
v THE CONDUCTIVITY OF ELECTROLYTES 111
gram-equivalent of OH ions it would be 165. If then
455 were found as the conductivity of the water, the
solution would be normal as regards the H and OH
ions. Instead of 455, 0*040 -10~ 3 has been found,
..-,., 0-040 10~ 3
therefore the concentration of these ions is
455
or 0'9 10~ 7 normal that is to say, 1 gram of hydro-
gen and 17 of hydroxyl ions are present in about
eleven million liters of water.
Supersaturated Solutions. The idea has been
prevalent for a very long time, and has not even yet
disappeared, that supersaturated solutions have a char-
acteristically different behaviour from saturated and
unsaturated solutions. The conductivity measure-
ments have proved, however, that the supersaturated
solutions manifest no peculiarities not also possessed
by the other solutions. If, for example, the conduct-
ivity of the solution of a salt, whose solubility in-
creases rapidly with rise of temperature, be measured
at different temperatures so chosen that at the lower
ones the solution shall be supersaturated, while at the
higher it is not, it will be found, by arranging the
results in a co-ordinate system, that the change of the
conductivity with the temperature has always been
regular, and that no irregularities in the curve are
present to indicate a change in the nature of the
solution on passing into the supersaturated condition.
Temperature -Coefficient. According to the ex-
periments of Kohlrausch, the change of conductivity is
a linear function of the temperature, and between wide
limits may be obtained from the formula A, = X lg (l -f
P(t 18)). In this formula \ and X lg are the con-
ductivities at the temperature t and 18 respectively,
and /3 is the temperature-coefficient, 18 instead of
112 ELECTROCHEMISTRY CHAP.
being taken as the starting-point. /3 is therefore given
by the formula
/>
A 18 (*-18)
It has been found to be true that with good conducting
eloctrolytes the temperature -coefficient is greater for
those whose equivalent conductivities are small, and
less for those whose conductivities are great. The
actual difference in magnitude of the temperature-
coefficients for solutions of different electrolytes are not
usually very great. For most dilute, strongly dissociat-
ing salt solutions it amounts to about 0'025 at 18.
In other words, the conductivity in such a case would
change by about 2 '5 per cent for a temperature-
difference of one degree. This shows the necessity of
making conductivity measurements at constant tem-
peratures.
If we imagine that the ions in their motion through
the water have to overcome a certain resistance, we
comprehend why there exists a parallelism between
the changes of the viscosity and the electrical con-
ductivity of many solutions with changes of tem-
perature. Strict proportionality does not, however, exist
between the two.
Finally, with regard to the temperature-coefficient
it is worthy of observation that negative values are
by no means uncommon that is, the conductivity
sometimes decreases with rise of temperature. The
conductivity of a solution is dependent upon the
number of the ions and upon their rates of motion.
It is. evident that these rates depend upon the
friction experienced by the ions in the water, and
since the internal friction of water diminishes with
v THE CONDUCTIVITY OF ELECTROLYTES 113
rising temperature, we can assume that the friction
of the ions would also decrease, especially in salt
solutions, where, owing to the already highly dis-
sociated state, a change in dissociation can only be of
small value, accompanied by a corresponding increase
in the conductivity. A diminution in conductivity
with rise of temperature is then only conceivable
through the assumption of such a simultaneous de-
crease in the number of ions ; in other words, the dis-
sociation decreases, so that the influence of the decreased
friction is over-compensated. To many this assump-
tion may seem unjustifiable in that it is in contradic-
tion with conclusions drawn from the kinetic theory
of gases, which suggests that with rising temperature
an increase in dissociation always takes place. From
the mechanical theory of heat we know that this
conclusion is erroneous. From this theory ,we have
the following general rule If one of the factors deter-
mining the equilibrium of a system is varied, the state of
equilibrium undergoes a change in that direction which
tends to counteract the original variation of the factor.
Suppose that at a certain temperature a saturated
solution of a substance is in contact with an excess
of that substance. On warming the solution, that
change takes place which is accompanied by a cooling :
if the salt dissolves with absorption of heat, more
salt will enter the solution ; if with generation of
heat, salt is precipitated. According to this method
of reasoning, all electrolytes which tend to associate
on raising the temperature, and consequently all those
possessing negative temperature - coefficients of con-
ductivity, must be characterised by negative heats of
dissociation, it being understood that the heat-evolution
occurring on combination of two ions to form an undis-
I
114 ELECTROCHEMISTRY CHAP.
sociated molecule is the heat of dissociation, and that
the quantity of heat communicated to the surroundings
is to be considered positive, that absorbed negative.
There is one possible method of testing the accuracy
of this conclusion, and that is the determination of
the heat of dissociation itself.
Heat of Dissociation. According to the dissocia-
tion theory, the process of neutralisation of a strong
base with a strong acid is nothing but the association
of the H ions of the acid with the OH of the base to
form undissociated water. We have already learned
that the degree of dissociation of water is very slight
that is, the product of the H ions and the OH ions is
extremely small. When H and OH ions come into
contact in a solution, the equilibrium between their
product and the quantity of undissociated water must,
in accordance with the laws of mass-action, attain a
certain value determined by the characteristic dissocia-
tion constant of water. We may consider the quantity
of undissociated water in a solution as constant compared
with the quantity of ions, since a change in conse-
quence of the magnitude of this quantity is usually
immeasurably small. Thus we are practically correct
in assuming that all H and OH ions entering the water
disappear, as the value of the ion product of the pure
water cannot be altered. Before mixing an alkali and
an acid solution we have in the one X and OH ions, and
in the other H and Y ions; after mixing, there are X and
Y ions, which compose the usually highly dissociated
salt. The acid and the basic radical play no rdle in
the neutralisation, therefore the heats of neutralisation
of all highly dissociated acids and bases must be equal,
and their ^alue, 13520 cal. (for 21 '5), really represents
the heat of dissociation of water that is to say, by the
v THE CONDUCTIVITY OF ELECTROLYTES 115
union of one gram -equivalent of H with one of OH
ions to form undissociated water, 13520 cal. are set
free. This heat of dissociation has nothing to do with
the heat evolved through the union of gaseous hydrogen
and oxygen to form water.
If we neutralise a partially dissociated acid with a
highly dissociated base, the heat evolved will be
dependent not only on the heat of dissociation of the
water, but also on the heat of dissociation of the acid.
If N be this heat of neutralisation, x the degree of
dissociation of the acid, and d the heat of dissociation
per gram-equivalent, then N = 13520 (1 x)d cal.,
,, 7 13520 -N , ',,,-.
and consequently d = 1 _ g cal. All dissociating
acids which exhibit a greater heat of neutralisation
than 13520 cal. must have negative heats of dissocia-
tion. It has actually been demonstrated by the in-
vestigation of Arrhenius l that all acids possessing
negative temperature-coefficients of conductivity have
also negative heats of dissociation.
Isohydric Solutions. If we determine the con-
ductivities of two solutions, and afterwards mix equal
volumes of them together, the conductivity of the result-
ing mixture will not in general, under the same circum-
stances, be the arithmetical mean of the two single
values, unless we are dealing with completely dissoci-
ated substances. On mixing solutions of sodium
chloride and potassium nitrate some undissociated
potassium chloride and sodium nitrate must result,
whereby the relations are complicated.
Bender called such solutions which do not influence
one another's conductivity " corresponding solutions."
Arrhenius, who specially studied the acids, called them
1 Zeitschr. physik. Ghem. iv. 96, 1889.
116 ELECTROCHEMISTRY CHAP.
" isohydric." We shall here briefly consider the
isohydrism of acid solutions, or more generally such
solutions as contain an ion common to both. In this
case two solutions are isohydric when the concentra-
tions of the common ion are identical, for then no
change in the degree of dissociation can take place on
mixing, as may be seen from the following considera-
tion. Suppose the one solution to be acetic acid and
c 2
the other sodium acetate, then the equation = k holds
c i
for the acetic acid and = k' for the sodium acetate.
c i
Furthermore c = c since the concentration of the com-
mon CHCOO ions in both are the same. If, for
example, one liter of the acid be mixed with four of
the salt solution, the concentration of the CH 3 COO ion
cannot change (leaving out of account the slight change
in volume of the solutions resulting from the mixing).
The concentration of the H ions and undissociated acid
is diminished to ^, that of the Na ions and undis-
sociated salt to ^ of the former values, and by
introducing these new concentration values into the
equations we obtain
c f 4c r
X 5 2 c x ~5~ c' 2
= = KJ <mci - ' f = / = KI j
that is, a change in the degree of dissociation does not
occur, the requirements of the conditions of equilibrium
being fulfilled. It is evident that on mixing two such
solutions the relative volumes have no influence on the
result, and also that if two solutions are isohydric with
a third, they are isohydric with each other.
v THE CONDUCTIVITY OF ELECTROLYTES 117
Dielectric Constants and Dissociating Power of
Various Solvents. According to Nernst l there is a
connection between the dielectric constant of a liquid
and its dissociating power, both varying together in
the same direction. An idea of the dielectric con-
stants may be obtained from the following considera-
tion. Imagine a metallic plate kept at a constant
potential by connection with the pole of a constant
element, the other pole of which is connected with
the earth. Suppose at a definite distance from this
first plate a second, which, being connected with the
earth, is at the potential zero. In such a case the
quantities of electricity, or the charges which the plates
contain, is dependent upon the medium, i.e. the dielectric,
which separates them. The magnitudes of the electric-
ally opposite, equivalent charges, or, in other words,
the capacities of the condenser when a specific medium
is used, give the dielectric constant directly, when
that of air is taken as unity. For water this di-
electric constant is relatively very great (79'6 at 18),
for ethyl alcohol it is 2 5 '8, for ethyl ether 4*25, and
for carbon disulphide 2 '6. The great dissociating
power of water as compared with other substances
agrees with these figures.
Degree of Dissociation. Reactive Power of
Electrolytes. As already shown under electrical
conductivity, different substances exhibit very various
degrees of dissociation in water as well as in other
solvents, and the question naturally arises whether
there exists any regularity in these different dissociation -
values, whether, for example, the degree of dissociation
is an additive property that is to say, whether a
definite atom or atom group always passes into the
1 Zeitschr. physik. Ghem. xi. 220, 1893.
118 ELECTROCHEMISTRY CHAP.
ionic state with exactly the same tendency or force.
If this were so, the dissociation degrees of all electro-
lytes with different negative but the same positive
ions would form a series parallel to any other series
where a different positive ion was chosen. In reality
this is not the case. For example, almost all salts
containing ions of the same valency are dissociated to
about the same extent, but the corresponding acids and
bases (the compounds of the same radicals with hydro-
gen and hydroxyl) exhibit extreme differences in the
degree of their dissociation. The halogen compounds
of zinc, cadmium, and mercury are, moreover, exceptions
to the general principle that all analogous salts are
about equally dissociated, while the other salts of these
metals dissociate in accordance with that principle.
No other law governing the dissociating tendency has
been established. We know that, in general, salts are
highly dissociated in aqueous solutions, while, as just
stated, acids and bases exhibit every possible degree
of dissociation. Other substances show practically no
conductivity when in solution. It is remarkable that
pure substances, at ordinary temperatures, show little
or no conductivity. For example, the pure acids, as
nitric and hydrochloric in liquid form, are almost
perfect insulators. That the chemical activity is
closely connected with the dissociation may be con-
cluded from the fact that such substances, in their
pure condition, possess scarcely any chemical action.
It may be stated as a general principle that chemical
processes between two substances are almost instant-
aneously completed when the compounds are at least
moderately dissociated (illustrated by most of the
reactions of analytical chemistry), while in cases where
only very few or no ions are present, reactions gener-
v THE CONDUCTIVITY OF ELECTROLYTES 119
ally proceed very slowly, if at all, at ordinary tempera-
tures. It is on this account that in the making of
many organic compounds higher temperatures have
usually to be employed in order to produce the desired
reaction within a moderate period of time.
Conductivity of Fused Salts. In the fused con-
dition pure salts are good electrolytes. According to
Poincare, their conductivities may be measured by using
metallic silver electrodes and adding to the electrolyte
a very small amount of that silver salt which has the
same anion as the salt to be investigated. The added
amount of silver salt, when this is extremely small,
does not affect the actual conductivity of the fused
mass, but prevents, in a manner later to be described,
the existence of , polarisation, and consequently the
measurement of the conductivity of the electrolyte
may be carried out as in the case of conductors of the
first class.
An idea of the magnitudes of the conductivities of
fused salts may be obtained from the following table,
which shows the molecular conductivities (in reciprocal
Siemens units) at the temperatures given :
A
KN0 3
NaN0 3
350
350
42-2
64-0
AgN0 3
350
57-3
KC1
750
85-2
NaCl
750
128-2
As will be remembered, the equivalent conductivity
of a JQ. normal KC1 solution at 18 is 112'2.
The mixtures of fused salts, in contradistinction to
solutions, exhibit, in the few cases yet investigated,
conductivities which are approximately the sums of the
conductivities of the component salts. Many salts
120 ELECTROCHEMISTRY CHAP.
possess not inconsiderable conductivities below their
melting-points as well as above. Graetz has shown,
from experiments on this point, that a sudden change
in the conductivity of a salt at its melting-point does
not exist. On the other hand, the temperature- coeffi-
cient of conductivity seems usually to possess a maxi-
mum value near the melting-point.
Absolute Velocity of the Ions. The actual rates
of motion of different ions in ', when they are under
sec.
the influence of a certain difference of potential, have
been calculated by E. Budde and F. Kohlrausch.
For simplicity let us again imagine a gram-molecule
of negative and of positive ion between two parallel
platinum electrodes which are one centimeter apart.
Suppose the difference of potential between the
electrodes to be one volt. If exactly 48270 coul-
ombs passed in the unit of time, and the anion and
cathion had the same rate of motion, they would each
move |- cm. in the time-unit, or their velocities would
be a ^, since the passage of 48270 coulombs through
the section means that at each electrode half a gram-
equivalent of ions separates. Through any cross-section
of the electrolyte half a gram-equivalent of ions in all
must pass, and therefore ^ gram -equivalent of the
positive and negative ions. In other words, an ion
which at the beginning of the electrolysis was |- cm.
from its proper electrode must cover exactly this
distance in the given time, and this is its velocity. 1
1 It may seem impossible that while only | gram - equivalent of
ions has come towards the electrode through its motion, half an
equivalent has separated there. We can, however, imagine that under
certain conditions, even when no excess of the ions concerned is present
at the electrodes, the failing positive and negative ions are supplied by
the water. A further consideration of this point will be deferred.
v THE CONDUCTIVITY OF ELECTROLYTES 121
The positive and negative ions together moved -^
cm. in unit-time :
48270_ 1
96540 ~ 2 '
The quantity of electricity which has passed in unit-
time that is, the current-strength C in amperes
when divided by 96540, under the above conditions,
gives the velocity of the ions in ^
If 96540 coulombs had passed through the solution,
the ions would evidently have traversed one centimeter.
, . Potential-fall 1
The current -strength is C = -^5 : , ^ r - =
Resistance ' Resistance
Conductivity, therefore, since the fall in potential is
here one volt, C is the conductivity expressed in ohms.
Here the conductivity is the equivalent conductivity
X, and consequently represents the velocity ; A,
must here be expressed in ohms, as before stated. If
the two ions have different velocities of migration
they share in the total motion in proportion to their
velocities.
Potassium chloride in 0*0001 normal solution ex-
hibits at 18 the equivalent conductivity 128*9 ohms,
therefore the total rate of motion of the ions is
128-9
96540
and they share in the conductivity in the ratio 49 : 51.
The potassium ion in a 0*0001 normal solution
must actually move at the rate of 0*000654 cm.
per second when the potential - fall is one volt.
The corresponding distance for the chlorine ion is
0*000681 cm.
122 ELECTROCHEMISTRY CHAP.
The following absolute velocities at 18 calculated
for infinitely diluted solution are given by Kohlrausch :
K =0-00066 cm. H = 0-00320 cm.
NH 4 = 0-00066 01 =0-00069
Na =0-00045 N0 3 =0-00064
Li =0-00036 C10 3 = 0-00057 ,.
Ag =0-00057 OH =0-00181
It is of interest to note that a direct experimental
proof of these calculated values is possible, and has
been carefully executed by Whetham * according to a
method given by Lodge. The values found by the
latter for the velocity of the H ion agreed roughly
with those of Kohlrausch, and were obtained in the
following manner. An acid solution was brought
into contact with a solution of potassium chloride in
gelatine which had been reddened by sodium-phenol-
phthalein. Under the action of the electric current
the hydrogen ions gradually penetrated the gelatine
solution and caused decolorisation, the rate of this
change being observed. Whetham improved the
method and determined the velocities of the copper,
chlorine, and bichromate (Cr 2 7 ) ions. The principle
involved may be gathered from the following quotation :
" Let us consider the surface between two differently
coloured salt solutions differing but little in density,
and having a common colourless ion. If an electric
current be passed through their contact-surface and we
represent the two salts by AC and BC, the C ions
move in one direction and the A and B ions in the
other. If A and B are the cathions, the surface separ-
ating the two colours will move in the direction of
the current, and the rate of this motion shows in every
case the velocity of the ions causing the change of the
1 Zeitschr. physik. Chem. xi. 220, 1893.
v THE CONDUCTIVITY OF ELECTROLYTES 123
colour." The observed values corroborated those
calculated.
Determination of Solubility by Means of Con-
ductivity. In closing this chapter an interesting
method for determining the solubility of salts difficulty
soluble in water may be described. The amount of
dissolved salt may be estimated, as shown by Holle-
mann, 1 F. Kohlrausch, and E. Kose, 2 from measure-
ments of the conductivities of the solutions ; far more
accurately, in fact, than is possible by the ordinary
methods.
When solutions are so dilute that a condition of
complete dissociation may be assumed, then \ = \^.
When the value of \ M is known, the equation
7 Va
A = k ,
cb
the letters having the values given them on page 95,
furnishes a method of determining V, the volume in
which a gram-equivalent is contained in the saturated
solution, and therefore the solubility.
k as well as are easily determined experimentally ;
X^ can usually be calculated.
1 Zeitschr. physik. Chem. xii. 125, 1893.
2 Ibid. xii. 234, 1893.
CHAPTEK VI
ELECTROMOTIVE FORCE
HAVING dealt in the previous chapters especially
with the one factor of electrical energy, the quantity
of electricity, the other factor, the electromotive force,
will now be considered.
Measurement of Electromotive Force. As in-
dicated in the introduction, the electromotive force
of an element may be determined by means of a
delicate galvanometer through an application of Ohm's
law, C = ^. Evidently E = E x + K 2 where Ej repre-
sents the internal resistance of the cell and E 2 that
of the rest of the circuit, and when E 2 is made so
great that Ej is inconsiderable in comparison with it,
the deflections of the galvanometer needle, caused by
two different elements successively introduced into
the same circuit, are in the same relation as their
electromotive forces. If one of the elements used
be a normal element, the electromotive force of the
other is thus easily obtained in volts. If the internal
resistance is not negligible compared with the external,
the unknown electromotive force may be found by
determining the galvanometer deflections caused by
the two elements when connected first in series and
CHAP. VI
ELECTROMOTIVE FORCE
125
secondly opposing each other. If C represent the
deflection of the needle,
and the desired electromotive force is
In more general use than the above method is that
of Poggendorf, called also the " compensation method."
Resistance.
UHPEIEIEIEinmElE
Element.
Earth.
FIG. 18.
In this the unknown electromotive force is exactly
compensated by a potential, the value of which is
known. The following arrangement, as described by
Prof. Ostwald, 1 may be advantageously employed.
The top of a wooden box (Fig. 18) is penetrated
by two parallel rows of ten brass pins ; of these pins
the two at the extreme right are connected by good
conducting plates with the binding screws, to which
an element (a) is attached. The two pins at the other
1 Zeitschr. physik. Chem. i. 403, 1887.
126 ELECTROCHEMISTRY CHAP.
end of the box are connected together by a good con-
ducting plate, as shown. Each pair of adjacent pins in
one row is united through a resistance of 100 ohms,
and in the other row through resistances of 10 ohms.
These resistances consist of insulated wires soldered to
the pins, and advantageously wound on glass reels
placed upon the pins inside the box. There are then
nine resistances of 1 and ten of 1 ohms. The two
pins thus remaining unconnected are united by a thick
copper wire. In the figure there is one pin too many.
This could be left out, and therefore also the heavy
copper wire.
When the binding screws are in connection with
the poles of an element, the resistance of the circuit,
exclusive of the element's internal resistance and the
insignificant resistance of the connecting wire, is
1000 ohms. Throughout this resistance there is a
certain regular potential-fall. Suppose this total fall
to be 1 volt, then for each resistance of 100 ohms
there is a potential-fall of exactly O'l volt, and for
each 10 ohms a fall of O'Ol volt. By placing brass
thimbles or caps upon the pins we may introduce
between them resistances from 10 to 1000 ohms in
steps of 10 ohms, and so embrace all potentials from
0-01 volt to 1 volt in steps of O'Ol volt.
The electromotive force to be measured (c) is con-
nected with the two thimbles, which are then moved
from one pin to another until compensation is reached ;
in other words, until the electromotive force to be
measured is equal to the potential-fall between the
thimbles. For the compensation of very great electro-
motive forces, one or more normal elements, such as
the Helmholtz calomel element, having the electro-
motive force of one volt when prepared in a fixed
vi ELECTROMOTIYE FORCE 127
manner, is used. Any desired number of these may
be connected against the electromotive force to be
measured and the remainder be determined as above.
In order to determine the potential-fall distributed
throughout the 1000 ohms of the resistance-box, when
a certain element is in use at a, it is advantageous to
proceed as follows : A normal element for instance, a
one-volt element is inserted in the secondary circuit,
which branches from the two thimbles ; the latter are
then moved until the position of compensation is
reached. Suppose, in such a case, that the electro-
motive force of a one- volt element is exactly compen-
sated when there are 800 ohms between the thimbles,
then there is a potential-fall of one volt through 800
ohms, or 1'25 volt through 1000 ohins. It is neces-
sary, of course, that the normal element used should
have a lower electromotive force than that at a.
A Lippmann electrometer, as arranged by Ostwald,
may be used to determine when equality has been
attained between the unknown electromotive force and
the potential -fall by which it is compensated. The
form shown in Fig. 1 9 is usually sufficiently sensitive,
and is described in the Zeitschr. physik. Chem. v. 4*71,
1890.
" A platinum wire, partly encased in a glass capillary,
leads from an insulated binding screw and passes into
the mercury at the bottom of the bulb &, which also
contains a 10 per cent sulphuric acid solution. The
capillary tube c opening into b is filled in its upper
part with acid; its lower part contains mercury, as
likewise the tube d, which is in connection with a
second binding screw. The position of the mercury
in the capillary tube c may be regulated through alter-
ing the inclination of the capillary by means of the
128
ELECTROCHEMISTRY
CHAP.
screw at /. That this apparatus may give satisfactory
results, it should be short-circuited just before use, and
consequently it was connected with a switch so con-
structed that on breaking the current the electrometer
was always short-circuited and on making the cur-
rent this connection within itself was destroyed. In
measuring electromotive forces, so much of the resist-
ance of the box was brought between the thimbles
that the mercury in the capillary remained at rest on
closing the circuit. A millimeter scale placed beneath
FIG. 19.
the capillary, and a lens above it, aided in the measure-
ment. It was possible to approximately estimate a
thousandth volt. One hundredth volt corresponded to
3-^- divisions of the scale."
This description suffices for the present purposes,
and a study of the theory of the phenomenon will be
taken up later.
The following normal elements are commonly
used :
1. The so-called Helmholtz calomel element, con-
sisting of zinc, zinc chloride solution of 1409 sp. gr.
vi ELECTROMOTIVE FORCE 129
at 15, calomel, mercury. This element, when made
in the prescribed manner, possesses an electromotive
force of one volt 1 at about 15 C. Its change with
the temperature is slight, being 0*00007 volt for 1.
2. The Clark element, composed of zinc, a paste
of zinc sulphate, a paste of mercurous sulphate, mer-
cury, has an electromotive force of 1'4 34 O'OOl
(15) volt, where t is its temperature.
3. The Weston or cadmium element, composed of
cadmium, a paste of cadmium sulphate, a paste of
mercurous sulphate, mercury, has an electromotive
force of about 1*02 volt. It is preferable to the
Clark element, because its temperature -coefficient is
much smaller.
Reversible and Irreversible Cells. Any arrange-
ment which, through chemical reaction or physical
processes, such as diffusion, etc., is capable of produc-
ing electrical energy is called a galvanic cell ; whether
the reaction takes place between a solid and a liquid
or between two liquids is of no account. Cells or
elements, as they are also called, may be divided into
two classes the reversible and the irreversible. For
sample, the Daniell element, consisting of zinc, zinc
1 Until recently the legal ohm (1*060 Siemens unit) was used
istead of the so-called international ohm (1*063 Siemens unit). It
therefore necessary to distinguish between the international and
il volts in order that the relation represented by -j = ampere re-
lin intact ; the latter is about 0*3 per cent less than the former,
[n scientific treatises both units are in use, and it is not uncommon to
ind that, through the use of the international unit in the calculations
id of the legal volt in the measurements, mistakes are made. In
le following theoretical considerations the international volt is the
lit used. In those illustrations which are taken from other writers'
it is not stated which unit is employed, but the experimental
errors are usually greater than the differences which are introduced by
the change of the unit.
K
130 ELECTROCHEMISTRY CHAP.
sulphate solution, copper sulphate solution, copper,
is classed with the former.
Imagine the electromotive force of a Daniell element
exactly compensated by a second electromotive force.
Diminishing the latter a little, the Daniell element
becomes active, zinc goes into solution, and copper
precipitates. Increasing the opposing electromotive
force so that it is greater than that of the Daniell,
the copper redissolves and zinc is precipitated ; thus
the cell will exactly assume its previous condition.
Of a reversible cell it is theoretically true that, at
constant temperature, the maximum electrical energy
which can be obtained through its action exactly
suffices to bring the cell back to its former condition.
This is at the same time the definition of a reversible
cell.
An example of an irreversible cell is that first
given by Volta, consisting of zinc, dilute sulphuric
acid, silver. When this cell is active, zinc dissolves
and hydrogen separates at the silver electrode, and is
evolved. From the latter fact it is evident that the
original condition cannot be reproduced by reversing
the current ; on the contrary, silver goes into solution,
and hydrogen separates at the zinc electrode.
A characteristic of the reversible elements is that
when the current strength is not too great, the
electromotive force which they possess immediately
after becoming active, remains nearly constant as long
as material necessary to the chemical reaction is pres-
ent. On the other hand, in the irreversible cells, the
initial high electromotive force falls considerably, and
reaches a nearly constant minimum only after some
time. Hence the terms polarisable and unpolarisaUe.
More definite information regarding this point will
vi ELECTROMOTIVE FORCE 131
be given in the chapter on polarisation. It may be
here stated that a metal dipping into a solution which
contains a sufficient number of its own ions, is an
unpolarisable electrode. In the Daniell cell both
electrodes are unpolarisable, and consequently the
whole cell.
Since the present condition of the science renders
a clear insight into the characteristics of reversible
cells essential, our attention may now advantageously
be devoted to them.
Relation between Chemical and Electrical
Energy II. As already known, shortly after the
discovery of galvanism, Yolta advanced the hypothesis
that the principal source of electromotive force was
the point of contact between different metals, and he
did not consider it impossible to make a cell consisting
only of metals, and thereby produce perpetual motion.
The law of the conservation of energy had not then
been clearly defined, and the feeling of the necessity
for a logical cause of a phenomenon was not always
present.
The assumption of Volta was later altered, so that
the electrical energy produced was considered as derived
from the chemical reactions taking place at the surfaces
of contact between electrode and liquid. To the points
of contact between the metals, however, the production
of considerable potentials was still accredited in accord-
ance with the former assumption. It certainly seems
as though even a superficial consideration would lead
an unbiassed mind to find something both remarkable
and improbable in the production of the electrical
energy at one point, and the chief potential difference
at another. In fact, there was no longer any reason
for imagining the production of any considerable
132 ELECTROCHEMISTRY CHAP.
potential differences between the metals in the circuit.
According to our present knowledge, these possible
potential differences between the metals amount, at the
most, to but a few hundredths of a volt. We now
consider the principal potential difference to be at that
point where the electrical energy is produced, and
are thus able to explain satisfactorily the existing
relations.
The question now arises : How may the amount of
electrical energy which an element is capable of pro-
ducing be calculated from the known chemical energy
or better from the heat-effects of the reactions,
since the latter constitute the measure of the chemical
energy ? We have seen in the introduction that the
assumption originally made by Helmholtz and William
Thomson, that the quantities of heat concerned changed
completely into electrical energy, is untenable. It is
only in certain rare cases that this simple condition
exists. About twenty years ago Gibbs, Braun, and
von Helmholtz succeeded in determining the existing
relations by means of calculation.
The first law of energy is : Energy cannot be
created nor destroyed, i.e. the total amount of energy
is constant. This does not, however, preclude the
possibility of the transformation of one kind of
energy into another. It is the second law which
deals especially with this point. This may be
enunciated in many ways. It is thus expressed by
Clausius : " Heat cannot pass of itself from a lower to
a higher temperature." The general statement of
Nernst expresses the same thing in a slightly different
way which is preferable to the above : " Every process
which takes place of itself (that is, without external aid),
and only such a process, is capable of doing a certain
vi ELECTROMOTIVE FORCE % 133
definite amount of external work. This principle must
be considered as a conclusion drawn from experience.
Conversely also we may deduce the principle that an
application of external work is necessary to cause a
process which takes place of itself to proceed in an
opposite direction." Accordingly work is necessary in
order to bring heat from a lower to a higher temperature
since the reverse process takes place of itself.
If we allow a body to change of itself isothermally
from a condition A into another B that is, in such a
manner that the temperature remains constant the
maximum amount of external work which can be ob-
tained is always the same, whatever may be the way in
which the process is completed, whether it be osmotic-
ally, electrically, or otherwise. Knowing the maximum
work obtainable in a certain way, e.g. osmotically, the
quantity of electrical energy is also known. If the
quantity of material be known, then from Faraday's
law the electromotive force or intensity of this electrical
energy is determined because TT = ^ r!f~r^~rr-
Quantity of Electricity
It is evidently the maximum of available work which
is of importance here. If any loss of work occurs,
the amount remaining would be quite indeterminable
by this principle. ,
It must be clear then how important it is, especially
for the calculation of electromotive force, to know
exactly the value of the maximum available external
work which a process represents. This we may deter-
mine by allowing the body under consideration to
change " reversibly " from one state into the other at a
constant temperature. Let us take, for example, the
case of a gas of volume v expanding isothermally from
the pressure p to that of p r The maximum external
134 ELECTROCHEMISTRY CHAP.
work can be obtained when the pressure of the gas
is almost completely compensated (i.e. to an infinitely
small residuum), the process being also reversible at
any time by the application of a pressure against
that of the gas, exceeding the latter by an infinitely
small amount.
Theoretically, in order to get the maximum work,
a state of equilibrium must exist, and when this is not
the case there is a certain amount of the available work
appears in the form of heat and is lost.
A body having passed from a condition A into an-
other, B,iri a reversible manner, and having also been then
reversibly returned to the condition A, has gone through
a reversible cycle. We shall make use of such a
reversible cycle in order to calculate the quantity of
work (so important for electrochemistry) which may
be performed when a certain quantity of heat passes
from a higher to a lower temperature. For this pur-
pose let us consider an ideal or perfect gas, since the
calculation of the quantities of work is thereby much
simplified. We must be able to determine the quan-
tity of work obtainable when a gas of volume V and
pressure p changes isothermally to a volume v l and
pressure p r This amount of work is the same as
would be produced if an " ideal " solution of volume v
and osmotic pressure p changed isothermally to v 1 and
p r As frequent use of the latter will be made, its
derivation here is of twofold interest.
When a gram -molecule of a saturated vapour is
in contact with its liquid, the volume and pressure of
the former being v and p, the maximum work obtain-
able by the expansion of the vapour to v l under the
constant pressure p is easily calculated. Imagine the
increase of the volume v divided into infinitely small
vi ELECTROMOTIVE FORCE 135
parts designated by dv, then the work obtainable during
p 1
the expansion dv is pdv, and the total work is p I dv,
vj
that is, p times the sum of these infinitely small
amounts dv, from the value v to that of v r con-
sequently =p(v l v). Attention is here called to the
introduction, p. 5, where it is shown that the pro-
duct pv, therefore p (V L v) = pv 2 , represents a quantity
of work.
In the case under consideration the relations are
not quite so simple, the pressure not remaining con-
stant, but changing on the other hand with change of
volume, until it reaches p r It is not enough then
merely to add together the values dv ; the sum of the
endless number of infinitely small amounts of work
pdv must be known, where the value of p is not a
constant but a function of v, that is, in this case always
possessing a value dependent upon that of the corre-
sponding v. It may be expressed
r
= \ pdv.
vj
The values p and v are dependent upon each other in
a definite and known manner. For molecular quan-
tities we obtain from the gas - equation pv = ET, p =
HT
. Substituting this value of p in the above
equation and placing the constants before the sign of
summation (the integral sign), we get
A =
136 ELECTROCHEMISTRY CHAP.
There is here only one variable, and the integral is
determinate. We know that
dv
where In signifies the natural and log the ordinary
logarithms ; consequently
Since = according to the Boyle-Mariotte law. we
P l v
have
A graphical method 1 may be advantageously em-
ployed to make the calculation simpler to those who
find difficulty in understanding the above expressions
of higher mathematics.
In a rectangular co-ordinate system measuring values
of p on the axis of ordinates and v on the axis of
abscissae, and using the values of p and v obtained from
the gas-equation pv = ET as applied to a given gas,
we obtain a curve as shown, which is a right-angled
hyperbola, the equation of such a hyperbola being
xy = constant where x and y are the rectangular co-
ordinates.
Suppose the values of a point a on the curve are
p and v, while those for fi are p 1 and v^ Allowing the
gas to change isothermally from the condition of a to
that of /:?, the value of the work done by the gas is
represented by the area a, /3, 7, 8 expressed in gram-centi-
1 Ostwald, Grundriss d. Allgem. Chemie, p. 71.
VI
ELECTROMOTIVE FORCE
137
meters, p being measured in grains and v in centimeters.
The magnitude of the quantity represented by this
area may be approxi-
mately obtained in
the following element-
ary manner. Imagine
the gas starting from
the condition repre-
sented by a changed
slightly so that it is
in the condition a!, its
pressure and volume
now being p f and v'.
The area a, a!, &', S
represents the avail-
able work as formerly,
and this is nearly ~- (v v f ). Proceeding in this
manner we obtain the larger area a, fi, 7, S as the
sum of many small areas, and the corresponding work
as the sum of the many small corresponding quan-
tities of work. The exact expression for the work
cannot be obtained in an elementary manner, but,
derived as above, has the value
ET p
loer .
6
0-4343
In this expression it is evident that the available
work is proportional to the absolute temperature of
the gas, and further, that it does not depend upon the
absolute values of the pressure or volume, but upon
the relation between the respective values of each.
Accordingly the amount of available work is, for ex-
ample, the same whether a gas passes from a pressure
138 ELECTROCHEMISTRY CHAP.
of ten atmospheres to one, or from one atmosphere to
one-tenth. It may be recalled that if it is desired to
express A in mean gram-calories, the value for B, is
1'96 ; if expressed in gram-centimeters, E = 84700.
If a gas expands so that its pressure is diminished
to a hundredth atmosphere, or its volume has become
one hundred times greater, the maximum work obtain-
able in the process at T= 290 (17 C.) is
1-96x290 100
0-4343
,
= g T~ S m -- caL = 2617
84700 X290, 100
0-4040 log gm.-cm. = 113120000 gm.-cm.
It may be well to remark that this work which is
obtained in the isothermal expansion of the gas is not
taken from the internal energy of the gas itself, but
the corresponding quantity of heat is extracted from
the surroundings. The gas only serves as a medium
for the transformation of heat into work (p. 4).
The previously described cyclical process may now
be considered and the quantities of work or heat there
coming into play calculated. 1
One gram-molecule of a gas is compressed from
volume v l to v at constant temperature. The work
which is necessary to do this is
A = KTln- 1 .
v
This work is converted into heat, which is absorbed by
the surroundings, and the quantity of heat thus set
1 The demonstration is here given as in Nernst's Theoretiscke
Chemie.
vi ELECTROMOTIVE FORCE 139
free must be equivalent to the work done, according to
the first law of energy, or
The gas is now brought into surroundings of tempera-
ture T + dT. The quantity of heat (m) thereby absorbed
by the gas is negligibly small as compared with W
(moreover, the same quantity is later given out). The
volume v being kept constant during the change of
temperature, no external work is done. If now the
gas be allowed to expand from v to v v the work
A, = R(T + dT) In - 1 = ET In- 1 + EdT In - 1
V V V
may be obtained. The equivalent quantity of heat is
taken from the surroundings :
W l = RT In - 1 + RdT In- 1 .
The gas is now brought into surroundings of
temperature T. After the same negligible quantity of
heat (m) as above has been given up by the gas, it is
in its original condition.
On consideration of the whole result it is found
that the quantity of work
T
has been obtained. The equivalent amount of heat
has been transformed into work, but at the same time
the quantity of heat
140 ELECTROCHEMISTRY CHAP.
has disappeared at the temperature T -f dT, and been
recovered at the temperature T. In other words : In
the fall of the quantity of heat ETlri- 1 = W from
T + dT to T, the heat represented by
has been changed into work.
This is a general result. It is always true that
when any amount of heat x is brought from a high to a
lower temperature, the maximum amount which can
be changed into work is represented by
dT
where dT is the change in temperature.
To aid the comprehension the following remarks
may be of use. The passage of heat from higher to
lower temperature may be compared with the parallel
case of the passage of electrical energy from higher to
lower tension. The quantity of electrical energy CTT
may be changed to 2e-, that is, the total quantity
of energy remains unaltered on transformation, the
two factors simply changing their values in inverse
proportion. The temperature T is the intensity-factor
of heat-energy (Q), accordingly Q = xT, x being the un-
known capacity-factor. Since x = , for Q the form
T is obtainable. Heat at a temperature of 100
may be expressed by ry ^ 100, heat at 50 by
3 50. The capacity -factor is double its previous
vi ELECTROMOTIVE FORCE 141
value, while the in tensity -factor is one -half. ^ is
called the entropy, and it is evident from the formula
that its magnitude is greater the lower the temperature.
Entropy tends towards a maximum.
The difference between the heat and the free trans-
formable energy lies in the fact that the transformation
in the case of the latter may theoretically take place
in either direction without the use of work, while in
the former a change from lower to higher temperature
can only occur through consumption of work.
Let us apply these considerations to the reversible
galvanic elements. If the heat evolved by the reactions
taking place within such an element having no internal
resistance, be entirely changed into electrical energy
while the element is immersed in a calorimeter, no
heating effect would be observed. The reason is that
just as much energy as was produced would be con-
sumed as electrical energy (capable of transformation
into work) in the external circuit. As a matter of
fact this simple relation very seldom exists, and there-
fore a generation of heat in the calorimeter can
usually be observed.
Imagine a reversible cell of electromotive force TT
at the temperature T, and suppose the quantity of
electricity 96540 coulombs or e be passed through
it, then the maximum electrical energy which may be
produced is e 7r. Let Q be the sum of the heats of
the corresponding reactions. The action of the cell is
attended by absorption of heat, the heat absorbed being
VT Q> according to the first law of energy. Suppose
the temperature increased by dT and the amount of
electricity e again sent through the cell, but in the
opposite direction, and under the new electromotive
force, TT + ^TT; the amount of work thus consumed
142 ELECTROCHEMISTRY CHAP.
will be e (7r + e?7r). The corresponding sum of the
heats of reaction in this reversed process has changed
but little, and, neglecting this change, is Q. The
heat generated in the element is in this case equal
to the difference between the electrical energy used
and the heat taken up in the chemical processes, and
is thus equal to e 7r + e e?7r Q. If the element be
brought again to the temperature T, it is once more
in its original condition.
As the end-result of the process, the work e^dir
has been performed, and accordingly the equivalent
amount of heat e efor produced. At the temperature
T the heat e 7r Q has been lost, but at T + dT the
heat 7r + e ^7r Q has been obtained. As e^dir is
derived from the work done, the amount of heat
O TT Q has been raised from the temperature T to
T + dT. Conversely, in order to change the quantity
of heat ^?r into work, the amount of heat e 7r Q
must fall from the temperature T + dT to T, con-
sequently the following expressions are correct in
accordance with page 140 :
dT
d7r = ( e()7 r-Q)Y (1).
e ^-Q = eo T^ (2).
- = 3 +T^ (3).
e dT
Since we can calculate Q from thermochemical
data, or can determine it directly, we are able, with
the help of the experimentally determined temperature-
coefficient of the electromotive force, to calculate the
maximum electrical energy obtainable, or the electro-
motive force of the element. In the thermochemical
vi ELECTROMOTIVE FORCE 143
data the numbers always apply to a gram-equivalent
or gram-molecule, the heat generated being considered
positive.
If the temperature-coefficient is positive, i.e. if the
electromotive force increases with rise of tempera-
ture, it follows from equation (2) that e ?r is greater
than Q : the element in activity tends to become
cooler, and so takes heat from the surroundings. If,
on the other hand, the temperature - coefficient is
negative, e 7r is less than Q, and the element becomes
warmer. If finally the temperature-coefficient is zero,
the heat of reaction is simply and completely trans-
formed into electrical energy, and the element itself
exhibits no thermal change. This latter condition is
nearly realised in the Daniell cell.
It is necessary to emphasise this fact that the heat
of the chemical reactions is not a strict measure of
the available electrical energy of a reversible element,
although experience has shown that in many cases it
enables us to estimate it approximately.
The above formula of Helmholtz has been quali-
tatively proven by Chapski and Gockel, and quanti-
tatively by Jahn. 1 Several apparent contradictions,
as later shown by Nernst, arose from erroneously
assumed values for the heat of formation of mercury
compounds.
For illustration the following values found by Jahn
are given. The numbers expressing calories apply to
two gram-equivalents.
1 Wied. Ann. xxviii. 21, 491, 1886.
[TABLE
144
ELECTROCHEMISTRY
CHAP.
Heat Effect in
E.M.F.
Change in
E.M.F. for
Elec.
Energy
Heat of
Reaction
Cell.
Volts.
r= dT
in
Calories.
in
Calories.
Calcu-
lated.
Found.
Cu, CuSO 4 +100H 2 0,
ZnSO 4 +100H 2 O, Zn.
1-0962
+0-000034
50526
50110
- 428
- 416
Ag, AgCl,
ZnCl 2 +100H 2 O, Zn.
Ag, AgN0 3 +100H 2 0,
1-0306
- 0-000409
47506
52170
+5148
.+4660
Pb^NOo^+lOOHj^O, Pb.
0-932
42980
50870
+7890
+7950
Ag, AgN0 3 +100H 2 0,
Cu(NO 3 ) 2 +100H 2 O, Cu.
0-458
21120
30040
+8920
+8920
As is evident, the agreement between the heat-
value of the element as observed in the calorimeter
and that calculated from the difference between the
electrical energy produced by the current and the
corresponding heat of reaction, is satisfactory in each
case.
It may be advisable to add that electrical energy
may be measured by inserting the element in a circuit,
the resistance of which is so great that the internal
resistance of the cell is negligible in comparison. The
electrical energy being allowed to change into heat,
the amount of the latter generated in the unit of time
is EC 2 , according to Joule's law (p. 18), where E
represents the resistance of the circuit, and C the
current -strength. Knowing the resistance E, and
having measured the current-strength, the amount of
electrical energy produced in unit time may be
calculated. From this the amount of energy pro-
duced when 96540 coulombs, or twice that number,
pass through the circuit may be easily determined,
the choice between these numbers depending upon
whether one or two gram-equivalents of the substances
take part in the chemical reaction. As the internal
resistance of the element itself is negligible compared
vi ELECTROMOTIVE FORCE 145
to the external, the Joule's heat produced within the
element is insignificant, and may be left out of con-
sideration. The heat generated in the element and
measured in the calorimeter, as previously described, has
evidently nothing to do with the Joule's heat, which is
a measure of the electrical energy, but is the difference
between the Joule's heat and the heat of the reactions
taking place in the element.
The formula previously derived enables us to
determine the electromotive force of a cell from a
knowledge of its temperature - coefficient and of the
heat of reaction. The electromotive force of reversible
elements may be determined in another manner as
already indicated on page 133. Before proceeding
with the calculation, we must first get a clear idea
of the electrolytic solution tension of Nernst, 1 or, as we
will call it, following Ostwald, the electrolytic solution
pressure.
Electrolytic Solution Pressure. The expression
" vapour pressure of a substance " is one commonly
understood. It signifies the tendency of a substance
to enter the gaseous state. If, for example, we allow
water at a certain temperature to evaporate in a long
cylindrical vessel in which there is a movable air-tight
piston, and if a pressure is exerted upon the piston
less than the vapour pressure of the water, the piston
is moved upwards and more water evaporates. A
condition of equilibrium is only established when a
I certain definite pressure is exerted upon the piston
Tom without. The latter will then remain stationary
.n whatever position it be placed as soon as equili-
arium between water and vapour obtains. If the
pressure on the piston be slightly increased, the
1 Zeitschr. physik. Chem. iv. 129, 1889.
'
146
ELECTROCHEMISTRY
CHAP.
vapour will be entirely condensed to water; if, on the
other hand, it be slightly diminished, all the water
will be changed into vapour. The weight of the
piston for equilibrium represents the vapour pressure
of water at the temperature of the experiment. The
" solution pressure " of a substance, for example sugar,
is spoken of just as the vapour pressure, and thereby
is meant its tendency to pass into the dissolved
state. This pressure may be measured in the same
manner as the vapour pressure. The apparatus
shown in Fig. 21 may be used. At the bottom
of a vessel there is an excess of the solid substance
A, over which is its saturated
solution B, and at C pure water.
s is a semi-permeable piston, that
is, one which can be penetrated
by the water but not by the
dissolved substance. If s be
weighted, the magnitude of the
load determines the direction in
which the piston moves. If the
load be less than the pressure derived from the dis-
solved particles, the "osmotic pressure," s will rise
and water penetrate into B, which being thereby
diluted, allows more of the substance A to dissolve.
If it be greater, s sinks, water passes from B into C,
and the solution becoming supersaturated, some of the
solid substance separates at A. Under a certain
weight the condition of equilibrium must exist and
the piston remain stationary at any part of the
cylinder. Evidently the relations are here exactly
analogous to those of the vapour pressure of water,
and the magnitude of the solution pressure of the
substance at a given temperature is measured by
vi ELECTROMOTIVE FORCE 147
the weight of the piston when in the condition of
equilibrium.
It may here be repeated that, as made evident
through these considerations, the vapour pressure of
water being that pressure exerted by the vapour in
contact with water, that is, the " saturated " vapour,
so also the " solution pressure " of a substance is the
osmotic pressure of the solution which is in equilibrium
with the substance, that is, the " saturated " solution.
This conception may finally be applied to the
passing of substances, chiefly elements, and especially
metals, into the ionic condition. Hydrogen and the
metals are capable of forming only positive ions ;
chlorine, bromine, iodine, etc., on the contrary, form
only negative ions. The magnitude of this " electro-
lytic solution pressure " may be conceived as de-
termined in exactly the same manner as the
ordinary solution pressure. We imagine the substance
in contact with water saturated with the ions in
question, under a similar piston, which separates the
saturated solution from the water, and is impermeable
for these ions. The equilibrium with the osmotic
pressure of the ions will be brought about by a certain
weight of the piston, and no ions will enter the
solution from the substance nor pass out of solution.
The weight of the piston in equilibrium represents the
value of the electrolytic solution pressure, which is
usually represented by P, and also expresses the
equally great and oppositely directed osmotic pressure
of the ions. This method is practically inapplicable,
because in no case can appreciable amounts of positive
or negative ions alone come into existence; this does
not, however, affect the value of the conception.
In order to explain the production of a potential
148 ELECTROCHEMISTRY CHAP.
difference through the contact of a solid substance
with a liquid, imagine a metal dipped into pure water,
and that a certain amount of metal ions is produced
owing to the electrolytic solution pressure. The metal
at the same time becomes negatively electrified, since
both kinds of electricity must be simultaneously pro-
duced whenever electrical energy comes into existence.
The solution is thus positively electrified and the metal
negatively, and there is found a so-called double layer
(" Doppelschicht ") of electricities of opposite signs.
The ions sent into the solution with positive charges
and the negatively charged metal attract each other ;
in other words, a potential difference is produced.
The solution pressure constantly tends to send more
ions into solution, while the electrostatic attraction
of the double layer opposes this action, and evidently
equilibrium is reached when the opposing tendencies
are equal. Since the ions have very high charges of
electricity, this condition of equilibrium occurs before
weighable quantities of the ions have passed into the
water. In the case of pure water the potential
difference or strength of the double layer depends only
upon the magnitude of the solution pressure, but if
the metal be in a solution of one of its salts, another
factor is introduced, due to the metallic ions already
present. The osmotic pressure of these ions opposes
the entrance of new ions of the same kind. It may
occur that this osmotic pressure is exactly in equi-
librium with the electrolytic solution pressure of the
metal, consequently the latter will yield no ions and
will not become negatively charged; in short, under
these circumstances there will be no double layer pro-
duced. The nature of the negative ions of the salt in
solution has no influence.
vi ELECTROMOTIVE FORCE 149
If the osmotic pressure of the metal ions differs
from the solution pressure, two different cases may be
distinguished according as the former or the latter is
the greater. In the second case ions pass from the
metal to the solution as in pure water, and a double
layer is the result. This would evidently not be as
great as in pure water, since so many ions cannot enter
the solution, owing to the fact that the electrolytic
solution pressure is opposed by the osmotic pressure
of the ions already present. In the other case ions
separate from the solution and are precipitated upon
the metal communicating their positively electric
charges to it. The metal thus becomes positively, the
solution, which formerly contained equivalent amounts
of positive and negative ions, negatively electrified,
and again the electrical double layer is produced, the
attraction of which opposes the previously superior
osmotic pressure and adds itself to the solution
pressure. This proceeds until the condition of equili-
brium is reached. Here also the quantity of ions which
are precipitated is unweighable. The strength of the
double layer and the electrostatic attraction due to it
is evidently dependent upon the osmotic pressure of
the metal ions in the solution.
In all, three cases must be distinguished :
(1) When P=p, where P is the solution pressure
and p the osmotic pressure of the metal ions con-
sidered, equilibrium exists and no potential difference
or double layer is present between solution and
metal.
(2) When P>^?, the metal is negatively electrified
and the solution positively. The electrostatic attrac-
tion opposes the solution pressure.
(3) Finally, when P<>, the metal is positively
150 ELECTROCHEMISTRY CHAP.
electrified and the solution negatively. The electro-
static attraction is added to the solution pressure.
On turning our attention to the actual experi-
mental facts it is found, as will be seen later, that
the alkali metals, and also zinc, cadmium, cobalt,
nickel, and iron, are always negatively charged when
placed in solutions of their salts ; the solution
pressure in these cases is so great that, owing to the
limited solubility of the salts, the osmotic pressure of
the metal ions can never be raised to equilibrium with
the solution pressure. With the noble metals, silver,
mercury, etc., the metal is usually positively electrified
in solutions of its salts. The solution pressure of
the metals is here slight, and it is only by employing
solutions containing very few of the ions in question,
i.e. such as have very low osmotic pressure due to these
ions, that it is possible to have the metal negatively
charged in the solution.
With such substances as produce negative ions, e.g.
chlorine, there is complete analogy. If the osmotic
pressure of the chlorine ions is greater than the electro-
lytic solution pressure, ions pass into the condition of
ordinary chlorine, and the " chlorine electrode " becomes
negatively charged. In the other case the electrode
becomes positively charged. As a matter of fact, as
far as we know, all substances which produce negative
ions have high solution pressures.
So far the electrolytic solution pressure of a sub-
stance has been referred to as if it were a constant,
but, just as with the vapour pressure and ordinary
solution pressure, it is only constant under certain
conditions, i.e. only when the temperature and the
concentration of the substance in question remains
unaltered.
ELECTROMOTIVE FORCE
151
ih
It is well known that the vapour pressure of
water changes greatly with the temperature, but that
it is affected by the concentration
of the water itself, and is higher
the greater this concentration, may
be less commonly recognised. The
fact may be recalled that if two
open vessels containing water at
different heights be allowed to
stand in a confined space, the water
distils from the higher level to the
lower. The water in each vessel
is under the pressure of the vapour
above it, and these columns of
vapour differ in height by the
difference between the water levels
(k). Consequently the system is
not in equilibrium, the tendency being for vapour to
condense under the greater pressure and be generated
under the lower, which process continues until the
surfaces of the water in the two vessels are at the
same level, or that in one of the vessels is exhausted.
In the accompanying figure, 1 F contains pure water
and L any solution, the two being separated by a mem-
brane permeable to the water only. In the conditions
represented the liquids are in osmotic equilibrium, but
the vapour pressure (p^ at the surface of the solution
is less than that (p) of the water at F, and the
equation p l + x=p must represent the existing con-
dition where x is the weight of the column of vapour,
whose height is equal to the difference of level between
the two liquids. If this were not true, water would
distil from one surface to the other, thereby destroying
1 Zeitschr. physik. Chem. iii. 115, 1889.
152 ELECTROCHEMISTRY CHAP.
the existiag condition of osmotic equilibrium, and
would also pass through the membrane in one direc-
tion in order to reproduce the osmotic equilibrium, etc.
In short, a perpetual motion would result, by which an
unlimited amount of the heat of the surroundings at
constant temperature could be transformed into work
(through the distillation of water vapour), which is in
conflict with the second law of energy.
If the upper end of the tube be closed by a mem-
brane, allowing the passage of water vapour only, and
a quantity of a gas insoluble in the liquid be placed
between this membrane and the surface of the liquid,
it will exert a certain pressure upon the latter, which
will consequently sink to a lower level. The con-
ditions of the equilibrium must again be that the
vapour pressure (p^) at the surface of the solution,
increased by the pressure of the column of water
vapour (hf) between the two levels, is equal to the
vapour pressure of the pure water (p), or pf + a/ = p.
Evidently p has remained unaltered, ~h! is less than h,
therefore p^ is greater than p lt that is, at the " com-
pressed" surface, where the water is at the greater
concentration, there is a higher vapour pressure than
when the water is under a lower external pressure.
The increase in the vapour pressure is evidently pro-
portional to the pressure acting on the surface. 1
Of the ordinary solution pressure it is also known
that the concentration of the substances plays an im-
portant part. This is shown by Henry's law, in
accordance with which the solubility of a gas, and
1 This conclusion was established by the work of Des Coudres and
the author, which preceded the appearance of the article of Schiller
on the same subject ( Wied. Ann. liii. 396, 1894). The experiments
in connection therewith were unavoidably interrupted and never
concluded.
vi ELECTROMOTIVE FORCE 153
therefore its solution pressure, since the two are
synonymous, is to a great extent dependent upon the
pressure, in other words, upon the concentration ; it is,
in fact, nearly proportional to the latter.
What has been said of vapour pressure and solu-
tion pressure applies equally well to electrolytic
solution pressure, and accordingly there are cells
possessing certain electromotive forces dependent only
upon the different concentrations of the same ion-
producing substances. It is true that usually but one
condition of concentration for solid substances is
recognised, and consequently a single definite electro-
lytic solution pressure. But even here the concen-
tration may be varied, as will be later described. The
electrolytic solution pressure also varies with the
temperature.
Calculation of Potential Differences by means of
the Electrolytic Solution Pressure. It is an easy
matter to calculate the potential differences between
an electrode and the solution with which it is in
contact when the electrolytic solution pressure P of
the electrode and the osmotic pressure p of the
corresponding ions in the solution are known. It is
evidently only the pressure of the corresponding ions
which here comes into consideration ; with a zinc
electrode it is only necessary to know the concentra-
tion of the zinc ions in the solution. The maximum
amount of work which might be obtained osmotically
is determined, and considered equal to that obtainable
electrically.
If a univalent element with solution pressure P is
to be changed into ions of the osmotic pressure p, then
the maximum work which may be obtained is equal
to that obtainable by the passage of the ions from the
154 ELECTROCHEMISTRY CHAP.
osmotic pressure P to that of p, no work being
performed by the simple change of a substance of
solution pressure P into ions of equivalent osmotic
pressure. As the laws applicable to gases also hold
for (dilute) solutions, the amount of work may be
calculated in the same manner through replacing gas
pressures by osmotic pressures. The osmotic work of
a gram-molecule is then represented by
RTln ?
P
The electrical work is e 7r, when TT represents the
potential difference between electrode and electrolyte,
consequently
V- p
RT_ P
TT = In
o P
Obviously TT is zero when P =p. This agrees with
the previous conclusion that in this case there is no
potential difference between electrode and electrolyte.
Since the passage of one gram-ion is being con-
sidered, e is 96540 coulombs when the ion is uni-
valent. Both kinds of energy in the above equation
must be expressed in the same units. According to
p. 17, 4*24 is the electrical equivalent of heat. E is
1-9 6 cal. For this reason the right side of the equa-
tion, which gives calories only, must be multiplied by
4*24 in order to change it into electrical units or
96540 x TT (volts) = (v^Za" T lo ~ '
At the temperature 17, T is 290, and
vi ELECTROMOTIVE FORCE 155
1-96 x 290 x 4-24 P P
" = 0-4343x96540 l ^ p V ltS = <>-0575 log - volts.
If the ion is not univalerit, then ?i e x96540
coulombs would be transported with one gram-ion,
where n e is the valency. The formula thus becomes
0-0575 P
7T = log - VOltS.
n e * p
This is a fundamental equation in the theory of
reversible cells.
In considering a cell composed of two metals and
two solutions, as, for instance, the Daniell zinc, zinc
sulphate, copper sulphate, copper there are four places
where potential differences are produced :
1. At the point of contact between the two metals.
2. At the point of contact between the two liquids.
3 and 4. At the points of contact of both elec-
trodes with the liquids.
The potential difference at the points of contact
between the two metals is so small that it may usually
be left out of account. This is also often true of that
existing between the two solutions. These magnitudes
will shortly be calculated. Considering only the
potential differences at the points of contact of the
electrodes with the liquids, the electromotive force of
the cell at 17 is expressed by the following equation :
0-0575 , P 0-0575, P'
7T = log log '
n e *p n e ' y
P represents the electrolytic solution pressure of
the one substance, the valency and osmotic pressure
of whose ions are n e and p. P', n e ' t and p f are the
corresponding values for the other substance. The
156 ELECTROCHEMISTRY CHAP.
minus sign is used because at one electrode ions enter
the solution, while at the other they pass from the
solution ; for example, in Daniell's cell zinc ions are
produced, and simultaneously an equal number of
copper ions separate at the other electrode, for the
same number of positive and negative ions must always
be present in the solution. The investigation of special
cases will now be taken up.
CONCENTKATION CELLS
A. Different Concentrations of the Substances
forming the Ions
l.-A cell formed of two differently concentrated
amalgams of the same metal, for example, zinc, in a
solution of one of its salts, as zinc sulphate, possesses,
according to the previous considerations, an electro-
motive force at T expressed by the formula
0-000198 P 0-000198 F
Since the concentration (p) of the zinc ions is the
same throughout the solution, the formula may be
simplified to
0-000198. P
P and P' are respectively the electrolytic solution
pressure of the zinc in the more concentrated and
more dilute amalgam. Weak amalgams may be con-
sidered as solutions in which the mercury is the
solvent and, in the above case, zinc the dissolved
substance. The zinc, like all dissolved substances,
exerts a certain osmotic pressure which, since the
amalgams are not of the same concentration, is different
vi ELECTROMOTIVE FORCE 157
at the two electrodes. Since these are proportional
to the concentrations, the electrolytic solution pressures
of the amalgams may be assumed proportional to the
osmotic pressures of the dissolved zinc. 1 From this
0-000198 c
TT = -T log -volts,
2i C-,
where c and c^ are the concentrations of the zinc in the
amalgams. That values of TT calculated in this manner
agree with those experimentally determined may be
seen from the following results obtained by G. Meyer : 2
Zinc Amalgam and Zinc Sulphate Solution
T c Cj TT found. TT calculated.
11-6 0-003366 0-00011305 0-0419 volt 0-0416 volt
18-0 0-0433 0-0425
12-4 0-002280 0'0000608 0'0474 0-0445
60-0 0-0520 0-0519
Cadmium Amalgam and Cadmium Iodide Solution
T c c x TT found. TT calculated.
16-3 0-0017705 0-00005304 0-0433 volt 0'0440 volt
60-1 0-0017705 0-00005304 0-0562 0'0507
13-0 0-0005937 0'00007035 0'0260 0-0262
Copper Amalgam and Copper Sulphate Solution
T c e 1 TT found. TT calculated.
17-3 0-0003874 0'00009587 0-01815 volt 0-0176 volt
20-8 0-0004472 0'00016645 0-0124 0'0125
The electromotive force IT of such cells can be
calculated in a second way, independent of the idea
of electrolytic solution pressure. The action of the
1 This is equivalent to assuming that the dissolved substance is
present in the mercury as atoms, which will be demonstrated from
considerations of concentration cells formed from gases (p. 163).
2 Zeitschr. physik. Chem. vii. 447, 1891 ; and Ostwald, Allgem.
Chem. ii. 861.
158 ELECTROCHEMISTRY CHAP.
cell consists in zinc passing from the more concentrated
amalgam into the solution, and at the same time from
the solution into the weaker amalgam. That is to
say, zinc at an osmotic pressure p, or the proportional
concentration c, changes to the osmotic pressure p l or
the concentration c r The maximum amount of work
thereby obtainable osmotically is
RT c
log-
0-4343
for a gram-atom, when the metal is assumed to be
present in the mercury in the form of atoms.
The electrical value of the same process is
2 X 96540 x TT, and since the maximum amounts of
work must be equal,
-prp
2X96540X^ = 0^108--,
or
0-000198^, c
TT = ; - T log - volts.
c i
This is the same formula obtained by the previous
method, and will also be later used in the calculation
of TT.
It was assumed that the metal is present in the
mercury in the atomic state, and since the experiment-
ally determined values of TT agree with those calculated,
this assumption may be considered justified.
If the metals had dissolved in the mercury in
complexes of two atoms each, the work obtainable
osmotically, through the transportation of the same
amount of metal as before, would have been
1 RT ^'c
20-4343 g '
vi ELECTROMOTIVE FORCE 159
because the number of separate particles to be trans-
ported is only half as great. The work obtainable
depends upon their number, but not upon their weight.
The corresponding electrical energy would be
2 x 96540 XTT',
therefore
and
10-000198
or in such a case the electromotive force of the cell
would be only half as great as is actually found. The
monatomic character of the metal molecules in mer-
cury solutions has also been proved from measurements
of the vapour-pressure diminutions.
As shown by the formula, TT depends only upon
the relation between the concentrations and upon the
valency of the metal, and is in other respects inde-
pendent of the nature of the metal.
The amalgams have been considered simply as
differently concentrated zinc electrodes ; it might be
asked if the mercury in them does not also play the
part of an electrode, and its electrolytic solution press-
ure come into consideration. This is not the case.
If two different metals, as in a solid alloy, are in
contact with the liquid, only that one is active which
produces the greater electromotive force, if the amount
present is not too small.
If an alloy of zinc and cadmium be placed in an
acid solution, the zinc in contact with the acid dis-
solves first, and the solution of the cadmium only
begins later. In employing such an alloy as electrode,
160 ELECTROCHEMISTRY CHAP.
the greater electromotive force of the zinc is very
nearly obtained at first, and later the smaller one,
that of the cadmium. If zinc ions are present this
metal has no effect when the osmotic pressure of
these ions is so great that the cadmium dissolves
more easily. If the solution originally contains cad-
mium ions, a secondary reaction is introduced, which
proceeds until as many cadmium ions have been
precipitated on the electrode and been replaced by
zinc ions as is possible at the existing electromotive
force.
2. The combination mercury, a solution of mer-
curous salt, amalgam of a noble metal, can also be
classed as a concentration cell. From what was said
of the osmotic pressure (p. 54), it is evident that
(leaving out of account electrostriction and chemical
reactions) the volume of a liquid should be slightly
increased by the solution of a substance in it, since
the particles of dissolved substance exert an outward
pressure upon the surface of the solution. The dis-
solving of the substance has, in this respect, the same
effect as a reduction of the external pressure which
acts upon the liquid; the latter expands, and thereby
the concentration (i.e. the mass in unit volume) is
reduced. In the above-mentioned cell there are
thus two differently concentrated mercury electrodes.
Evidently only those metals may be used to dilute
the mercury whose solution pressure is weaker, since
that of the mercury only ought to come into con-
sideration. Gold and platinum, the so-called noble
metals, adapt themselves to this end. A mercurous
salt must be used as the electrolyte. Mercuric salts
are immediately reduced in contact with metallic
mercury.
vi ELECTROMOTIVE FORCE 161
The electromotive force of this mercury concentra-
tion cell may be easily calculated, as was that of the
previously described cell, either with or without the
use of the idea of electrolytic solution pressure. It
will be sufficient to apply the shorter method, since
the electromotive force of such a cell has not yet been
experimentally determined.
In the action of the cell mercury dissolves from
the pure mercury electrode, where the solution pressure
is greater, and is precipitated upon the amalgam elec-
trode. The maximum work available osmotically will
now be calculated and considered equivalent to the
maximum available electrical work.
Suppose the pure solvent (mercury) separated from
the solution (the amalgam) by a movable semi-per-
meable diaphragm. Let p represent the osmotic press-
ure of the solution, and v be the volume in which
one gram-molecule of dissolved substance is contained.
Let the semi-permeable diaphragm be moved under
the constant pressure p in the direction of the pure
solvent, until an amount of the latter equal to v enters
the solution. If v be one cubic meter, for example,
one cubic meter of the solvent passes through the
diaphragm into the solution, and the former is moved
through the volume v of one cubic meter at the con-
stant pressure p. Let the amount of the solution be
so great that the introduction of this volume v causes
no appreciable change in the concentration. The
maximum work which can thus be obtained is repre-
sented by the product pv, since v is the volume con-
taining a gram-molecule of dissolved substance. But
pv = ET and consequently ET is the osmotic work.
To obtain the equivalent electrical energy, that amount
(m) of mercury gram-molecules which is contained in
M
162 ELECTROCHEMISTRY CHAP.
the volume v must pass from the one electrode to the
other ; therefore
me 7r = RT,
and
The values of E, T, and e are known ; m is the number
of gram-molecules of mercury containing one gram-
molecule of the dissolved metal in the amalgam.
Hence the value of TT is easily reckoned.
This method serves also for determining the mol-
ecular weight of the metals dissolved in the mercury ;
m is the number of gram-molecules of mercury con-
taining one gram-molecule of the dissolved metal. By
measuring TT, m is obtained, and from the known con-
centration of the amalgam, the weight of the dissolved
substance in m, which represents the molecular weight,
is calculable.
3. A second mercury concentration cell is the
following: Mercury under greater than atmospheric
pressure, mercurous salt, mercury under atmospheric
pressure. In such a cell mercury passes from the
former electrode through the electrolyte to the latter.
Des Coudres l arranged this cell as follows : A column
of mercury of height h formed one electrode ; the lower
end of the tube containing it, closed by means of
parchment paper, was placed in a salt solution. The
paper was impervious to. the mercury as such, but
allowed the passage of the ions. The surface of the
second mercury electrode was at the same height on
the parchment membrane. The height of the mercury
column decreases by a definite amount when a gram-
molecule of mercury passes from one electrode to the
1 Wied. Ann. xlvi. 292, 1892.
vi ELECTROMOTIVE FORCE 163
other. The maximum work thus obtainable may be
calculated, and is equivalent to the electrical energy.
The work necessary for the transport of the ions
through the solution may be left out of account. If
200 gms. thus leave the column of mercury, which is
of great height A, the effect is the same as though
200 gms. of mercury had fallen the distance A, and
the maximum available mechanical energy is 200 h
gm. cm. where h is expressed in centimeters. There-
fore, since according to p. 17 the gm. cm. units must
be divided by 10210 in order to obtain electrical
units, -
_ 200/i
()7r= 10210'
and the electromotive force has the value
200/1
~ 96540 x 10210 V
The following shows experimentally determined
values compared with those calculated, and considering
the difficulty of accurately measuring these small values,
the agreement must be considered satisfactory.
Pressure in cm. IT calculated. TT found.
36 7-2 x 10~ 6 volts. 7-4 x 10~ 6 volts.
46 9-3 10-5
113 23 21
4. Finally, concentration cells may be produced
from gases or aqueous solutions of different concentra-
tions as ion-producing substance. At the first glance
it may seem improbable that gases or liquids, which
possess no metallic conductivity, can serve as electrodes,
but through the use of a special arrangement this end
164 ELECTROCHEMISTRY CHAP.
is easily reached. A platinised platinum electrode is
passed from beneath into a tube closed above, the
lower end of which stands in a liquid. The tube is
so filled with the gas under consideration that the
platinum plate is for the greater part in the gas, the
remaining portion being in the liquid. The platinised
platinum absorbs a certain quantity of the gas, and
may be considered as a gas electrode. The only other
part the platinum plays in these cells is that of con-
ductor of the electricity. Because of its power of dis-
solving the gases the platinum allows of the change
from the gaseous to the ionic state, and the reverse,
without resistance. Such an electrode, e.g. one of
hydrogen, belongs to the reversible class as experi-
mentally shown by Le Blanc. 1 The quantity of work
developed by the passage of a certain amount of gas into
the ionic condition is exactly the quantity necessary and
sufficient to produce the reverse action. Since this is
true, the material of the metallic electrode can have
no effect upon the electromotive force, and, in fact,
equal values have been obtained with platinum and
palladium electrodes.
By means of such platinised platinum electrodes
reversible chlorine, bromine, and iodine electrodes may
be prepared. By arranging a reversible cell of two
such electrodes, using as ion-producing material the
same substance for each, but in different concentra-
tions, a concentration cell entirely analogous to that of
the amalgams is the result. The electrolyte to be used
is evidently one containing the same ions as the gas
produces. If hydrogen be the gas, an acid is used ; if
oxygen (the corresponding ions of which are OH), a
solution of a base must form the electrolyte. This
1 Zeitsclir. physik. Chem. xii. 333, 1893.
vi ELECTROMOTIVE FORCE 165
kind of a cell is independent of the nature of the
electrolyte, except for the above consideration defining
one of the ions.
In the calculation of the electromotive force of a
gas cell, for example one consisting of two hydrogen
electrodes under the pressures p and p lt the process is
the same as with the amalgam cell, except that it must
be borne in mind that the hydrogen molecule contains
two atoms. In the reversible change of one gram-
molecule of hydrogen from the pressure p to p v the
maximum work is represented by
Pi
The corresponding energy, when the process is
considered as an electrical one, is 2e 7r, because the
molecule produces two univalent ions ; therefore
KT 1 p
TT = In .
2e o Pi
The factor 2 occurs here in the denominator, even
though the equation applies in this case to univalent
ions.
If the calculation be made in accordance with the
osmotic process, using solution pressures as on p. 156,
the formula is
RT P
P and Pj_ being the solution pressures corresponding to
the gas pressures p and p l respectively. Evidently
the two must be equal, or
RT ^_RT ] _P
2^ n ^~V n V
166 ELECTROCHEMISTRY CHAP.
and
I, P p
2 - ln ]rr ln V
therefore
That is, the squares of the solution pressures are in
the same ratio as the corresponding gas pressures. This
result is not difficult to understand. It may be re-
called that P and P I represent osmotic pressures (p.
14*7). If the osmotic pressure P exists in a solution
at the one gas electrode whose gas pressure is p, while
at the other the osmotic pressure is P x and the gas
pressure p v there is no potential difference at the elec-
trodes. There is a condition of equilibrium between
the gas molecules and the corresponding ions. When
such a condition exists that undissociated and dis-
sociated portions are in equilibrium, the concentration
of the undissociated portion, divided by the product of
the concentrations of the dissociated portions, is a con-
stant. Moreover, the gas and osmotic pressures are
proportional to the concentration, hence
and also
therefore
PI
Experimentally determined values of the electromotive
forces of such cells have not as yet been published, so
vi ELECTROMOTIVE FORCE 167
that a comparison with the calculated values is at
present impossible.
The consideration of a second kind of concentration
cells will now be taken up.
B. Different Concentrations of the Ions
1. The combination : silver, silver nitrate solution
(concentrated), silver nitrate solution (dilute), silver, may
be considered as a type of these cells. In such a cell,
where the electrode furnishes positive ions, the current
always flows through the cell from the dilute solution
to the concentrated. Silver is dissolved in the dilute
solution and precipitated from the other, this process
continuing until the two solutions are of the same
concentration. That the silver ions must precipitate
from the more concentrated solution is evident when
it is remembered that the osmotic pressure here
directed against the solution pressure is greater than
in the dilute solution.
Leaving out of account for the present the poten-
tial difference which exists at the point of contact
between the two solutions, the electromotive force of
such a cell is
KT p RT p
TT = In In ,
*o Pi e o P
where p and p t are the osmotic pressures of the silver
ions in the concentrated and dilute solution respectively.
Since the solution pressures are the same, the formula
may be simplified to
RT. p
TT = In .
e o Pi
This expresses the fact that the electromotive force
168 ELECTROCHEMISTRY CHAP.
of such a cell is dependent only upon the relation
between the osmotic pressures of the metal ions, and
is independent both of the nature of the metal and of
the negative ions of the electrolyte.
The electromotive force may also be ascertained
by the second method, through calculating the maxi-
mum of energy represented by the osmotic change
when one gram -ion of silver migrates from one
electrode to the other. For this purpose the con-
ditions of the cell before and after the electrolysis
are compared.
If one gram-ion dissolves in the dilute solution, the
silver concentration is increased by one gram-ion, but at
the same time some silver also passes from the dilute to
the concentrated solution. If n be the share of trans-
port of the silver, n gram-ions leave the dilute solution,
and the actual increase in the concentration of the
latter when one gram-ion dissolves is (1 n) gram-ions.
The stronger solution must evidently have its concen-
tration reduced by this amount. A migration of NO 3
ions also takes place. If n' represent the share of
transport for this ion, then n' N0 3 gram-ions pass from
the concentrated to the dilute solution, since the
motion is in the direction opposite to that of the
silver ions. But n r is equal to 1 n, consequently
I _ n gram-ions of silver and the same number of
N0 3 gram-ions move from the concentrated solution
to the dilute during the passage of 96540 coulombs,
i.e. from osmotic pressure p to p r The relation of the
osmotic pressures of the p^ anions as well as of the
cathions is . The work is expressed by
Pi
Pi
vi ELECTROMOTIVE FORCE 169
and
^(LzjWhJt.
o Pi
On comparing this formula for univalent metals
with that obtained above, it is seen that when n ^,
i.e. when the two ions have equal rates of migration,
the formulae become the same. When this is not the
case, a potential difference exists at the point of con-
tact between the solutions, and this requires the
application of a correction to the previous formula ;
consequently the formula just derived is more general
in its application. It will be assumed for the present
that n = ^.
The following formula is the most general one :
n e irc n = ni(l- n)RT In - ,
ft
or
p l
Here n e is the number of e which must be transported
to cause (1 n) gram-molecules of the electrolyte to
pass from the concentrated to the dilute solution.
The highest valency represented by the ions in a given
case gives the value of n e directly. If zinc chloride
be the electrolyte, n e = 2. In the concentration cell :
thallium, concentrated thallium sulphate solution, dilute
thallium sulphate solution, thallium, n e is also 2. If
the electrolyte be thallium nitrate, n e =l, and so on.
The number of ions formed from a molecule of the
electrolyte is %
For dilute solutions the relation between the con-
centrations may be used, instead of that between the
osmotic pressures. For example, for the cell : silver,
170 ELECTROCHEMISTRY CHAP.
silver nitrate solution (0*01 normal), silver nitrate
solution (O'OOl normal), silver, 10 is substituted for -
of the formula, and the electromotive force calculated
should agree closely with that measured.
Nernst 1 measured the electromotive force of the
cell : silver, silver nitrate solution (O'l normal),
silver nitrate solution (0*01 normal), silver, and found
7r=0'055 at 18. From conductivity determinations
it was calculated that the relation between the con-
centrations of the silver ions, instead of being 1:10,
was 1:8*71; consequently
TT = 0-000198 x 291 log 8-71 =0-054.
The agreement of the experimentally found value with
that calculated is evidently very satisfactory.
The following statements will serve to give a general
idea of the magnitude of the numerical values. Since
at 17
0-0575 . p .
7T = log VOltS,
n e Pi
it follows, where the concentrations of the ions to be
considered are in the ratio 1:10 and the metal uni-
valent, that
TT = 0-05 75 volt.
If the relation of the concentrations is increased to
1:100 or 1:1000, the values of TT become twice or
three times as great, since IT increases in logarithmic
ratio.
If the ion be other than univalent, the corre-
sponding values must be divided by the valency.
Thus the cell consisting of copper and copper sulphate
1 Zeitsckr. physik. Chem. iv. 129, 1889.
vi ELECTROMOTIVE FORCE 171
solutions, in which the concentrations of the copper
ions are 1:10, would give an electromotive force of
about one half that of the corresponding silver con-
centration cell. Measurements by Moser corroborate
this statement.
The accompanying diagram graphically represents
the electromotive force of concentration cells of uni-
Volt.
0-3
0-2
0-1
J 3 4- tog --
FIG. 23.
valent ions, the concentration of one solution being
unity, that of the other varying from this value to
0-0001.
2. Another kind of concentration cell is represented
by the combination : silver, silver nitrate solution,
potassium chloride solution, silver coated with silver
chloride. In spite of the apparent difference between
this and the cell last described, the two are entirely
analogous. In calculation of the electromotive force
172 ELECTROCHEMISTRY CHAP.
only the* osmotic pressures of the silver ions in the
nitrate solution and in the solution of the silver
chloride require to be taken into account. The
potassium chloride is used to increase the conductivity
of the silver chloride solution. In practice a solution
of potassium nitrate is inserted between the potassium
chloride and silver nitrate solutions, in order to present
the formation of a precipitate. The formula
0-000198 m p
TT = - I log
n e *P!
holds good.
In calculation of TT the ratio alone need be
known. In the nitrate solution the concentration of
the silver ions may be known, if a solution of a
certain strength be prepared, for if not very dilute,
so that complete dissociation may be assumed, the
degree of dissociation may be determined. In the
case of the solution of silver chloride the concentra-
tion of silver ions is not so easily ascertained. On
account of the slight solubility of the chloride it
is certainly very low. By means of the electrical
conductivity (p. 123) the solubility in pure water may
be determined, and it has thus been found that the
saturated silver chloride solution at 18 is O'OOOOllV
normal. In such a dilute solution the salt is doubtless
practically all dissociated into the ions Ag and Cl ;
moreover, as they are present in equivalent amounts,
the solution is 0-0000117 normal for silver or for
chlorine ions, and the product of these concentra-
tions is
AgxCl = (0-00001l7) 2 = s 2 .
Instead of a pure aqueous solution of silver
vi ELECTROMOTIVE FORCE 173
chloride, that of the cell also contains potassium
chloride. From p. 87 the product of the concentra-
tions of the ions, divided by the concentration of the
undissociated molecules, is a constant independent of
the dilution; and since in a saturated solution the
undissociated portion must be considered constant, the
same is true also of the product of the concentrations
of the ions. When a relatively large amount of potas-
sium chloride is added to a saturated aqueous silver
chloride solution, the number of chlorine ions is greatly
increased, and, in consequence, a certain amount of
undissociated silver chloride must form and be pre-
cipitated, since the solution is already saturated with
it. If c is the concentration of the silver ions after
the addition, and also that of the chlorine ions derived
from the silver chloride, while ^ is the concentration
of the added chlorine ions, then
and since C T is very great compared with c, the equation
may be written
S 2
C= - .
C l
To obtain the concentration of the ion correspond-
ing to the material of the electrode, the square of the
solubility (s) of the salt used is divided by the con-
centration of the other ion, of which an excess is
added. Supposing a 0*1 normal potassium chloride
solution to be used, ^ for complete dissociation would
be O'l, but since in this concentration it is only about
85 per cent dissociated, e l = 0'085 ; and therefore
_ (0-00001 17) 2
0-085
174 ELECTROCHEMISTRY CHAP.
Since the osmotic pressures are proportional to the
concentrations, and the silver nitrate is 82 per cent
dissociated, when the silver nitrate solution is O'l
normal, the following holds for 18 :
, = 0.000198x291x^^2^=0-44 volt.
The corresponding experimentally determined value
is 0'46 volt, a satisfactory agreement.
Another example of such cells is one consisting of
silver, KN0 3 solution saturated with AgBr0 3 , KBr0 3
solution saturated with AgBr0 3 , silver. 1 The con-
centration of the silver ions in the nitrate solution
is nearly the same as in pure water, since the nitrate
yields neither Ag nor Br0 3 ions, and consequently has
no influence on the state of dissociation of the AgBr0 3 .
The concentration of the silver ions in the potassium
bromate solution may be calculated as before, from
the solubility of the silver bromate in water and the
concentration of the Br0 ions added. . When the
o
values so obtained are substituted in the formula,
TT= 0-0612 volt for O'l normal, and 7r=0'0454 for
0'05 normal potassium bromate solution. The ex-
perimentally determined magnitudes are 0*0620 and
0'04*71. The current, as before, passes in the cell
from the weaker to the more concentrated solution of
silver ions, or from the bromate to the nitrate solution.
Electrodes in which the metal is in contact with
one of its difficultly soluble salts, and also in the
presence of a solution of a soluble salt with the same
negative ion, were called by Nernst electrodes of the
second order, or as regards the negative ions, reversible
electrodes. Ostwald showed that these are not to
1 Zeitschr. physilc. Ohem. xiii. 577, 1894.
vi ELECTROMOTIVE FORCE 175
be distinguished from ordinary metal electrodes in a
solution of one of their salts.
3. A third kind of concentration cell consists of
those in which one of the electrolytes is a complex
salt. As a type of this class may be mentioned the
combination : silver, silver nitrate solution, potassium
cyanide solution containing a little silver cyanide,
silver. In the latter solution the complex salt
KAg(CN) 2 is formed, the ions being K and Ag(CN) 2 .
This negative ion is in turn dissociated to an extremely
slight extent into 2 (ON) and Ag, and it is the con-
centration of this latter silver ion which in this
solution is to be taken into account in considering the
electromotive force of the cell. It is evidently some-
what dependent upon the quantity of silver cyanide.
Since it is at present impossible to measure the
concentration of this small quantity of ions in the
solution of the complex salt, it is also impossible to
calculate the electromotive force of such cells. On
the other hand, the measurement of the electromotive
force gives a means of calculating the concentration.
A determination of a parallel case is here given in
which the electromotive force of the cell : Mercury,
mercurous nitrate (O'l normal), mercurous sulphide in
sodium sulphide, mercury, was measured. 1 The value
of TT at 17 was found to be 1'252 volt, or
1-252 = 0-000198 x 290 log ,
Pi
where p and p 1 represent the osmotic pressures or con-
centrations of the mercury ions in the nitrate and in
the sodium sulphide solutions. Further,
1 Zeitschr. physik. Chem. xi. 466, 1893.
176 ELECTROCHEMISTRY CHAP.
log 21-8,
and
.
ft
Assuming complete dissociation, there are 20 grams
of mercury ions in a liter, or 1 mg. ion in '00005
liter, of the O'l normal mercurous nitrate solution.
This latter number, multiplied by 10 21 ' 8 , gives the
number of liters of the sodium sulphide solution con-
taining one milligram of mercury ions.
A means of determining the solubility of the diffi-
cultly soluble salts, and thereby the ion concentration,
has already been observed in the electrical conductivity.
These considerations furnish, however, a second method
far surpassing the first in delicacy. In fact, it is
exactly at those extremely low concentrations, where
all other methods are without avail, that the advantages
of this one are most prominent, since the electromotive
force becomes higher the greater the difference in the
concentrations. In those cases where determinations
by both methods have been possible, satisfactorily agree-
ing results were obtained.
Attention may be called to the following important
fact. In the three cells : (1) Silver, O'l normal silver
nitrate, O'l normal potassium chloride with silver
chloride, silver; (2) Silver, O'l normal silver nitrate,
O'l normal potassium bromide with silver bromide,
silver; (3) Silver, O'l normal silver nitrate, O'l normal
potassium iodide with silver iodide, silver, the electro-
motive force increases from the first to the third.
This is a consequence of the fact that the silver
chloride is more soluble than the bromide, and this
in turn more soluble than the iodide. In such cells
vi ELECTROMOTIVE FORCE 177
as these the electromotive force is greater the less
soluble the salt. With the complex instead of the
insoluble salts, as is illustrated by the O'l normal
potassium cyanide solution, to which some silver
cyanide was added, the electromotive force is greater
the fewer the metal ions furnished by the salt (in
this case silver). If a series of such cells be
arranged in the order of their electromotive forces,
beginning with the lowest, the order is also that of
the solubility, or, in the last -mentioned case, of the
decomposition.
Each salt in the series will dissolve in, or else
react with, any of the saturated solutions of the cells
following in the series. For example, silver chloride
added to the potassium bromide solution forms silver
bromide ; silver bromide in the potassium iodide solu-
tion forms silver iodide, etc. Cyanide of silver added
to sodium sulphide changes into silver sulphide, as the
cell: Silver, O'l normal silver nitrate solution, O'l
normal sodium sulphide with silver sulphide, silver,
has a higher electromotive force than the correspond-
ing cyanide cell. On the other hand, silver sulphide
does not dissolve in dilute potassium cyanide solution.
The reason for this is easily seen when it is remem-
bered that the more insoluble or complex a salt is, the
lower is also the value of the product of the corre-
sponding ions. If to a saturated silver chloride solu-
tion an amount of iodine ions (as in potassium iodide)
be added equal to the chlorine ions present, silver
iodide must precipitate ; otherwise the product of the
iodine and silver ions would be greater than is possible.
This precipitation of silver iodide proceeds until the
product of the ion concentrations has reached the con-
stant value corresponding to the saturated silver iodide
N
178 ELECTROCHEMISTRY CHAP.
solution. Such an arrangement of concentration cells
is given in the following table of Ostwald (Allgem.
Chem. ii. 882):
Volt.
Silver nitrate 0*1 normal silver chloride in normal potas-
sium chloride . . . . . . .0-51
Silver nitrate O'l normal silver nitrate in normal
ammonia . . . . . . . . O54
Silver nitrate O'l normal silver bromide in normal potas-
sium bromide . . . . . . . 0'64
Silver nitrate O'l normal silver nitrate in normal sodium
thiosulphate 0'84
Silver nitrate O'l normal silver iodide in normal potas-
sium iodide . . . . . . . . 0'91
Silver nitrate O'l normal silver nitrate in cyanide of
potassium . . . . . . . . 1'31
Sitver nitrate O'l normal silver nitrate in normal sodium
sulphide . 1'36
Evidently the order of such a series may be changed
by altering the concentrations of the electrolytes added
to the silver salts. This might be done, for example,
by adding a very concentrated solution of potassium
chloride to the silver chloride solution ; the concentra-
tion of the silver ions would thus be reduced below
that of the O'l normal bromide solution, which contains
silver bromide. In this case the electromotive force
of the chloride cell would be greater than that of the
bromide, and even if O'l normal potassium bromide
solution be added to the chloride solution, silver
bromide would not be precipitated ; on the other hand,
silver bromide could be dissolved in it. Similarly,
silver sulphide would dissolve in concentrated potas-
sium cyanide solution.
4. Finally, a concentration cell, which might also
be included under description 1, may be here con-
sidered, because of its peculiar characteristics. Atten-
vi ELECTROMOTIVE FORCE 179
tion was first called to it by Ostwald. A cell consist-
ing of one hydrogen electrode in an acid solution, and
another in an alkali solution, the two solutions being in
contact, is a concentration cell with regard to hydrogen
ions. It has already been learned (p. 109) that water
is slightly dissociated into H and OH ions, and con-
sequently a certain quantity of H ions is present in
the alkali solution. The electromotive force of this
cell is
RT. p
TT = In ,
o Pi
p being the concentration or osmotic pressure of the
hydrogen ions in the acid solution, and p l those in the
alkali. Suppose the alkali and acid used to be normal
solutions. The concentration (p) of the H ions in the
acid solution, when the incomplete dissociation is taken
into account, is about 0*8, and p l may be calculated
from the measured electromotive force of the cell. In
this case a considerable potential difference exists at
the surface of contact between the two solutions, which
must be taken into consideration, since the sum of the
potentials at the electrodes alone is desired. With the
correction given by Nernst, 1 the value of TT at 18 is
0-81 volt; that is,
0-81 = 0-0575 log-,
or
-10".
Pl
Since p is 0'8, p r or the concentration of the hydrogen
ions of the alkali solution, is 0*8 X 10~ 14 .
According to the law of mass-action the product of
1 Zeitschr. physik. Ghem. xiv. 155, 1894.
180 ELECTROCHEMISTRY CHAP.
the hydrogen and hydroxyl ions must again give a con-
stant when divided by the concentration of the undis-
sociated water. The latter concentration is so great as
compared with the concentration of the ions, that it
may be considered invariable. Consequently the pro-
duct of the ion concentrations must also be practically
constant. The concentration of the hydrogen ions of
the alkali solution is 0'8 x 10 ~ 14 , as indicated above,
and the concentration of the hydroxyl ions according
to the supposition is 0*8 ; therefore the product is
(0'8) 2 X 10~ 14 . From this result the degree of dis-
sociation of pure water may be directly ascertained.
The product of the ion concentrations in pure water
must be (0'8) 2 x 10~ 14 , and the concentrations of the
H and OH ions are here the same. If c be the con-
centration of one of these ions,
C 2 = (0-8) 2 x 10- 14 and c = 0'8 x 10~ 7 .
In other words, pure water is 0*8 xlO" 7 normal with
regard to its hydrogen or hydroxyl ions. The con-
ductivity measurements of Kohlrausch (p. Ill) gave
0'9 x 10~ 7 . This is a very remarkable agreement, and
its significance is made greater by the fact that other
methods for reaching the same end, as through the
study of the hydrolysis of salts and the saponifying
effect of water, have led to very nearly the same value.
Oxygen electrodes may be used instead of hydro-
gen, and the cell still have the same electromotive
force, because the concentrations of the hydrogen ions
in the two solutions are in the same relation to each
other as those of the corresponding hydroxyl ions.
This follows from the fact that the product of the con-
centrations of the H and OH ions of the solutions in
the element is a constant. The fact that the platinum
vi ELECTROMOTIVE FORCE 181
does not absorb oxygen as readily as it does hydrogen,
and that it reaches a condition of equilibrium with the
surrounding gas more slowly, makes it more difficult
to obtain constant values. The current passes through
the cell from the more concentrated solution to the
other, as is always the case when the electrode pro-
duces negative ions. The direction of the current is
considered as that in which the positive ions move.
It may be repeated here that, except for the potential
difference existing between the solutions at their point
of contact, the electromotive force of such cells does
not depend upon the nature of the negative ion of the
acid, nor upon the positive of the alkali. On the other
hand, when acids of the saine molecular concentrations
are used, the degree of dissociation comes into . play.
The cell, hydrogen, acetic acid, potassium hydrate,
hydrogen, would exhibit a lower electromotive force
than the cell of corresponding concentration of hydro-
gen, hydrochloric acid, potassium hydrate, hydrogen.
The slightly dissociated acetic acid contains less hydro-
gen ions than the highly dissociated hydrochloric
acid ; consequently in the latter cell the difference in
concentration between the hydrogen ions of the acid
and alkali solutions is greater than in the former, and
therefore its electromotive force is also greater. That
the same considerations apply to bases may be safely
concluded from the measurements which have already
been made in that direction.
182 ELECTROCHEMISTRY CHAP.
C. Concentration Double Cells
Another form of concentration cell, differing from
the previously described liquid concentration cell, is
made by connecting two such cells as a double element.
The so-called calomel cell, which is often used, serves
as a type of this form. Its arrangement is as follows :
Zinc, zinc chloride solution (concentrated), mercurous
chloride, mercury, mercurous chloride, zinc chloride
solution (dilute), zinc. The mercurous chloride is in
excess, and covers the mercury. This cell differs from
the simple cell : Zinc, zinc chloride solution (concen-
trated), zinc chloride solution (dilute), zinc, in having
the combination mercurous chloride, mercury, mercurous
chloride, between its two differently concentrated solu-
tions of zinc chloride. Consequently the processes of
electrolysis and the electromotive forces of these arrange-
ments differ from those of the simpler cells. In the
case, zinc, dilute zinc chloride solution, concentrated
zinc chloride, zinc, when 2 x 96540 coulombs pass, there
is a migration of zinc and chlorine ions from one solu-
tion to the other, and simultaneous solution and pre-
cipitation of two equivalents of zinc at the electrodes.
In the calomel concentration cell such a migration
cannot occur. When 2 x 96540 coulombs pass through
this cell, two equivalents of zinc dissolve in the dilute
chloride solution, and two of mercury separate from
the mercurous chloride. Here the current always
passes from the dilute to the concentrated solution
within the cell. The mercury ions come from the dis-
solved mercurous chloride, and those precipitated are
immediately replaced by the further solution of mer-
curous chloride. In the concentrated solution, on the
vi ELECTROMOTIVE FORCE 183
other hand, two equivalents of zinc separate at the
electrode, and two of mercury are dissolved. It must
be borne in mind that when two equivalents of metallic
mercury have been produced from the solid mercurous
chloride in the dilute solution, two equivalents of
chlorine ions have also been formed, and when two
equivalents of metallic mercury have changed to mer-
curous chloride in the concentrated solution at the
same time, two of chlorine ions have disappeared.
When the quantities of the solutions are imagined
so great that these changes take place without
sensible influence on the concentration, the processes
may be summarised as follows. Two equivalents of
zinc and two of chlorine that is, one gram molecule
of zinc choride have been transported from the con-
centrated solution to the dilute, while the quantity of
mercury and of mercurous chloride remains unaltered.
If the osmotic pressure of the zinc ions in the concen-
trated solution be p, and in the dilute solution p v then
the corresponding osmotic pressures of the chlorine
ions are 2p and 2p r The maximum osmotic work is
easily calculated, and is
Pi *PI Pi
The electrical energy is 27re ; therefore
2 o %i '
In general
rn f /n
ll e e O Pi
where n i is the number of ions -produced by one
184 ELECTROCHEMISTRY CHAP.
molecule of the electrolyte, and n e the number of e
necessary for the passage of a gram-molecule of the
electrolyte from the concentrated to the dilute solution
(see p. 169).
From the formula it may be seen that only the
ratio , n i} and n e have influence on the value of TT.
As Ostwald predicted, and as Goodwin l experimentally
demonstrated, it follows that :
1. The mercurous chloride and mercury of the
calomel cell may be replaced by silver chloride and
silver without altering the electromotive force.
2. Instead of zinc chloride, zinc bromide or iodide
may be used when the depolariser 2 is a difficultly
soluble bromide or iodide, without changing the electro-
motive force.
3. The electromotive force of the cell will not be
changed if cadmium chloride and cadmium be sub-
stituted for zinc chloride and zinc.
4. If the zinc and zinc chloride be replaced by
thallium and thallium chloride, the electromotive force
will be considerably increased.
5. If instead of the chloride of zinc, the sulphate
be used, with a difficultly soluble sulphate as de-
polariser, the electromotive force will be less than
before. Whether lead or mercurous sulphate be used
as depolariser can make no difference. The accom-
panying tables confirm these statements. For brevity
the cells are designated by their soluble salts and
depolarisers.
1 Zeitschr. physik. Chem. xiii. 577, 1894.
2 The difficultly soluble salt is here called a depolariser, because,
through its presence, the electrode is made unpolarisable.
VI
ELECTROMOTIVE FORCE
185
ZnCl 2 - HgCl and ZuCl 2 - AgCl Cells at 25 C
Concentration
of the ZnCl 2 .
Observed E.M.F.
of ZnCl 2 -HgCl.
Observed E.M.F.
ofZn01 2 -AgCl.
Calculated
E.M.F. in Volts.
0-2 -0-02
0-0787
0-0767
0-0797
O'l -O'Ol
0-0800
0-0780
0-0818
0-02-0-002
0-0843
0-0843
0-0844
o-oi-o-ooi
0-0861
0-0847
0-0853
Considering the experimental errors of 1 2
thousandths of a volt, the agreement is very satis-
factory.
II
ZnBr 2 - HgBr and ZnBr 2 - AgBr Cells
Concentration of
the ZnBr 2 .
Observed E.M.F.
of ZnBr 2 - HgBr.
Observed E.M.F.
of ZnBr 2 - AgBr.
Calculated
E.M.F. in Volts.
0-2 -0-02
0-0793
0-0793
0-0797
o-i -o-oi
0-0808
0-0802
0-0818
0-02-0-002
0-0860
0-0852
0-0844
o-oi-o-ooi
0-0863
0-0858
0-0853
Through replacement of zinc and its chloride by
cadmium and cadmium chloride, the value of the
electromotive force could not be calculated, the
concentration of the cadmium ions not being deter-
minable (by the conductivity method). This is ex-
plained by the fact that CdCl 2 dissociates not only
into Cd u and Cl, Cl, but probably also, in concen-
trated solutions, into CdCl and Cl. In dilute solutions,
where only the former dissociation is considerable, the
values calculated agreed with those experimentally found.
186
ELECTROCHEMISTRY
CHAP.
Ill
TICl-HgCl Cells.
Concentration
of the T1C1.
Observed
E.M.F.
Calculated
E.M.F.
0-0161 -0-00161
0-102
0-114
O'OOS -0-0008
o-ioo
0-115
0-0161 -0-008
0-0328
0-033
IV
ZnS0 4 - PbS0 4 Cells
Concentration
of the ZnS0 4 .
Observed
E.M.F.
Calculated
E.M.F.
0-2 -0-02
0-0427
0-0453
o-i -o-oi
0-0440
0-0471
0-02-0-002
0-0522
0-0500
i
ZnS0 4 - Hg 2 S0 4 Cells
Concentration
of the ZnS0 4 .
Observed
E.M.F.
Calculated
E.M.F.
0-2-0-02
o-i-o-oi
0-047-0-034
0-045-0-033
0-045
0-047
The formula
Pi
vi ELECTROMOTIVE FORCE 187
is only applicable when the solubility of the depolariser
is inappreciable. If, for example, the difficultly
soluble mercurous chloride of the calomel cell be
replaced by the comparatively easily soluble thallium
chloride, it must be taken into account that the
concentrations of the zinc and the chlorine ions are no
longer in the same relation. Chlorine ions from the
thallium chloride are thus added to those of the zinc
chloride, and from the law of mass-action the pro-
duct of the ion concentrations of the thallium and
chlorine in the saturated thallium chloride solution is
constant, and more chlorine ions must enter the dilute
than the concentrated zinc chloride solution. From
this consideration, taking into account the previous
deduction, p and p l being the osmotic pressures or
the concentrations of the zinc ions, and p' and p^
those of the chlorine ions,
2e 7r = RT In ^ + 2RT In -L
Pi Pi
In general
RT/1, p ,, t /1N
_(_l n ^ + i n _ 1 (l).
e o V 2 Pi Pi
n *L + n/RT In . ,
Pi Pi
where % and n t ' represent the number of cathions and
anions which the molecule of the electrolyte produces,
and n e the number of e corresponding to the trans-
portation of one molecule of the electrolyte from the
concentrated to the dilute solution.
The electromotive force of the cell may also be
calculated from the solution pressures of the two
metals coming into consideration (in the calomel cell,
the zinc and mercury). In this case the electro-
188 ELECTROCHEMISTRY CHAP.
motive force of the cell consists of four potential
differences, existing at the four points of contact
between metal and liquid. If P Zn and P Hg represent
the solution pressures of the zinc and mercury respect-
ively, and p, p v p', and p^ the concentrations of the
zinc and mercury ions in the concentrated and in the
dilute solutions, while % n and % Hg are the valencies of
the metals, the electromotive force is represented by
the following formula (the fact that the current passes
in the element from the dilute to the concentrated
solution being taken into account) :
RT/ 1_ P^ _Li Pi_
i PI n Hg Png
n Hg p
This may be shortened to the form
RT / 1 , p 1 , ,
"Pi ^ Hg " P'
or
Pi P
Formulae (1) and (2) lead to the same result, in
p'
spite of their apparent difference. In (1) , repre-
sents the concentration relation of all the negative
ions of the solutions, while in (2) ^- represents that of
the cathions of the depolariser. It must be remem-
bered that saturated solutions of the depolariser are being
considered ; consequently the product of the concentra-
tions of all the anions and cathions of the depolariser
is a constant (the anions of the electrolyte and depol-
ariser being alike, as in the case of ZnCl 2 and HgCl).
vi ELECTROMOTIVE FORCE 189
The separate concentrations are also in a definite
relation to each other. When, for instance, the
cathions and anions are of the same valency, as in
the example, their different concentrations in the
solutions are inversely proportional to each other.
If the anion be bivalent and the cathion imivalent,
the concentration of the latter is inversely propor-
tional to the square of that of the former, and so on.
This explains the agreement of the two formulae.
LIQUID CELLS
It has already been stated in the considerations of
the concentration cells that potential differences occur
at the points of contact between the solutions. This
assumption has been entertained a long time, but a
clear conception of the derivation of such potentials
did not exist. The Becquerel acid-alkali cell is well
known; two platinum electrodes connected together
are placed one into acid and the other into alkali
solutions. That in the acid becomes positively and
the other negatively charged ; the potential difference
varying with the conditions often amounts to more
than 0*6 volt. Formerly the source of this electrical
energy was erroneously thought to be in the heat
generated by the neutralisation of the acid and alkali.
As previously explained, this is practically a con-
centration cell. Oxygen of the air is present at the
two electrodes, and in the acid solution there are few,
while in the alkali there are many OH ions. Since
the electrodes are of ordinary platinum instead of
being coated with platinum black, it is easily ex-
plicable that the electromotive force of such a cell is
variable. Ordinary platinum does not absorb oxygen
190 ELECTROCHEMISTRY CHAP.
to a very great extent, so that the condition of equi-
librium which should be established, in which the
concentration of the oxygen dissolved in the platinum
corresponds to the pressure of the surrounding oxygen,
as in the case of platinised platinum, is practically
unrealisable ; consequently the cell has an uncertain
and varying value. This cell cannot generate a
perceptible current, because the quantity of oxygen
absorbed by the electrodes is very small, and, being
exhausted, is replaced by that of the air only very
slowly. The presence of other gases also has an
influence upon the electromotive force of this cell.
We are indebted to Nernst 1 for satisfactory ex-
planations of the phenomena of these liquid cells,
their theory having been developed by him. If a
solution of hydrochloric acid, for example, be placed
in contact with a more dilute solution or with pure
water, the acid will diffuse into the water. The
hydrogen and chlorine ions of the acid are, to a certain
extent, independent particles capable of moving with
different velocities from places of higher osmotic
pressure to those of lower. Since the hydrogen ions
migrate more rapidly than those of chlorine, the fore-
most of the diffusing ions are hydrogen, and since
these possess positive charges, the water or the dilute
solution as a whole exhibits a positive, and the stronger
solution a negative charge. Owing to the mutual
attraction of the positive and negative charges of the
hydrogen and chlorine ions, this separating process
does not actually take place to any measurable extent,
the hydrogen ions are delayed, and the chlorine ions
increase their speed, so that a condition is reached in
which both migrate at the same rate. The electrostatic
1 Zeitschr. physiTc. Chem. iv. 129, 1889.
vi ELECTROMOTIVE FORCE 191
attraction, as well as the potential difference between
the solutions, exists until both solutions are homogene-
ous. The unequal velocities of migration of the ions are
therefore the cause of the potential differences at the
contact surfaces of differently concentrated solutions.
If the negative ions have the greater velocity of
migration, the more dilute solution will evidently be
negative to the concentrated. In other words, the
dilute solution always presents the electricity of the more
rapidly moving ion.
Moreover, it is thus not only possible to foresee the
nature of the potential difference at the point of con-
tact between two liquids, but also in many cases
quantitatively to calculate the magnitude of such
potential differences, and prove the calculations by
actual experiment. To illustrate this point, two
differently concentrated solutions of an electrolyte,
consisting of two univalent ions, may be imagined
in contact. Let n be the share of transport of the
positive ion, and (Ln) consequently that of the
negative. The quantity of electricity e is now con-
ducted through the solutions from the concentrated
to the dilute, then n positive gram-ions pass from the
concentrated into the dilute, and at the same time
( 1 n) negative gram-ions from the dilute into the
concentrated solution. Let p represent the concentra-
tion of the positive and negative ions in the concen-
trated solution, and p l the same in the dilute solution.
The maximum work, the process being completed
osmotically, is
n -
Pi Pi
Pl
192 ELECTROCHEMISTRY CHAP.
or if n be replaced by - , u being the velocity of
migration of the positive, and v that of the negative
ions,
u + v Pl
Consequently
M-vRT. p
TT = - In (a)
u + v e Pl
because 7re = A.
If u be greater than v, the electric current passes
from the concentrated to the dilute solution in the
element itself; if v be greater than u, the current is
in the opposite direction. If, finally, u = v, no potential
difference exists between the solutions, and conse-
quently there is no current.
Nernst arranged such liquid cells so that the only
potential observed was that at the point of contact
of two solutions, and compared the experimentally
determined values of the electromotive force with
those calculated from the formula. The following
arrangement was used : Mercury mercurous chloride
i. ii.
O'l normal KC1 O'Ol normal KC1 O'Ol normal
III. IV.
HC1 O'l normal HC1 O'l normal KC1 mercurous
chloride mercury. Since the two ends are identical,
the potential differences occurring there neutralise
each other, and only those differences at the four
contact points I. II. III. and IV. are to be taken into
account.
It is to be observed that, as far as experience has
gone, the rule holds for liquid cells that only the
ratio, not the absolute values of the osmotic pressures,
comes into consideration. Therefore the potential
difference of II. is equal and oppositely directed to
vi ELECTROMOTIVE FORCE 193
that of IV.; thus the potential differences at I. and
III. alone remain, and may be calculated from the
above formula. If u^ and ^ are the velocities of
migration of the potassium and chlorine ions respect-
ively, while u 2 and v 2 ( = v 1 here, because they
represent the same negative ions) are the migration
rates of the hydrogen and chlorine ions, then the sum
of the potential difference is represented by
%/_
u 1 + v l e Pl u 2 + -o z e Pl "
and as
Pl Pl
therefore
p and p 1 are the osmotic pressures or concentrations
of the potassium and chlorine ions in the concentrated
and dilute potassium chloride solutions, p l and p^ the
corresponding values of the hydrogen and chlorine
ions in the corresponding hydrochloric acid solu-
tions. The actual measured potential difference was
0*0357 volt, taken negative, since the current in
the cell flowed in the direction IV. to I., and has,
in the calculation, been considered positive when it
passed from the concentrated to the dilute potassium
chloride solution. The potential difference resulting
from calculation by the formula, taking into considera-
tion the incomplete dissociation of the substances,
differs from the above by about ten per cent.
The formula (a) only permits of calculation of the
potential difference at the points of contact of two
differently concentrated solutions of one and the same
194 ELECTROCHEMISTRY CHAP.
binary electrolyte. If it is desired to make it appli-
cable to electrolytes whose ions have different valencies,
it takes the form
U V
n ~ n' RT , p
7T =
u + v e Pl
n representing the valency of the positive and n' that
of the negative ion.
If two different electrolytes are in contact, as, for
instance, potassium chloride and hydrochloric acid, the
calculation is more difficult. Only for the case in
which the total concentration of ions in each of the
two solutions is the same, the following simple ex-
pression holds :
RT u' + v"
TT = In , (c),
where u' and v' are the migration rates of the ions of
one electrolyte, u" and v" those of the other.
The calculation is still more difficult when one of the
electrolytes contains polyvalent ions. If all the ions
of the two solutions of binary electrolytes are poly-
valent and of the same valency, then when the ion
concentrations are the same,
RT. u' + v"
TT = In , , (d).
fl 11 _J_ /y
It is worthy of special attention that in general
there can be no arrangement of solutions in an electro-
motive series such as Volta formed for the metals.
This is evident from the fact already mentioned, that
such solution cells as the one measured by Nernst (p.
192) produce a current. A circuit consisting of
metals only, at a common temperature, does not
vi ELECTROMOTIVE FORCE 195
generate an electric current. If, on the other hand,
the solutions of the above cell, without the mercury
and mercurous chloride, be arranged
in a circuit, as shown in Fig. 24,
an electric current is obtained whose
electromotive force is that previously
calculated. The existence of this
current may be demonstrated by
its power of induction, and it lasts
until the concentration of the
various ions is the same throughout the system.
The law of electromotive series applies only to
differently concentrated solutions of the same electro-
lyte in juxtaposition. That it holds in this case may
be shown by adding the potential differences occurring
at the different points of contact, and comparing the
sum with the potential difference actually observed
between the first and last solutions placed directly in
contact. The intermediate members of the series are
thus shown to play no part.
In considering concentration cells, such conditions
were usually chosen that the potential differences
occurring at the contact points of the solutions were
negligible. Under such circumstances the electro-
motive force as previously given, for a cell in which
the metal electrodes dip into the two differently con-
centrated solutions of the salt, is
RT p
TT = m
n#o Pi
This formula was obtained by adding the potential
differences existing at the electrodes that is, with the
application of the idea of electrolytic solution pressures.
In the addition the solution pressures were cancelled
196 ELECTROCHEMISTRY CHAP.
from the equation, as they have the same value for the
two similar electrodes and are oppositely directed.
It was also found possible to obtain the value of
TT, without any assumption of solution pressure, by the
so-called purely energetic method. It was only neces-
sary to take into account the condition of the system
before and after the passage of a certain quantity of
electricity, without attempting to understand why a
potential difference and electric current are manifested.
The maximum work obtainable osmotically by the
change of the system from its original to its ultimate
state is calculated, and this maximum is considered
as the equivalent of the electrical energy. The values
of -TT calculated in both ways agreed without ex-
ception.
It remains to be seen whether, when a potential
difference occurs at the point of contact of the liquids,
the two methods of calculation still yield the same
result. For this purpose the concentration cell : zinc,
zinc chloride (concentrated solution), zinc chloride (dilute
solution), zinc is selected.
1. Calculation of TT by means of the electrolytic
solution pressure.
The electromotive force of the cell consists of three
potential differences : the two at the electrodes and
that at the point of contact between the two liquids.
The sum of the first two is
RT
where p and p l are the osmotic pressures of the zinc
ions in the concentrated and dilute solutions respect-
ively, the corresponding pressures of the chlorine ions
being 2p and 2p r
vi ELECTROMOTIVE FORCE 197
The third potential difference is calculated according
to the formula (6), p. 194, and is
U V
2~I
7To =
A U+V
where u and v are the rates of migration of the zinc
and chlorine ions. The sum of 71% . and TT Q is
1 > 6
ET, p (\ u-2v\ 3v ET/ p
TT= ln^ (s-s7T-r-v)=szr-rrN ln -
or if the transportation ratios are introduced, n
u
and 1 n =
u + v
2e o Pi
7r 3 must be subtracted from TT^, as indicated, since the
calculation of 7r 3 presupposes the direction of the
positive current from the concentrated to the dilute
solution within the cell, while with TT^ the current
passes in the opposite direction.
2. Calculating with respect to the energy change
alone, the process is exactly that outlined on p. 192.
If 2e be allowed to pass through the cell, a gram-ion
of zinc passes into the dilute, while the same quantity
is deposited from the concentrated solution. In
addition, the quantity n gram-ions of zinc pass from
the dilute to the concentrated solution, n being the
transportation share of the zinc ions. The dilute solu-
tion is now richer by (1 n) gram-ions of zinc, while
the concentrated one has lost this amount. Simul-
taneously, however, an amount of chlorine ions equiva-
lent to the (1 n) zinc ions has also passed from the
concentrated to the dilute solution ; consequently the
198 ELECTROCHEMISTRY CHAP.
quantity (1 n) of zinc and its equivalent of chlorine
ions have been moved from the concentrated to the
dilute solution. The maximum osmotic work corre-
sponding to the zinc ions is
and since there are two chlorine ions to each zinc, it
has for the. chlorine ions the value
Pi
or, added together,
3(1 - ri)UT In - .
Pi
The electrical energy is 2e 7r, and therefore
2e o %i'
the same as the previous formula.
This agreement in the methods gives also a method
for determining the magnitude of potential differences
at the contact points of liquids. It is only necessary
to calculate as above, the sum of the potential differ-
ences occurring at the two electrodes, and subtract it
from the actually measured electromotive force of the
whole cell, to obtain the desired value.
GENERAL CONSIDERATION OF CONCEN-
TRATION AND LIQUID CELLS
All the cells thus far described have the common
characteristic that their electrical energy is not generated
from chemical energy. In every case there was simply
a passage of material from a higher to a lower pressure,
vi ELECTROMOTIVE FORCE 199
and whether it be a gas or a dissolved substance which
undergoes this change, the process does not affect the
internal energy. The work done does not therefore come
from the internal energy, but is derived from the heat
of the surroundings. Consequently the galvanic cells
thus far considered are really machines for turning the
heat of their surroundings into electrical energy.
According to the generally applicable formula of
Helmholtz (see p. 142),
dir
In the present case Q, the heat generated by the
chemical reaction, is zero ; therefore
_ dir TT dir dir
This, on integration, gives In TT = In T + k or = k.
The change of the electromotive force of these cells
with the temperature is determined by the relation
existing between the electromotive force and the corre-
sponding absolute temperature. The electromotive
force itself is proportional to the absolute temperature.
When in activity the cell cools itself and takes up
heat from the surroundings.
The same conclusions are reached on proceeding
in still another way. The electromotive force of one
of the previously mentioned concentration or liquid
cells is in general
from which
RT. p . .
= X In (a\
o Pi
200 ELECTROCHEMISTRY CHAP.
On differentiation with respect to T,
dir E p
is obtained, if x and In for " ideal " solutions are con-
sidered as practically independent of the temperature.
By combination of (b) and (c)
7T f/7T
T = dT
is again obtained.
It will be well to bear in mind that the electro-
motive force is only correctly calculable by this method
when the solutions are so dilute that the laws of gases
are applicable, for it is upon this assumption that the
maximum work is estimated. Moreover, it must be
possible to obtain the total energy in the form of
electricity. Since, as a matter of fact, neither of these
limitations is actually reached, the observed electro-
motive force cannot exactly agree with that calculated.
Eegarding the first point the error is not negligible.
One proof of this is that solutions are often used
which, on being mixed, generate considerable quantities
of heat, and are therefore far from being ideal solutions.
For such solutions the Q of Helmholtz's formula is
evidently not zero, and the relation rp = ^ no longer
holds good.
From these observations it is furthermore evident
that it is unreasonable to consider the heat generated
by the mixing of solutions used in the cells as the
source of, or the reason for, the electrical energy pro-
duced. In the concentration cell, for example,
platinum black with hydrogen, alkali, acid, plati-
vi ELECTROMOTIVE FORCE 201
num black with hydrogen, the electromotive force
depends principally upon the difference of the con-
centration of the hydrogen ions in the two solutions.
The process of neutralisation which may take place at
the point of contact between the alkali and acid is not
to be considered as determining the electromotive force
of the cell, nor can it be looked upon as the principal
reason for its existence. The same considerations
apply to the cells in which an electrode is covered
with one of its difficultly soluble salts, as, for example,
mercury, mercurous chloride with potassium chloride,
mercurous nitrate, mercury. The process of solution
of the mercurous chloride has nothing directly to do
with the production of the electromotive force.
THERMOELEMENTS THE ELECTRO-
MOTIVE SERIES
In connection with the foregoing a few words may
well be devoted to the thermoelements. Heat is here
subjected to a transformation into electrical energy
caused by a difference of temperature. On the other
hand, in the concentration cells heat at a constant
temperature is changed into electricity. This cannot
be considered as contrary to the second law of thermo-
dynamics, because, according to this law, it is only in
a cyclic process that no heat at constant temperature can
be changed into work. In other processes such a
transformation may well occur.
The potential difference at one electrode may be
expressed by the formula,
RT P
TT = In
n e Q p
202 ELECTROCHEMISTRY CHAP.
and is accordingly proportional to the absolute tem-
perature. The arrangement : zinc, zinc sulphate
solution, zinc, will produce no electrical energy at
constant temperature, since the two potential differ-
ences of such a cell are equal and oppositely directed.
But if one of the contact points between electrode and
solution be warmed, the corresponding potential differ-
ence changes and an electric current is produced. As
the potential difference at the point of contact between
two solutions is also proportional to the absolute
temperature, it is immediately clear that the following
cyclic arrangement should produce an electric current :
Solution of concentration C t at temperature Tj
Solution of concentration C 2 at temperature T 1
Solution of concentration C 2 at temperature T 2
Solution of concentration C l at temperature T 2
Since the osmotic pressure, the solution pressure, and
the transportation ratios are functions of the tempera-
ture, the electromotive force of a thermoelement cannot
be simply calculated. For further considerations of
this point the reader is referred to the original work
of Nernst (Zeit. physik. Chem. iv. 169, 1889).
More important to us than these thermoelements
are those in which only conductors of the first class
enter. In this case the measurement of the electro-
motive force, when the temperature difference between
the points of contact is known, gives a method of
determining the potential difference actually existing
between two metals when at the same temperature.
Since a thermoelement generates an electric current
by the change of heat energy only into electricity, the
equation of page 199 applies :
TT _ dw dir
= 5 ' '
vr ELECTROMOTIVE FORCE 203
and this applies equally well to the combination as a
whole as to the individual potential differences, since a
cell can always be conceived in which there exists only
the potential difference considered. It is, therefore,
only necessary to know the change of the potential
with the temperature (^) at the point of contact
between two metals, in order to be able to calculate TT,
or the potential difference at the temperature T. The
value of -= may be directly obtained from the
electromotive force of a thermoelement consisting of
the two metals in question, the temperature at one
contact point being T, and that at the other T + dT.
If the temperature T is common throughout, the
electromotive force is zero, as the two potential differ-
ences are equal and opposite. It is only because one
of the potential differences may be changed by a
temperature change that the electromotive force
assumes a certain value, namely, that of the alteration
in the potential difference. From the formula it is
evident that if dT is unity, the electromotive force of
the element is T^TT.
The values of TT, calculated for pairs consisting of
the most widely differing metals at the ordinary
temperature, are very small, and amount, even in
exceptional cases, to but a few hundredths of a volt.
In the preparation of thermopiles the latter metals or
alloys are especially valuable. The above results are
in perfect agreement with the previous assumption
that in the majority of cells the principal source of the
electrical energy is at the surface between electrode
and solution.
The law of the electromotive series must evidently
apply to the minute potential differences existing
204 ELECTROCHEMISTRY CHAP.
between the metals themselves. A cell composed of
only two metals cannot, therefore, generate an electric
current when the temperature is the same throughout.
This conclusion is necessitated by the second law of
thermodynamics, otherwise any desired quantity of
heat at constant temperature could be changed into
electrical energy without any permanent alteration
taking place in the system ; which is equivalent to
saying that a cyclic process may continually change
heat into work. That this electromotive series exists
does not explain that discovered by Volta, since in
the latter the forces are very much greater. Volta
thought that the potential difference now ascribed to
the surface between liquid and metal was really pro-
duced at the contact point between the metals. To
corroborate his conclusions, the existence of a similar
law governing the potential differences at the surface
between metals and liquids must be demonstrated.
In the following pages it will be seen that, theo-
retically, a certain definite potential difference exists
between a metal and an electrolyte. If, for example,
zinc, in contact with an electrolyte whose potential
is zero, exhibits a potential of 3, while cadmium is 2
and copper 1, then, according to the electromotive
series, the potential difference between zinc and copper
must be equal to the sum of that between zinc and
cadmium and that between cadmium and copper. As
this is actually the case, the law of electromotive series
may be considered correct. Very accurate measure-
ments with an electrometer would evidently give slight
deviations, because in all cases another metal is
brought into contact with that of the electrometer, and
thus also another, though possibly very small, potential
difference is introduced. In a similar manner the
vi ELECTROMOTIVE FORCE 205
electromotive series is roughly applicable to the
galvanic cells. The arrangement : zinc, zinc sulphate,
cadmium sulphate, cadmium, cadmium sulphate, copper
sulphate, copper, in accordance with this law, should
exhibit the same electromotive force as the combina-
tion : zinc, zinc sulphate, copper sulphate, copper,
the concentrations of the zinc and copper sulphate
solutions being the same in both cases. This is
only exceptionally the case because of the disturbing
influence of the potential differences at the surfaces
between solutions. That the law applies to simple
liquid cells in a certain definite case only has already
been mentioned.
CHEMICAL CELLS
A distinction is to be made between the previously
described cells, in which heat, and the " chemical cells," in
which chemical energy is changed into electrical energy.
A type of this latter class is the well-known Daniell
element : zinc, zinc sulphate, copper sulphate, copper.
When in activity zinc passes from the metallic into the
ionic, and copper from the ionic into the metallic state.
In this process (in contradistinction to the ideal con-
centration cells) a change in the internal energy of the
system takes place, and this difference in energy may
be considered as the principal source of the electrical
energy produced. Instead of the change of positive
ions to metal at one pole, and the metal to ions at the
other, the negative ions may also perform this process.
The cell, platinised platinum in oxygen gas, potassium
hydrate, potassium chloride, platinised platinum in
chlorine gas, causes OH ions to be produced in the
alkali solution, and chlorine ions to change into
206 ELECTROCHEMISTRY CHAP.
molecular chlorine in the potassium chloride solution.
(The current and process may be reversed under certain
circumstances.)
Finally, positive ions may form at one electrode
simultaneously with the negative ions at the other.
An example is seen in the combination: zinc, zinc
sulphate, potassium chloride, platinised platinum in
chlorine gas. It is also well to remember that in all
such cells there is a small potential difference produced
at the surface between the solutions.
The electrical energy may be calculated by the
Helmholtz formula, from the heat generated by the
chemical processes and the experimentally determined
temperature coefficients. The element during activity
must yield as electrical energy the maximum work
obtainable through the change of state. This work
bears that relation to the heat of the chemical reaction
measured in the calorimeter which is given by the
Helmholtz formula. As this formula shows, there
may be elements in which the chemical or internal
energy change is exactly equal to the electrical energy
obtained. These may be considered as machines which,
in their action, will change all the energy put into
them into another energy form. There are also cells
in which only a portion of the chemical becomes
electrical energy, and these may be looked upon as
machines which transform only a portion of the energy
introduced into another form of available energy, while
the remainder is lost as heat. A third kind of cell is
also known, by which more electrical energy is pro-
duced than corresponds to the chemical reactions taking
place, and such elements may be considered as machines
transforming not only the applied energy into work,
but absorbing and changing into work the heat of the
vi ELECTROMOTIVE FORCE 207
surroundings. Imagine in this last class the amount
of work which really comes from the heat of the
surroundings, continually increased ; cells are finally
reached in which (as in the concentration cells) the
internal energy remains unaltered and the electrical
energy is derived entirely from the heat of the sur-
roundings. It then becomes a question whether these
are to be designated chemical cells or not.
From these remarks it may be seen that a sharp
line of demarcation between the chemical and other
cells does not exist, and one form passes into the
other. The distinction is justifiable in so far as the
chemical reaction is the chief characteristic of the
cells, the only other cells at constant temperature
being liquid and concentration cells, where there is no
chemical reaction. Here, naturally, the Helmholtz
formula gives no aid, because of its general nature.
Again employing the idea of electrolytic solution
pressure, the electromotive force of the Daniell cell
may be represented by the formula (see p. 154)
BT P KT P' RT/ P P'\
TT = -- In In = I In In r 1.
2e o P 2e o P 2e o\ P P)
The inconsiderable potential difference between the
solutions is here omitted.
In writing the formula it was assumed that the
current passes from the zinc through the solution to
the copper. If this were not the case, a negative
value would be obtained for TT on taking the difference
between the separate potential differences, which would
signify that the current was oppositely directed. It
is evidently impossible to foresee whether P is less
or greater than p, and whether P' is less or greater
than p', that is to say, whether the expressions for the
208 ELECTROCHEMISTRY CHAP.
separate potential differences are positive or negative ;
but, as seen, it is unnecessary to give attention to this
point. When it is desired to represent the electro-
motive force of a cell in which the electrodes yield
only positive ions, as composed of the single potential
differences, it is only necessary to represent the value
for each electrode in the form
and write the expressions after one another. Having
arbitrarily established the direction of the current, a
positive sign is placed before the expression for that
electrode which produces positive ions when the cell is
active, and a minus sign before the expression corre-
sponding to the electrode where positive ions leave the
solution. The sum of these quantities is then the
desired value.
For those cells or systems in which the current is
due to changes in the negative ions alone, those
expressions corresponding to electrodes at which
negative ions disappear are to be written with the
negative, and the others with the positive sign. For
the cell : platinised platinum in oxygen gas
potassium hydrate solution potassium chloride solu-
tion platinised platinum in chlorine gas, it may be
assumed that the current, that is, the positive elec-
tricity, passes from the oxygen electrode through the
solutions to the chlorine electrode ; then
BTA P . P'\
= I In In 1
o \ P Pi
where P and p are the solution pressure of the chlorine
and osmotic pressure of the chlorine ions, P' and p r the
vi ELECTROMOTIVE FORCE 209
solution pressure of the oxygen and osmotic pressure
of the hydroxyl ions.
If, finally, both kinds of electrodes are present,
special care must be exercised in order to avoid
mistakes in the signs used. Those expressions are
considered positive which represent electrodes where
positive or negative ions are produced, and the minus
sign is applied where positive or negative ions disappear.
Accordingly, the electromotive force of the system :
zinc zinc sulphate solution potassium chloride solu-
tion platinised platinum in chlorine gas platinised
platinum in oxygen potassium hydrate solution
copper sulphate solution copper, the direction of the
current being assumed to be from zinc to copper
through the solutions, is
ET, P RT, P' ET P" RT P"'
TT = In h m r --In 77 In -777
2e p e p e p 2e p
ETA P P'"\ ETA F P"\
-(in- - In, ) + (in -, - In-).
% \ P P J e Q \P P J
P, P', P ;/ , P //r represent the solution pressures of the
zinc, chlorine, oxygen, and copper respectively ; p, p',
p ff , and p" f the corresponding osmotic pressures of the
ions.
In order thus to carry out the calculations of the
electromotive forces, the solution pressures must be
known. To learn these it is necessary to know some
one potential difference (TT) at the electrodes in question,
from which, at known osmotic pressure, the required
magnitude may be determined once for all, since all
the values excepting P in the formula
In
are known.
210 ELECTROCHEMISTRY CHAP.
DETERMINATION OF SINGLE POTENTIAL
DIFFERENCES
By the experimental investigations of Lippmaim
upon the connection existing between the surface
tension of mercury in sulphuric acid and the potential
difference at the point of contact, the measurement of
single potential differences was first made possible.
The principal result of Lippmann's research was ex-
pressed by him as follows : The surface tension at the
contact surface between mercury and dilute sulphuric
acid is a continuous function of the electromotive force
of the polarisation at that surface.
Helmholtz later made the researches of Lippmann
better understood by an application of the theory of
electrical double layers. If mercury be brought into
contact with a liquid, e.g. dilute sulphuric acid, it
assumes a positive electrical charge. This may be
explained by assuming that the electrolyte contains
mercury ions, very possibly from the dissolving of a
little oxide, which may be present on the surface of
even the purest mercury. The work of Warburg has
also shown that the mercury may be oxidised by the
oxygen dissolved in the liquid, and may thus enter
the ionic state. Because of its very low solution
pressure the mercury itself is positively charged in a
solution containing very few of its ions.
Qn account of the electrostatic attraction, a number
of negative ions group themselves about the positive
electrode, and a double layer is formed (see also p.
148). If it be assumed that the mercury is "polaris-
able," i.e. no ions can pass from the mercury to the
solution nor in the opposite direction (a condition only
vi ELECTROMOTIVE FORCE 211
approximately attained), and if negative electricity be
added to the mercury surface, a portion of the positive
charge there present is removed, and at the same time
the surface tension of the mercury is increased. This
is the result of the mutual repulsion of the quantities
of positive electricity on the surface of the mercury as
well as the negative in the electrolyte, with the conse-
quent expansion of the surface in opposition to the
surface tension. If a portion of this electricity be
removed, the surface tension naturally increases. By
continued introduction of negative electricity a con-
dition may be reached in which the double layer
disappears and the surface is electrically neutral.
Evidently at this point the surface tension has reached
its maximum value. If still more negative electricity
be introduced, the mercury becomes negatively charged,
and the attracted positive ions of the solution form a
new double layer, differing from the former in the
relative position of the two kinds of electricity. The
surface tension of the mercury must now decrease with
increased negative charges at the surface because of
the mutual repulsion of the quantities of electricity.
It is desired to ascertain the potential difference
brought about by the electrostatic attraction of the
double layer when the mercury in ordinary condition
is immersed in dilute sulphuric acid. In order to
make the mercury just neutral a potential difference
must be brought about equal to that of the electrostatic
attraction. Consequently that potential difference at
which the maximum surface tension of the mercury is
reached, when the latter is connected with the negative
pole of a source of electricity, is the desired value.
The mercury in this case does not differ in potential
from the liquid, there being no double layer present.
212
ELECTROCHEMISTRY
CHAP.
The execution of the above experiment is simple in
principle ; the difficulties which have practically to be
overcome in accurate investigations need not be dis-
cussed here. The apparatus depicted in Fig. 25 l may
be used. The capillary c, as well as the greater part
of the tube A, attached to c by a rubber tube, are tilled
with mercury, c dips into the cup B, which contains
Zn C
a little mercury, and above this the electrolyte. The
position of the mercury in the capillary is observed by
means of a microscope. The bulb Gr, which contains
mercury, permits of the application of desired pressures
through its elevation and depression ; it is attached to
the manometer (M) by a rubber tube. A bent glass
tube D leads from the latter to A, the connections
1 Zeitschr. physik. Chem. xv. 1, 1894.
vi ELECTROMOTIVE FORCE 213
being made with short pieces of rubber tubing.
Paraffin oil serves as the liquid of the manometer,
increasing the delicacy of the reading. A small vessel,
as shown at E, containing both paraffin oil and
mercury, is connected to the apparatus between the
manometer and rubber tube. P is an arrangement
for the introduction of any desired potential difference
(see p. 125).
It is to be recalled that when a capillary is placed
in water, the latter rises to a level above that of the
surrounding liquid, as it wets the surface of the glass.
On the other hand, with mercury the level in the
capillary is below that of the surrounding liquid, and,
if the surface tension be increased, sinks still lower,
that is, it moves against the pressure of the mass of
mercury. It is only in this way that a diminution of
the surface, the result of increased surface tension, can
occur.
If now a certain potential from the source of
electricity be applied to the mercury in the capillary
c, the surface tension of the mercury increases and the
meniscus begins to rise. In order to hold this in its
original position, a certain pressure must be exerted by
means of the manometer. As the applied potential
difference is increased the necessary pressure also
increases, until at a certain potential difference a
maximum in the pressure is observed, which, on
further increase of the potential difference, again
diminishes. The potential difference corresponding to
the maximum pressure is that which is naturally
assumed by the mercury in the electrolyte.
In order that the results may not be variable, it is
necessary to add some mercury salt to the electrolyte,
that this may have a certain concentration of mercury
214 ELECTROCHEMISTRY CHAP.
ions throughout, since the potential difference of the
metallic mercury is dependent thereon. The question
is naturally raised : Is not the electrode an unpolaris-
able one when sufficient mercury ions are present?
Why can it be considered as almost perfectly un-
polarisable, as has been done ? In answer, attention
is directed to the following : By adding mercury
ions to the liquid, the mass of mercury in B
becomes a nearly unpolarisable electrode, which main-
tains the same potential difference towards the
electrolyte, no matter what other potential differences
are inserted at P. Because of its % small surface the
metallic mass in the capillary only comes into direct
contact with a very small part of the electrolyte.
Consequently on the application of a potential differ-
ence only very few mercury ions pass from the electro-
lyte into metallic mercury, and new ions can diffuse
into the layer at the surface but slowly ; therefore this
electrode is practically polarisable. The relative extent
of the surfaces of mercury evidently plays the import-
ant part. What is actually measured is the potential
difference at the larger mercury surface, since this
alone is constant. When the two quantities of
mercury are in connection, that in the capillary
changes its surface tension until it possesses the same
potential difference as the lower mass. Such is
evidently also the case when the larger electrode is an
amalgam instead of pure mercury. For instance, if it
be copper amalgam and the solution above it contains
a copper salt, the potential difference will be less than
before, since the amalgam assumes a less positive
charge. The mercury in the capillary again assumes
the potential of the lower electrode when the two are
connected, and on introducing external potential differ-
vi ELECTROMOTIVE FORCE 215
ences a lower value than with pure mercury is
sufficient to bring about the maximum surface tension.
There is a second method which can be used for
the determination of single potential differences, the
principle of which was explained by Helmholtz.
Ostwald l first showed that it could be used for this
purpose, and through his efforts, as well as those of
Paschen, the method has been developed.
If an insulated mass of mercury be allowed to flow
in a stream through a fine opening and drop into an
electrolyte, there ought to be (in the ideal case) no
potential difference between the mercury and the
electrolyte. As already seen, mercury in contact
with an electrolyte becomes charged with positive
electricity. By allowing the mercury to drop into
the electrolyte .the area of its surface is continually
increased, and the charge must spread over the entire
surface; in other words, the potential difference between
mercury and electrolyte must approach zero. Helm-
holtz expressed himself on this point in the following
manner :
" Consequently I conclude that when a quantity of
mercury is connected with an electrolyte by a rapidly
dropping fine stream of the mercury, and is otherwise
insulated, the two cannot possess different electrical
potentials, for if a potential difference did exist, for
example, if the mercury were positive, each falling drop
would form an electrical double layer on its surface,
requiring the removal of positive electricity from the
mass, and diminishing its positive charge until that
of the mercury and solution reached equality."
An experiment by A. Konig had already shown
that the charge of the mercury could be almost com-
1 Zeitschr. physik. Cliem. i. 583, 1887.
216
ELECTROCHEMISTRY
CHAP.
FIG. 26.
pletely removed in the manner described. This result
was later confirmed in other ways. Fig. 26 represents
the arrangement employed by Konig.
The mercury cup (a), beneath dilute
sulphuric acid, was connected by a
wire (c), with mercury dropping
from the capillary into the acid.
A galvanometer (G) was con-
nected into the circuit as shown.
This indicated that the positive
electricity was removed with the
dropping of the mercury in agree-
ment with the previous explanations.
If the upper mercury, through the dropping, be
brought to practically the same potential as the
solution, the polarisable mercury in the cup has the
same potential, and therefore the maximum surface
tension. This could be determined by means of an
ophthalmometer. As still further proof, a weak
electromotive force, positive or negative, on being
introduced into the circuit on the wire connecting the
two electrodes, caused the surface tension to decrease,
since a potential difference was produced between the
liquid and the mercury of the cup. In this case it is
desirable to have the electrode as polarisable as possible,
for the potential of an unpolarisable dropping electrode
cannot be altered in this way.
By these two methods it is possible to ascertain the
magnitudes of the individual potential differences
which constitute the electromotive forces of reversible
cells. Obviating as far as possible the potential differ-
ences at the contact surface between the solutions by
suitable choice of electrolytes and concentrations, any
potential which an electrode assumes when in contact
vi ELECTROMOTIVE FORCE 217
with a liquid containing the corresponding ions (other-
wise variable values are obtained) can be determined.
On the one hand, the potential difference between
mercury and a normal potassium chloride solution, for
example, saturated with mercurous chloride, may be
obtained by the pressure method. Then this electrode
of known potential difference may be used in con-
nection with the one whose potential difference is
to be determined. Supposing the potential difference
of silver in contact with a normal silver nitrate
solution to be desired, the electromotive force of the
combination : mercury normal potassium chloride
solution saturated with mercurous chloride normal
silver nitrate solution silver, is measured. From
this the value of the potential difference due to the
mercury electrode is subtracted, and the desired
potential difference remains. On the other hand, the
same end may be reached by arranging the mercury
in the above combination as a drop electrode, whereby
the mercury and electrolyte are brought to the same
potential. The measured electromotive force of the
cell has its origin in the potential difference at the
silver, and represents the latter. The mercury may
be allowed to drop directly into the second electrolyte,
which is often preferable.
Eesults obtained by these two methods agree satis-
factorily, although differences of a few hundredths of a
volt exist, probably due to the difficulty of measure*
ment. For the determination of single potential
differences it is customary to make use of a so-called
"normal" electrode 1 as shown in Fig. 27. At the
bottom of a small upright vessel, about 8 cm.
high and 2 or 3 cm. in diameter, pure mercury is
1 Ostwakl, Phisiko-chemische Messungen, p. 258.
218
ELECTROCHEMISTRY
CHAP.
placed, and is covered with a layer of mercurous
chloride ; the vessel is then filled with a normal
potassium chloride solution and closed with a rubber
stopper carrying two glass tubes. Through one of
these a platinum wire is introduced, which is in con-
tact with the mercury ; the other tube is filled with
the chloride solution, which also fills the rubber tubing
and bent glass tube at its end. The latter is placed
into the liquid, the potential difference between which
FIG. 27.
and an electrode is to be determined, and the electro-
motive force of the cell thus formed is measured.
If the potassium chloride produces a precipitate
with the second electrolyte, as with silver nitrate, a
third and indifferent solution, e.g. sodium nitrate, is
introduced between the two. The use of potassium
chloride solution for the normal electrode offers the
advantage that it does not favour the formation of
potential differences at the contact points of the
solutions, since the rates of migration of its ions
vi ELECTROMOTIVE FORCE 219
are very nearly the same. The potential difference
produced between the solutions at their point of con-
tact is a disturbing factor, and affects the value of
single potential differences by several thousands of a
volt. It may even amount to a few hundredths under
certain circumstances.
At present 0*56 is accepted as the most probable
value for the potential difference between mercury and
normal potassium chloride solution saturated with
mercurous chloride. The mercury ions possess the
tendency represented by 0*56 volt of leaving the
ionic and entering the metallic state. The metal is
therefore positively and the electrolyte negatively
electrified. This fact must always be borne in mind
in order to be able properly to carry out the calcula-
tion. Hereafter the potential of the metal or electrode
will be considered as zero and the + or sign will
indicate whether the electrolyte is positive or negative
to the electrode. 1 In accordance therewith mercury
mercurous chloride in normal potassium chloride
solution = 0*56 volt.
Through the aid of this value, any other single
potential difference may be determined. Suppose the
electromotive force of the cell : zinc normal zinc
sulphate solution mercurous chloride in normal
potassium chloride solution mercury, has been
measured and found to be 1/08 volt, and that the
current passes from the zinc to the mercury through
the solutions, the potential difference, zinc normal
1 Another form of expression occurs in the literature. The + sign
is used by some investigators to designate that potential difference by
the action of which ions are produced, no matter whether these be
positive or negative. The above use of the signs is considered simpler
for the calculations.
220 ELECTROCHEMISTRY CHAP.
zinc sulphate, may be calculated as follows. According
to p. 208 the electromotive force of the cell is
RT P RT, F
7T = In In - = 7T, 7T ,
2e p p
P and^> referring to the zinc, P' and^/ to the mercury.
7T=1-08,
and also
7r 2 = -0-56 ;
therefore
1-08 = ^ + 0-56,
and
Zinc - normal zinc sulphate = ir 1 = +0-52 volt.
Zinc has the tendency, represented by the electro-
motive force 0*52 volt, to send its ions into the normal
solution of its sulphate, and the solution is therefore
positively while the metal is negatively electrified.
Experience has shown that this calculation is not
at first easily understood by students, and therefore
two other illustrations are given.
A measurement of the cell : copper normal copper
sulphate solution mercurous chloride in normal
potassium chloride solution mercury, gave 0'025
volt as electromotive force, the direction of the positive
current being from the mercury to the copper through
the electrolytes.
RT P RT P'
7T = In 1 In = - 7T, + 7T 9 ,
2e p e p
P and p referring to the copper, and P' and p f to the
zinc. Since TT = 0*025 volt and
TT = -0-56 volt,
vi ELECTROMOTIVE FORCE 221
therefore
0-025= -TTj-0-56
and
Copper normal copper sulphate solution TT I = 0'585 volt.
The cell, consisting of platinised platinum in
oxygen at atmospheric pressure normal sulphuric
acid mercurous chloride in normal potassium chloride
solution mercury, exhibited an electromotive force of
0'75 volt, the current passing from the mercury to
the oxygen through the electrolytes. Since
RT. P RT p'
7T = -\ hi + - In 7 = - 77% + 7T 9 ,
o P o P
where P and p refer to oxygen and P' and p f to the
mercury, therefore
0-75= -7^-0-56.
Hence it is seen that the combination : oxygen under
atmospheric pressure normal sulphuric acid = TTJ =
1-31 volt.
Oxygen has therefore the tendency to generate OH
ions with a considerable electromotive force. The
electrolyte thereby becomes negatively and the elec-
trode positively charged.
In the avoidance of error the following method of
consideration is particularly advantageous. The
electromotive force and direction of current of the
measured cell and of the normal electrode are known,
also the fact that the total electromotive force is com-
posed of the two single values ; therefore for every
cell the following graphic scheme may be adopted,
and is here applied to the second of those above
described :
222 ELECTROCHEMISTRY CHAP.
Copper 1 / 1 n. copper sulphate mercurous chloride, etc.
mercury.
v^
0-560
0-025
The third value is now definitely determined. If
there is a potential difference between the mercury and
its electrolyte of 0'560 volt, and its direction be re-
presented by the arrow, while the electromotive force
of the combination is 0*025 volt in the opposite
direction, it is evident that between the copper and
its electrolyte there must be a potential difference of
0'585 volt in the same direction as the total electro-
motive force of the cell, or
Copper n. copper sulphate mercurous chloride, etc.
mercury ;
./ N^_
0-585 0'560
0-025
and
Copper n. copper sulphate solution = 0*585 volt.
If the direction of the arrow be from electrolyte to
electrode (always within the element), the electrolyte is
negative to the electrode ; otherwise it is positive.
As is evident, the electromotive force of single cells
consists in general of two potential differences, which
may be in the same direction, their sum constituting
the electromotive force of the cell, or they may be
oppositely directed, when they partially neutralise each
other. The first of the three examples corresponds
to the former case, and the two others to the latter.
Of the accompanying figures the first graphically
represents the changes of potential for the three closed
elements under the assumption that the external
VI
ELECTROMOTIVE FORCE
223
Zero.
Mercury pole.
0-56
1-08-E.M.F. of the cell.
Zinc pole. FlG. 28.
-Q-O2Z5 0-
Mercury pole.
-0-585* 1 - 0-5825
b
Zero.
Mercury pole.
Zero.
Mercury pole.
-0'025 = E.M.F. of the cell.
Mercury pole.
FIG. 29.
Zero.
Mercury pole.
224 ELECTROCHEMISTRY CHAP.
resistance (a) and the internal (b) are the same per
unit length, and that (a) as a whole is nine times as
great as (b). The three other figures illustrate the
potential differences when the cells are open. In the
first two the positive, and in the last two the negative
poles are connected with the earth.
The following explanations apply to Fig. 30 (see
also p. 13). If the mercury of the cell be brought
to the potential zero, the potential of the potassium
chloride solution is evidently 0*56 when the circuit
is open. Therefore, when the circuit is closed the
potential of that layer of the electrolyte in immediate
contact with the mercury is given, and is indicated in
the. figure by the perpendicular at A. At the point B,
or the place of contact between electrolyte and oxygen,
there is a potential difference of 1'31 volt, and the
electromotive force of the whole cell is 0*75 volt.
That is, with open circuit, when the mercury electrode
is connected with the earth, the oxygen electrode has
a potential of 0*75 volt. When the circuit is closed
and the internal resistance of the cell is one-tenth of
the total, the oxygen electrode indicates a potential
of but O^Sx^, or 0*675 volt; consequently a
perpendicular must be erected at B corresponding to
this 0*675 volt, and a layer of the electrolyte in the
immediate neighbourhood must have a potential of
0*635, since the electrolyte is negative towards the
electrode and the potential difference is 1'31 volt.
The perpendicular at B must therefore be continued
below the line AB to a point corresponding to 0*635
volt. It is now only necessary to draw the lines (a)
and (b), representing the fall of potential corresponding
to the resistance of the circuit, to complete the figure
for the closed circuit.
VI
ELECTROMOTIVE FORCE
225
The cases illustrated by the other figures are
analogous, and their consideration is recommended to
the student.
Neumann 1 determined the following potential
+0'675 Oxygen pole.
t
B oL
^N^ Zero.
Of" 9/10
b -0-635
+075-E.M.F. of the cell.
Oxygen pole.
Zero.
Mercury pole.
FIG. 30.
differences for the metals in normal or saturated solu-
tions of their salts.
1 Zeitsclir. physik. Chem. xiv. 229, 1894,
Q
226
ELECTROCHEMISTRY
CHAP.
Metal.
Sulphate.
Chloride.
Nitrate.
Acetate.
Magnesium
+ 1-239
+ 1 -231
+ 1-060
+ 1-240
Aluminium
+ 1 '040
+ 1-015
+ 0-775
Manganese
+ 0-815
+ 0-824
+ 0-560
Zinc .
+ 0-524
+ 0-503
+ 0-473
+ 0-522
Cadmium .
+ 0162
+ 0-174
+ 0-122
Thallium .
+ 0-114
+ 0-151
+ 0-112
Iron .
+ 0-093
+ 0-087
...
Cobalt
-0-019
-0-015
- 0-078
- 0-004
Nickel .
-0-022
-0-020
- 0-060
Lead .
...
-0-095
-0-115
- o'-079
Hydrogen .
- 0-238
-0-249
-0-150
Bismuth .
-0-490
-0-315
- 0-500
Arsenic
-0-550
Antimony
-0-376
Tin .
-0-085
Copper
-0-515
-0-615
- 0-580
Mercury .
-0-980
-1-028
Silver
-0-974
-1-055
-0-991
Palladium .
- 1-066
Platinum .
-1-140
Gold .
-1-356
The values for bismuth, arsenic, antimony, and tin are
not comparable with the others, as the corresponding
solutions contained free acid, and nothing is certainly
known regarding the quantity of ions contained in such
solutions. They were made by dissolving one equiva-
lent in grams of the solid substance in a liter of water,
the resulting precipitate being removed by filtration.
Because of undetermined conditions in the cases of the
gold chloride and the hydro-chloroplatinic acid solu-
tions, the values for these metals cannot be considered
fixed. Nothing is known in these cases concerning
the numbers of ions present. Finally, the values of
magnesium, aluminium, and manganese, the water-
decomposing metals, are only to be considered as
lower limits, their action upon the water causing
the values of cells containing them to diminish immedi-
ately after introduction of the electrode.
vi ELECTROMOTIVE FORCE 227
For the remaining solutions the numbers of ions in
the corresponding electrolytes were approximately the
same ; they are, however, not identical, as the solutions
were by no means completely dissociated. In order
to make them perfectly comparable, i.e. to give them
all the same ion concentration (it being upon this that
the magnitude of the potential difference depends), it
would be necessary to take into consideration the
degree of dissociation in each case. The values as
given, however, suffice for comparison. The order of
the electromotive forces, as the formula
RT. P
TT = In
n e^ Q P
shows, where p has nearly the same value for all the
electrolytes, presents also the order of the solution
pressures (P) of the various elements. This is then
the actual electromotive series of the metals.
Influence of Negative Ions upon the Potential
Difference : Metal Metal - Salt Solution. The
question may still be asked : Is the nature of the
negative ion without influence upon the potential
difference ? This cannot be surely answered from the
above values for chloride, sulphate, and acetate.
Differences occur in these cases from differences in
degree of dissociation in the individual solutions. But
since the degrees of dissociation are not known with
sufficient certainty, it cannot be determined whether
the differences of the dissociation degrees completely
explain the irregularities or not. Neumann (I.e.)
consequently prepared 0*01 normal solutions of over
twenty different thallium salts (mostly salts of organic
acids), and determined the potential difference when
these are in contact with metallic thallium. In these
228 ELECTROCHEMISTRY CHAP.
solutions the salts may be considered as equally dis-
sociated, and the same potential differences might be
expected in each case. As the measured values do not
differ by more than O'OOl volt, the conclusion is
justified that the nature of the negative ion is without
influence upon the potential of the metal. Negative
ions by which the metal is chemically affected as, for
instance, N0 3 are, of course, excluded from this
generalisation. This explains why the nitrate solutions
cause very different potentials from the chloride, not-
withstanding a nearly equal dissociation.
Electrolytic Solution Pressure. The magnitudes
of the electrolytic solution pressures of the metals may
be directly ascertained from the above measurements.
The potential difference at the electrode is
KT p
TT = In - ,
n e e P
and since the values of TT and p are known, P is
calculable. If p be expressed in atmospheres, P is
obtained in the same unit.
Assuming the osmotic pressure in the totally dis-
sociated normal solution to be 22 atmospheres, Neu-
mann 1 obtained the following values for P. Special
attention was given to the degree of dissociation at the
ordinary temperature (1*7).
Zinc . . . = 9-9 x 10 18 Atmospheres.
Cadmium . . = 2'7xl0 6
Thallium . . = 7'7xl0 2
Iron . . . = l'2xl0 4
1 Newmann calculated the values from the incorrect formula
RT /. P n \
TT = ( In 1 ),
n e e \ p J
and they have consequently been corrected.
vi ELECTROMOTIVE FORCE 229
Cobalt . . . =1-9x10 Atmospheres.
Nickel. . . =1-3x10
Lead . . =l'lx!0- 3
Hydrogen . . =9'9xlO~ 4
Copper . . =4-8xlO~ 20
Mercury . . =l'lxlO~ 16
Silver . . . =2'3x 10~ 17
Palladium . . =l'5x!0- 36
This may be considered as the absolute electromotive
series of the metals. Each metal, when placed in a
solution of one of those following, causes the precipita-
tion of the latter or the evolution of hydrogen. It has
already been seen that hydrogen ions are present in
pure water, and accordingly also in the solution of any
substance. Whether hydrogen is generated or not
depends upon which of the two positive ions, the
hydrogen or the metal, changes more easily into the
non-electric condition. Hydrogen ions can be continu-
ally generated from the undissociated water.
A word of explanation may be added concern-
ing the hydrogen. In considering the concentration
cells (p. 163) it was seen that the solution pressure
of the hydrogen depends upon its gas pressure (and
this also applies to other gases). The electrode
material, platinised platinum, does not come into
account. The above value for hydrogen is that for
atmospheric pressure. Theoretically, the solution
pressure of the hydrogen may be increased or diminished
as desired by altering the pressure under which it is
confined. The limits in both directions are, however,
practically soon reached. According to page 166, the
gas pressures vary as the squares of the solution
pressures. If, for example, hydrogen under a pressure
of 10,000 atmospheres be used, its solution pressure is
relatively little changed : it becomes 9 '9 X 10~ 2 instead
230 ELECTROCHEMISTRY CHAI-.
of 9*9 x 10~ 4 atmospheres. Such pressures can
scarcely be attained.
In agreement with the table, it has been shown
that platinum black, charged with hydrogen at atmo-
spheric pressure, is capable of precipitating the metals
following it from their salt solutions. If ordinary
platinum were used, the process would require a very
long time, because of its slight solvent action.
Influence of Dilution. The essential points con-
cerning the reversible cells, such as the Daniell, where
the ion-producing substances are elements, have already
been treated. The effect of dilution upon the electro-
motive force of an element will next be considered
because of its importance. The electromotive force,
when the electrodes are capable of producing only
negative or positive ions, is given by the equation
(p. 208).
RT, P RT , P'
TT = In --- -. In 7 .
^e e O P
As is evident from the formula, an increase in the con-
centration of the one solution diminishes the electro-
motive force, and of the other increases it. In the
Daniell element, for example, the electromotive force
is increased by concentrating the copper sulphate solu-
tion, and decreased by concentrating the zinc sulphate.
For both kinds of cells it may be said that
concentration of the solution from which the ions
separate causes an increase, while concentration of that
in which new ions are produced causes diminution of
the potential difference. This is easy to comprehend
when it is remembered that the osmotic pressure
opposes the solution pressure. In the first case the
passage of the ions from the solution is made easier,
vi ELECTROMOTIVE FORCE 231
and the electromotive force increases ; in the second
their entrance is made more difficult, and the electro-
motive force diminishes. If the two metals of the
electrodes have the same valency, equivalent changes
in the concentrations of the two solutions do not affect
the electromotive force.
If, finally, one electrode produces negative and the
other positive ions, the following holds :
RT. P RT P'
TT = In + In -, .
.0 P n e P
In this class of cells an increase in the concen-
tration of either solution causes a diminution of the
electromotive force, since ions are simultaneously pro-
duced at both electrodes, and the increased osmotic
pressure opposing the introduction of ions reduces the
electromotive force. The magnitude of the changes of
electromotive force, produced by given alterations in
the concentrations, may be recognised from p. 170.
A single exception to this generalisation is the gas
cell : Platinised platinum in hydrogen, electrolyte, e.g.
sulphuric acid solution platinised platinum in oxygen.
The above formula applies also to this cell, p and
p r being the osmotic pressures of the hydrogen and
hydroxyl ions. But as the product of the concentra-
tion of these ions in pure water, or in any aqueous
solution, always has the same value, the electromotive
force of the cell cannot be altered by changing the
concentration of the electrolytes, nor in general by
changing the electrolytes themselves. If p increases to
a certain extent above its original value, p f diminishes
to the corresponding degree. This is true so long as
the two electrodes are in contact with solution homo-
geneous as regards the H and OH ions, for the electro-
232 ELECTROCHEMISTRY CHAP.
motive force only depends upon the layers of electrolyte
at the electrodes. If the electrodes are originally
placed in different solutions, or if the portions about
the electrodes become altered during the passage of the
current, as when a salt solution is used for electrolyte,
acid appearing at one electrode and base at the other,
this cell may be included in the ordinary class.
Heat of lonisation. The Helmholtz formula,
is applicable not only to the whole, but also to each
individual potential difference in the cell. Q then
represents the heat effect produced at the electrode in
question, and -^ the temperature coefficient of the
potential difference. The electromotive force of the
cell consisting of two or more single potential differ-
ences, the temperature coefficient is composed of their
individual temperature coefficients.
If, for example, the potential difference between zinc
and zinc sulphate solution be known, and its temperature
coefficient determined, the value of Q may be calculated.
This is the heat generated by the passage of metallic
zinc into the ionic condition, that is, the heat of
ionisation of the zinc. The thermo-chemical data are
always sums or differences of two or more of these
heats of ionisation. The precipitation of copper from
its solution by zinc gives the difference between the
heats of ionisation of zinc and copper. On the other
hand, if the heat of ionisation for a single element be
known, as here the zinc, that of the others may be
obtained from the thermo-chemical data. The follow-
ing table containing the heats of ionisation is given by
vi ELECTROMOTIVE FORCE 233
Ostwald. 1 Because of uncertainty of some of the ex-
perimental data, the values are only approximately
correct. K is very nearly equal to a hundred small
calories.
For one For one
Atomic Weight. Equivalent Weight.
Potassium ....
+ 610 K
610 K
Sodium .....
+ 563
563
Lithium ....
+ 620
620
Strontium ....
+ 1155
578
Calcium ....
+ 1070
535
Magnesium ....
+ 1067
534
Aluminium ....
+ 1175
392
Manganese ....
+ 481
240
Iron (ferrous ions) .
+ 200
100
(ferrous ions in ferric ions)
121
-121
Cobalt
+ 146
+ 73
Nickel
+ 135
68
Zinc
+ 326
163 ,
Cadmium ....
+ 162
81 ,
Copper (cupric ions)
175
88 ,
(cuprous ions)
170 (?)
-170 ,
Mercury ....
- 205
-205 ,
Silver
- 262
-262
Thallium ....
+ 10
+ 10
Lead .....
10
5
Tin .....
+ 20
+ 10
Direct Measurement of both Potential Differ-
ences in a Cell. Instead of measuring one of the
potential differences and determining the other by sub-
traction, it is possible to measure the potentials singly.
The difference at the point of contact of the two liquids
being reduced as much as possible, the sum of the two
measured potential differences must be very nearly
equal to the electromotive force. Eothmund 2 corro-
borated this, which again proves that no considerable
1 Zeitschr. physik. Chem. xi. 501, 1893.
2 Ibid. xv. 1, 1884.
234 ELECTROCHEMISTRY CHAP.
potential differences exist at the contact points between
metals.
For determining the single potential differences,
Eothmund made use of the Lippmann method already
described. For mercury he substituted amalgams of
the baser metals, which, in moderate concentration
(about '01 per cent), act very nearly as the pure
metals. He determined, for example, the potential
difference when lead amalgam is in contact with
normal sulphuric acid solution saturated with lead
sulphate, copper amalgam in contact with normal sul-
phuric acid solution containing '01 molecular weight
in grams of copper sulphate per liter, and constructing
cells with the normal electrode whose value is directly
determined, he measured the resulting electromotive
force, and compared it with the sum of the known
values for the two single potential differences. In
order to reduce the magnitude of the potential differ-
ence at the contact surfaces between the solutions, the
combination, mercury mercurous sulphate in normal
sulphuric acid was used instead of the normal electrode
described. This combination will be represented by N',
and its potential difference is 0*926, being greater
than that of the other normal electrode, because mer-
curous sulphate is more soluble than the chloride.
The following values were obtained :
Copper amalgam normal sulphuric acid,
with -01 mol. CuS0 4 per liter. . = - 0'445 V.
N' . ' . . . " . . . = -0-926
Lead amalgam normal sulphuric acid
saturated with lead sulphate . . = + 0-008
The electromotive force of the copper-N' cell should
therefore be 0'481 volt, and that of the lead amalgam-
vi ELECTROMOTIVE FORCE 235
N x cell 0'918 volt. The experimentally determined
values are 0*458 and 0'926. It is therefore impossible
that greater potential differences can exist between the
metals themselves than the differences between these
values.
CELLS IN WHICH THE ION-PEODUCING
SUBSTANCES AEE NOT ELEMENTS
A class of chemical cells, apparently very different
from that represented by the Daniell element, will now
be considered. If a platinised platinum electrode is sur-
rounded by a solution of stannous chloride, and another
by one of ferric chloride, and the two are placed in
metallic connection, an electric current is obtained,
which passes within the cell from the former solution
to the latter. The trivalent ferric ions give up an
equivalent of electricity, becoming ferrous ions, while
each stannous ion takes up two electrical equivalents,
becoming a stannic ion. The process may be imagined
in detail as follows : The stannous ions change into
stannic, and thereby positive electricity is produced.
Since this can never come into existence alone in a
change of chemical into electrical energy, electricity
must be produced upon the electrode. This electricity
passes through the wire to the other electrode, where
it unites with the positive electricity derived from the
change of ferric into ferrous ions.
The cell, platinised platinum in hydrogen, electro-
lyte A, electrolyte B, platinised platinum in chlorine,
is evidently completely analogous to the above com-
bination. It was previously stated (p. 163) that
platinised platinum in hydrogen may be considered as
236 . ELECTROCHEMISTRY CHAP.
a hydrogen electrode. In a similar manner the above
combination may be characterised as stannous and
ferric electrodes, and just as a tendency to go into the
ionic (or of the ions to go into the neutral) state was
ascribed to the hydrogen and chlorine electrodes, so a
tendency of the stannous and ferric to form stannic
and ferrous ions may be recognised. The electromotive
force of this cell also consists principally of the two
independent potential differences occurring at the elec-
trodes. But these potential differences depend not
only upon the solution pressures of the substances in
question, but also upon the osmotic pressures of the
ions forming. Therefore the concentrations of the
stannic ions formed at the one electrode, and of the
ferrous ions at the other, are important factors ; a
certain constant potential difference, as in the Daniell
element, could only be expected when the solutions
already contained stannic and ferrous ions. Moreover,
the concentration of the altering compounds must be
considered, for the solution pressure of a substance at
constant temperature is invariable only at a definite
concentration.
From what has been said, it is obvious that there
is essentially no difference between the Daniell and
the so-called reduction and oxidation cells. The laws
governing the former may be expected to control the
latter.
Experimental investigation has not been carried
out sufficiently to demonstrate the accuracy of all the
theoretical deductions. Thus the influence of the con-
centration of the substances formed at the electrodes has
been almost entirely neglected, and it is probable that
the varying values of such cells are due to this. The non-
reversibility of these cells may be similarly accounted
vi ELECTROMOTIVE FORCE 237
for. If, instead of allowing the stannous chloride
ferric chloride cell to act, it be opposed by a cell of
greater electromotive force, oxygen must separate at
one electrode (at least in dilute solution) and metallic
tin at the other. Stannic and ferrous chlorides being
present, a change of the stannic into the stannous,
and of ferrous into ferric salt, would certainly
take place instead of the above, and the cell be
reversible. 1
A cell whose electrodes are zinc and chlorine, and
whose electrolytes do not contain zinc and chlorine
ions, is no longer a reversible cell. If a stronger
opposing current be sent through such a cell, the posi-
tive ions of one electrolyte separate at the zinc, and
the negative of the other at the chlorine electrode,
while zinc and chlorine ions are liberated through its
own activity as a cell.
Bancroft proved that the electromotive force of
such cells is essentially the sum of the two single
potential differences.
Although our knowledge of the values of such
quantities leaves much to be desired, the following
list of potential differences, including the elements,
chlorine, bromine, and iodine, is given, it being not
only of considerable interest, but presenting, in addi-
tion, a measure of the " strength " of the substances.
The following values were obtained from platinised
electrodes surrounded by the liquids mentioned. Most
of the solutions contained about ^ molecular weight in
grams per liter : 2
1 It is very doubtful if the processes even of most of such cells
are practically capable of proceeding reversibly. At any rate, this
circumstance complicates the relations.
2 Zeitschr. physik. Chem. xiv. 193, 1894.
238
ELECTROCHEMISTRY
CHAP.
SnCl 2 + KOH . .
Na 2 S . . .
Hydroxylamine, KO
Chromous acetate,
KOH . . .
Pyrogallol, KOH .
HydrocMnone, KOH -0-231
Hydrogen, HC1 .
Potassium ferrous
oxalate . .
Chromous acetate .
K 4 FeCy 6 , KOH .
I 2 , KOH. . .
SnCl 2 -HCl . .
Potassium arseniate .
NaH 2 P0 2 . .
CuCl 2 . . .
Na 2 S 2 3 . . .
Na 2 S0 3 . . .
Na 2 HP0 3 . .
K 4 FeCy 6 . . .
FeS0 4 (neutral) .
In electrical processes the so-called oxidations and
reductions may be clearly distinguished, for it may be
said that the process is always one of oxidation when
negative electricity is produced on an ion or positive
disappears. When positive electricity appears or
negative disappears the process is one of reduction.
According to these definitions there must be, in every
galvanic element, an oxidation at one electrode and a
reduction at the other. In the Daniell element the
reduction takes place at the zinc electrode, and the
oxidation at the copper. The precipitation of one
metal by another, the process of substitution, is thus
to be considered as one of oxidation and reduction.
It is evident, then, that the metals can only serve as
reducing agents, since they are only capable of pro-
ducing positive ions.
+ 0-301
Hydroxylamine
-0-636
+ 0-091
NaHS0 3 .
- 0-663
+ 0-056
H 2 S0 3 .
-0-718
FeSO , + H 9 SO,
- 0-794
+ 0-029
Potassium ferric
-0-078
oxalate
- 0-846
-0-231
I 2 -KI .
-0-888
- 0-249
K 3 FeCy 6 .
-0-982
K 2 Cr O r .
- 1-062
- 0-285
KNO* .
-1-137
-0-364
C1 2 - KOH
-1-186
- 0-474
FeCl 3 . .
- 1-238
- 0-490
HN0 3 .
- 1-257
- 0-496
HC10 4 .
- 1-267
-0-506
Br 2 - KOH .
- 1-315
-0-516
H 2 Cr 2 0. .
- 1-397
-0-560
HC10 S .
- 1-416
-0-576
Br 2 - KBr
- 1-425
-0-583
KI0 3 . .
- 1-489
- 0-593
Mn0 2 -KCl .
- 1-628
-0-595
C1 2 - KC1
- 1-666
-0-633
KMnO,
- 1-763
vi ELECTROMOTIVE FORCE 239
The negative elements, on the other hand, or the
substances producing negative ions, act exclusively as
oxidising agents. Salt solutions in general may be
reducing as well as oxidising agents, for they contain
both positive and negative ions, and are therefore
capable of yielding positive and negative electricity.
If zinc be placed in a solution of cadmium bromide,
cadmium is precipitated, the solution acting as an
oxidising agent ; but if chlorine be conducted into the
solution, bromine separates, the solution acting as
reducing agent.
Similarly, the substances in the above table may
be examined to discover whether they are reducing or
oxidising agents. From the above it is, moreover, not
surprising that a dissolved substance may have a
reducing or oxidising action according to circumstances.
This may even be the case when only the single ion
enters the reaction ; the bivalent ferrous ion may change
into the trivalent ion, on the one hand, or into metallic
iron, on the other, that is, it may act reducing or
oxidising.
In reversible cells each electrode may be made the
seat of the oxidation or reduction at will.
It may be well to say a word here concerning the
conditions which determine the actual production of
the electric current. 1 It has been seen that in all
galvanic elements a reduction and oxidation take
place, that is, at one electrode ions come into existence,
and disappear at the other. That the reaction may be
the source of an electric current, the two processes must
take place at points separated from each other. If they
both occur at the same point, no electric current
1 Ostwald, Chemisette Fernewirkung. Zeitschr. physik. Chem. ix.
540, 1892.
240 ELECTROCHEMISTRY CHAP.
results. Zinc being placed in a copper sulphate
solution, both the oxidation and reduction proceed
simultaneously at the surface of the metal. The
electric charges of the dissolving zinc and precipi-
tating copper have the opportunity of neutralising
each other there, and the possibility of a removal of
this neutralisation to some other point (and thereby
the production of an electric current) is lost. Hence
the statement that a chemical reaction between two
substances can only be used as a source of the electric
current when electricity is produced or disappears in
the reaction (i.e. by changes in the charges of the
ions), and also when the two substances separated
from each other are still capable of undergoing this
reaction.
If zinc be in contact with a solution of zinc
sulphate, and a platinum wire be placed therein, no
current is obtained on connecting the wire with the
zinc. If it be desired to dissolve the zinc, that is, to
cause it to pass into the ionic state and produce a
current, this may be accomplished by surrounding the
platinum with a solution of a copper salt, or an acid
whose positive component has a smaller tendency to
produce ions than zinc. The addition of the copper
or acid solution directly to the zinc solution would
evidently not produce an electric current.
In the production of galvanic currents many
different oxidising agents have been used to achieve
the highest possible efficiency, without the theory of
the phenomena being clearly understood. One of the
most common cells is the bichromate element con-
sisting of zinc chromic acid (or sodium bichromate
and sulphuric acid) carbon. The process essentially
consists in the formation of zinc ions at the negative
vi ELECTROMOTIVE FORCE 241
(zinc) electrode, and the reduction of chromium ions
at the positive (carbon) electrode from higher to lower
valency, whereby electricity is given up to the electrode.
The electromotive force of this cell is great, because
the zinc has a strong tendency to go into the ionic
state, and the chromium ions of high valency also
tend strongly to change into ions of lower valency,
the two tendencies additively producing the high
electromotive force. Furthermore, it is clear that the
electromotive force of this cell, when active, must
gradually diminish, because zinc ions are continually
forming, while the concentration of the chromium ions of
higher valency is decreasing, and that of those of lower
valency increasing. Each of the three changes reduces
the electromotive force.
The energetic oxidation of the zinc and the high
electromotive force of the cell is therefore obtained by
the addition of the oxidising agent not to the zinc but
to the carbon.
It is also possible to dissolve the noble metals or
change them into ionic state in a similar manner. A
cell consisting of platinum sodium chloride solution
gold, produces no electric current, though one is
produced when chlorine water is introduced at the
platinum electrode, the gold dissolving. The great
tendency of the chlorine to yield ions may be looked
upon as forcing the resisting gold to act similarly.
Addition of the chlorine water to the gold electrode
alone would not result in the production of a current
(the platinum being unaffected), and the gold would
oxidise very slowly.
242 ELECTROCHEMISTRY CHAP, vi
POTENTIAL DIFFERENCE BETWEEN SOLID AND
LIQUID METALS AT THE MELTING POINT
Before ending the chapter on reversible cells a
special case may receive brief mention. Imagine two
electrodes of the same metal in contact with an electro-
lyte at the melting point of the metal, and suppose one
of the electrodes to be liquid and the other solid ;
would such a cell produce an electromotive force ?
For instance, would the current pass from the liquid
to the solid electrode, and perhaps the heat of fusion
be the source of the resulting electrical energy ? The
impossibility of such a process may be easily grasped.
Suppose electrical energy could be produced by such
an arrangement, and that all the material has passed
from the liquid to the solid electrode through the
action of the cell. This being then melted by the
application of heat from the surroundings at the
constant temperature of its melting point, a current
could be produced in the direction opposite to the
first, and so on. In this way heat of constant tem-
perature would perform any desired amount of work
in a cyclic process, which is contrary to the second
law of thermodynamics.
CHAPTEE VII
POLARISATION
THE phenomena observed when an electric current is
conducted through an electrolyte between inactive
electrodes, as gold, platinum, carbon, etc., will now be
considered. It has long been known that the current
produces a decomposition of the electrolyte at the
electrodes, and that its electromotive force is thereby
reduced. The two facts are evidently related. The
performance of an amount of work, "more or less con-
siderable according to circumstances, is necessary to
bring about the decomposition of an electrolyte (as,
for example, hydrochloric acid into hydrogen and
chlorine), and this work is done by the electric current.
When such reduction of the electromotive force occurs,
polarisation is said to take place. The phenomenon
was formerly very little understood, and it is only
within the last few years that its explanation has
become possible.
If a current flows for a time through the above-
described arrangement, and is then interrupted, the
two electrodes being connected through a galvano-
meter, it will be observed that an electric current,
which rapidly becomes weaker, passes between the
electrodes in a direction opposite to that of the first
244 ELECTROCHEMISTRY CHAP.
or applied current. This is spoken of as the
" polarisation current," and its electromotive force is
called the " electromotive force of polarisation." From
the following it will be evident that this current is
derived from the tendency of the material separated in
the neutral condition to return to the ionic condition.
Ohm's law, applied to a circuit possessing a certain
primary electromotive force 7r v and containing a
" polarisation cell/' is represented by
where 7r 2 is the electromotive force of polarisation, C
the 1 current-strength, and E the total resistance of the
circuit.
Method of measuring Polarisation. As already
seen, the electromotive force of polarisation is not a
constant, but rapidly diminishes when the primary
electromotive force is removed ; its magnitude is there-
fore best determined during the passage of the primary
current. The accompanying figure represents an
arrangement which may be used for the measurement.
One circuit is represented by 1, 2, a, 1, and the
other by 2, e, b, a, 2 ; 1 is the source of the electricity,
2 the polarisation cell, e a compensation electro-
meter, b a known electromotive force, which may be
altered at will, and a a tuning-fork commutator,
which vibrates very rapidly. The arrangement is such
that at a one circuit is opened and the other simul-
taneously closed, then the latter opened and the
former closed, etc., with each vibration of the tuning-
fork. The result is practically the same as though
both primary and polarisation current were inde-
pendently active. Thus the electromotive force of the
VII
POLARISATION
245
latter may be measured under the same conditions as
if the primary circuit were continually closed. It is
only necessary to alter I until the electrometer
FIG. 31.
shows a condition of equilibrium; I is then the
desired value.
As the electromotive force of galvanic elements is
due to two or more potential differences, so also in the
n a
1
\ n
electromotive force of polarisation two single potential
differences are found 1 located at the two electrodes.
In order to measure them separately, the method of
Fuchs is employed. Its arrangement is shown in
Fig. 32. A double U tube is filled with the solution
of the electrolyte (e), whose polarisation is to be
1 The fall of potential due to the resistance of the electrolytes is
avoided by the method.
246 ELECTROCHEMISTRY CHAP.
measured. a and & are two indifferent electrodes
connected with the source (Q) of the primary or
polarising current. If the potential difference at I
is to be measured, the bent glass tube of the normal
electrode (N) (p. 217), filled with normal potassium
chloride solution, is inserted at c in the electrolyte
(e), and I is connected with the mercury of the
normal electrode by means of the platinum wire of
the latter. An element thereby results, consisting of
two electrodes and two electrolytes, and the electro-
motive force of the combination is measured by the
usual apparatus at M. The potential difference
between 6 and e may then be determined by sub-
traction of the normal electrode potential, and that at
the surface of contact between the liquids from the
total electromotive force. For determining the
potential difference between a and e the process is
analogous, and using a primary or polarising current,
whose electromotive force gradually increases from zero,
it is observed that the electromotive force of polarisa-
tion is at first very nearly equivalent to that of the
primary current. As the latter becomes higher the
former falls gradually away from it in magnitude,
nevertheless always increasing to some extent. The
much -sought -after maximum of polarisation does not
actually exist.
Decomposition Values of the Electromotive Force.
There is another characteristic point for the different
electrolytes. A continuous current and continuous
decomposition only take place when the electromotive
force exceeds a certain value. If an electromotive
force less than the above be inserted, only an in-
stantaneous passage of electricity takes place, which
may be made evident by a galvanometer in the circuit.
vii POLARISATION 247
The needle of the galvanometer is at first deflected,
but returns very nearly to its original position (the
effect of secondary disturbing influences will be
considered later), which does not happen when the
applied electromotive force has reached the value in
question.
Le Blanc determined the magnitudes of these
decomposition values for a great many electrolytes,
chiefly in normal solutions. They may be very exactly
determined for salts from which a metal is precipitated
by the current, but for other salts, as well as for acids
and alkalies, they are less easily found. The following
decomposition values were found for salts from which
the metal is precipitated. 1
ZnS0 4 = 2-35 Volts Cd(N0 3 ) 2 = 1 '98 Volts
ZnBr 2 =1-80 CdS0 4 = 2'03
NiS0 4 =2-09 CdCl 2 =1-88
Ni01 2 =T85
Pb(N0 3 ) 2 =l'52 CoS0 4 =1-92
AgNO 8 =0-70 CoCl 2 =1-78
The decomposition values for sulphates and nitrates
of the same metal, as shown by the experiments with
cadmium salts and other experiments with the alkalies,
are nearly equal. As is evident, the values for the
various metals are different. The conclusion to be
drawn from the corresponding values for the acids and
bases is that there exists a maximum decomposition
point, which is exhibited by most of the compounds
and exceeded by none. This is about 1*70 volt.
Among the acids, however, several gave various values
below this maximum. The following tables contain
the values for acids and bases :
1 Zeitschr. phijsik. Chcm. viii. 299, 1891.
248 ELECTROCHEMISTRY
Acids
Sulphuric =1 '67 Volt
Nitric =1-69
Phosphoric ..... = 1'70
Monochloracetic . . . . = 1'72
Dichloracetic . . . . =1'66
Malonic =1'69
Perchloric . . . . . = T65
Dextrotartaric .... =1*62
Pyrotartaric . . . . =1*57
Trichloracetic . . . . =1*51
Hydrochloric . . . . =1'31
Hydrazoic = T29
Oxalic =0-95
Hydrobromic .... =0*94
Hydroiodic . . . . = 0'52
Sodium hydrate . =1-69 Volt
Potassium hydrate . . . = T67
Ammonium hydrate . . = 1'74
J n. Methylamine . . . = 1'75
^ n. Diethylamine . . . =T68
^ n. Tetramethyl ammonium hydrate = T74
The alkali and alkaline earth salts of the strongly
dissociating acids with maximum decomposition values,
as sulphates and nitrates, have nearly the same
decomposition point about 2 '20 volts. The chlorides,
bromides, and iodides have lower values, independent of
the nature of the alkali metal. Additivity is exhibited
owing to the mutual independence of the potential
differences produced at the two electrodes. Differ-
ences between the values for the various halogen
compounds of the alkalies, hydrogen, and the metals
are nearly equal ; for example, the difference between
vii POLARISATION 249
hydrochloric and hydrobromic acid is the same as that
between sodium chloride and bromide.
The salt of a slightly dissociating acid, as sodium
acetate, or of a slightly dissociating base, as ammonium
sulphate, always exhibits a lower value than that of a
highly dissociating acid or base, presupposing that the
acid and base possess the maximum decomposition
value. The halogen salts of ammonium have lower
decomposition values than the corresponding salts of
the alkalies ; and, in fact, the differences between corre-
sponding salts are equal.
Concerning the effect of dilution in the case of
bases and acids which on electrical decomposition
evolved oxygen and hydrogen at the electrode, the
decomposition values were independent of the dilution,
and this is true for all the acids excepting those whose
decomposition values are below the maximum. For
these the value rises with increasing dilution, and
finally reaches the maximum. This is very marked in
the case of hydrochloric acid.
Decomposition Point.
f Normal hydrochloric acid, T26 volt
1 \J A ,,
1-69
It is also worthy of note that when the maximum
value is reached, the acid solution is no longer decom-
posed into chlorine and hydrogen, but into hydrogen
and oxygen.
The above experiments were carried out with plati-
num electrodes. If other electrodes be used, as gold
or carbon, different numerical values are obtained, but
the general relations between them remain unaltered.
250 ELECTROCHEMISTRY CHAP.
Iii order to obtain a better insight into polarisation
phenomena, Le Blanc 1 investigated the potential
difference at the electrode, where the metal is electro-
lytically deposited (the cathode), when the electromotive
force of the primary current is gradually increased
from zero. The result of this investigation is that the
potential difference at the decomposition point was
found to be equal to that which the precipitating metal
would itself exhibit in the solution. For example, a
normal solution of cadmium sulphate was decomposed
at a primary electromotive force of 2 '03 volts. The
potential difference of the electrode where the cadmium
separated was + O'l 6 volt with regard to the electrolyte.
Metallic cadmium placed in the solution also gave O'l 6
volt. In many solutions the electrode exhibited the
potential difference due to the separating metal before
the decomposition point of the solution was reached.
For instance, in , silver nitrate the electrode had the
value of pure silver in silver nitrate even below the
decomposition point (0*70). This is due to the great
tendency of the silver ions to separate as electrically
neutral metal.
It could also be demonstrated that the material of
the indifferent electrodes is without influence upon the
magnitude of these potential differences. The results
were the same whether gold, platinum, carbon, or any
other metal more negative than that in solution was
used. From this it is evident that the electrode itself
possesses no " specific attraction " for the electricity,
as formerly imagined.
The process of precipitation and solution of the
metals is, therefore, to be considered irreversible. It
may be represented as follows. If an indifferent
1 Zeitschr. physik. Chem. xii. 333, 1893.
vii POLARISATION 251
electrode be placed in the solution of a metallic salt, a
very small quantity of the ions must leave the ionic
state and be deposited upon the electrode as metal ;
for if the electrode contained absolutely none of the
metal of the salt solution, the potential difference
between electrode and electrolyte would be infinitely
great, in accordance with the formula, which is also
applicable to. polarisation phenomena,
RT , P
TT = In .
n e^Q P
If P = 0, TT must be infinite, but TT must always have
a finite value (otherwise an infinite amount of work
could be done) ; therefore it must be assumed that upon
the electrode, and also in the solution, there are
always traces of the metal. The metal must, therefore,
separate upon the electrode until the tendency of the
ions to precipitate is exactly compensated by the
electrostatic attraction due to the electrode becoming
thus positively and the solution negatively charged.
The amount precipitated is, therefore, dependent upon
the tendency of the ions to change into the metallic
state. Previously only the tendency of the metals
to go into the ionic condition has been mentioned ;
evidently a tendency of the ions to form neutral sub-
stance, or to separate out as metal must likewise exist.
A certain potential difference must, therefore, exist
at the electrode, there being some metal upon it and
. the corresponding ions in the solution. The magnitude
of this potential difference need not be, and almost
never is, the same as found when the massive metal is
in contact with the solution, for the metal deposited
upon the electrode does not reach the concentration of
the massive metal. This conclusion seems strange at
252 ELECTROCHEMISTRY CHAP.
first, for it is customary to consider the concentration
of a metal as unalterable. This is only the case above
a definite limit. If the metal is not present in a
molecular layer, it does not act as the massive metal.
This has been shown by Oberbeck. 1 When the metal
of a salt solution was precipitated upon a platinum
plate the latter exhibited in the corresponding metal
solutions the potential difference characteristic of the
massive metal as soon as a certain amount had been
deposited. Below this point the electrode exhibited
smaller potential differences corresponding to the lower
concentration. This fact need not be surprising when
it is recalled that gases and dissolving substances have
solution pressures dependent upon their concentration.
If the source of an electromotive force be connected
with the electrode, the electrostatic attraction is counter-
acted and more ions can separate as metal. The con-
centration of the metal upon the electrode is thereby
increased, and consequently also its solution pressure
(P), which tends to prevent a further deposition
of the metal, and soon entirely prevents it. To
deposit more metal it is necessary to insert a still
greater potential difference. This continues until the
maximum concentration of the metal is reached that
is, until the electrode acts as the massive metal. A
continual deposition may then take place without
further increase of the applied electromotive force, the
osmotic pressure of the ions (p) remaining unaltered.
When strong currents are used p does not remain
constant, but gradually diminishes, and consequently
the potential difference at the electrode increases.
It must be observed that the separation of the
positive ions at one electrode as neutral substance is
1 Wied. Ann. xxxi. 336, 1887.
vii POLARISATION 253
necessarily accompanied by the simultaneous deposi-
tion of the corresponding amount of negative ions at
the other. Considerations analogous to the above
evidently apply to the negative electrode. If, for
example, oxygen is set free, the concentration of
the gas gradually increases, and, when the solution
is saturated, has its greatest value, and consequently
its maximum solution pressure (which opposes the
further decomposition of the electrolyte). If more
separates, it escapes into the air. It will now be
understood why a certain electromotive force is
necessary to induce continuous decomposition in an
electrolyte : this only occurs when the concentrations
of the two substances separating at the electrodes
have reached their maximum values. It is also
evident that the electrodes upon which metals are
deposited should exhibit the potential characteristic of
the massive metal when the decomposition point is
reached. But it is evidently unnecessary that these
maxima of concentration for both electrodes should be
reached simultaneously: it may sometimes be reached
before the decomposition point of the solution can be
attained, as is the case with a silver solution, for
example. The decomposition point of normal silver
nitrate is 0'70 volt, but the potential difference at the
electrode upon which silver is deposited is of the same
magnitude as that between massive silver and the
solution long before this decomposition value is reached.
The polarisation due to metal ions having been
considered, attention will now be directed to the
phenomena presented when gaseous or dissolved sub-
stances are separated. These are somewhat more
complicated, and have greatly increased the difficulty
of comprehension of polarisation in general. As a
254 ELECTROCHEMISTRY CHAP.
simple case, the cell : platinised platinum in hydrogen
an electrolyte as sulphuric acid solution platinised
platinum in oxygen, both gases being under atmo-
spheric pressure, will be considered. The cell at 17
has an electromotive force of about 1'07 volt, and is
to be considered reversible. If an opposing electro-
motive force of 1'07 volt be connected with this cell,
a condition of equilibrium exists ; when a lower
electromotive force is applied, water is produced by the
oxygen and hydrogen of the cell, and when the electro-
motive force of the opposing current is greater than
1*07 volt, water is decomposed. Smale 1 calculated
the temperature coefficient of this cell from the
Helmholtz formula, using the known heat of formation
of water under constant pressure (68300 cal. at 17)
and the measured electromotive force as data :
m d7T
96540 x 1'07 -
41500
96540 x 290 dT
g-- 0-00148.
/ Q O A A
Q is - , since the heat effect corresponding to one
equivalent of the substance is employed. Experi-
mental determinations gave as a mean value between
and 68 0'00141, which is a satisfactory agreement
with the calculated value.
1 Zeitschr. physik. Chem. xiv. 577, 1894. On account of an error in
the original calculations, the value above given differs slightly from
that in the article referred to.
vii POLARISATION 255
It may now be predicted that if the hydrogen and
oxygen, instead of being at atmospheric pressure, be at
a lower pressure, the electromotive force of the cell
will be lower. In fact, if the pressures of the gases be
reduced almost to zero, the electromotive force will
nearly disappear. Under such a condition water may
evidently be decomposed by currents of minimum
electromotive force, it being only necessary to apply
one which exceeds that of the cell itself by a very
small amount, from which it is clear that the electrical
energy obtainable through the formation of water from
oxygen and hydrogen, or necessary for its decomposi-
tion (the two being equal and of opposite sign), may
assume any magnitude from zero to a certain value
dependent on the pressures of the gases or their
concentrations. The heats of formation at constant
pressure, on the other hand, are independent of the
pressure, and this is the most direct evidence that a
simple relation cannot exist between the heat of reaction
and the electrical energy obtained. It is certainly
possible in this case to calculate the amount of one of
these forms of energy from a knowledge of the other
when the changes of the temperature coefficient due to
pressure changes are known.
That water may thus be decomposed by minimum
quantities of electrical energy seems at first a contra-
diction of the law of the conservation of energy. This
is, however, in no wise the case. The law referred to
declares that by the reversible changes of a system
from one condition to another, the same amount of
work must always be done, and this condition exists
in the present case. The decomposition of water into
hydrogen and oxygen at atmospheric pressure may be
accomplished, on the one hand, by the application of
256 ELECTROCHEMISTRY CHAP.
electrical energy alone. A gas cell such as described,
the gases being under atmospheric pressure, may be
used, an opposing electromotive force just exceeding
that of the cell being connected with it. Electrical
energy alone then causes the decomposition of the
water into hydrogen and oxygen at atmospheric press-
ure. This same result may, however, be brought
about in another way. For instance, a hydrogen-
oxygen cell in which the pressure of the gases is
one-tenth atmosphere may be employed. The electro-
motive force of this cell being lower than the
previous one, less electrical energy is required to pro-
duce the hydrogen and oxygen at the reduced pressure.
But the work which corresponds to the difference
between the two quantities of electrical energy em-
ployed must exactly suffice to compress the gases pro-
duced at one-tenth atmosphere to the pressure of one
atmosphere, and thus the total work in the two cases,
although done in different ways, has remained the same.
When platinised electrodes are used, the formation
and decomposition of the water are reversible. At
atmospheric pressure water may be decomposed by an
electromotive force of 1'07 volt. If the electrodes
are not platinised, the electrolysis does not take place
until the electromotive force is I'^O volt. This is
that maximum for decomposition found for the acids
and bases, hydrogen and oxygen being the products.
It was long considered surprising that the decomposi-
tion point in the latter case was so high, notwithstanding
the fact that only the partial pressure of the atmo-
sphere is exerted upon each of the gases. Furthermore,
the fact that the decomposition point was dependent
upon the nature of the indifferent electrode appeared
curious.
vii POLARISATION 257
These results can now be understood. In the
first place, when electrodes such as ordinary plati-
num or gold 1 are employed, the process is no
longer a reversible one. These electrodes have too
feeble absorbing power to remove the gases as rapidly
as formed. With the platinised electrodes there is
equilibrium between the gas dissolved in the solution,
that dissolved in or taken up by the electrode, and
the volume of gas surrounding the electrode. If the
applied electromotive force be great enough to over-
come that of the gas cell, gas separates at the
electrodes, and thereby its concentration in the solution
as well as in the electrode is increased. The former
condition of equilibrium is soon reproduced, for the
electrode yields its excess of gas to the space about it,
which is considered so great that no change in the
concentration is produced, and in this manner also
prevents supersaturation of the liquid. The gas
formed by continued decomposition of the electrolyte
is thus added to the gas volume at constant concentra-
tion, arid the generation can therefore always result
from the same electro motive force.
The conditions are entirely different where the
electrodes are gold or unplatinised platinum. These
have practically no absorbent action on the gases, and
1 If carbon be used as electrode, the kind plays an important
part. Carbon is capable of taking up gases to a considerable extent,
and this property increases its value as positive electrode of a galvanic
element. In the Leclanche element, for example, hydrogen is evolved
at the carbon pole, and this causes it to pass quickly from the liquid
to the air, thus reducing the polarisation at this electrode. For long-
continued activity of the cell the carbon is often incapable of removing
the hydrogen, and polarisation is the result. If the action of the cell
be stopped for a time, the hydrogen dissolved in the liquid has an
opportunity to escape, and the element, becoming thus depolarised,
exhibits its original electromotive force. It recovers.
S
258 ELECTROCHEMISTRY CHAP.
there is thus no medium to bring about equilibrium
between the solutions of the gases as formed in the
cell and the gases in the space about the electrodes.
Proceeding on this assumption, the result of a gradually
increasing electromotive force opposing such a gas cell
would be exactly as observed. Beginning with a low
electromotive force, a scarcely perceptible decomposi-
tion of water would take place, the concentrations of
the hydrogen and oxygen in the water being at first
inconsiderable. At each subsequent increase of the
applied electromotive force so much water at the most
may be decomposed that the concentration of the gases
in solution at the electrodes is made exactly that which
would produce an equivalent electromotive force with
platinised electrodes. A higher concentration of the
gases can evidently not be produced, otherwise per-
petual motion would be possible. This explains the
temporary current observed in the galvanometer.
Diffusion alone causes disturbances, the gases being
thereby very slowly removed from the electrodes and
the concentration reduced so that further decom-
position takes place. The galvanometer corroborates
this, since, after the first deflection, the needle does
not return quite to its former position, and thus
a slight current is indicated. Gradually increasing
the electromotive force, the concentration of the
separated gases continually increases, until finally
a point is reached where gas bubbles are formed.
That such an evolution of gas only occurs when
the electromotive force is relatively high is ex-
plicable on the assumption that the application
of considerable work is necessary for the produc-
tion of the bubbles. When this point has been
reached, water may be decomposed without further
vii POLARISATION 259
increase in the concentration of the solutions of the
gases at the electrodes. The gases are continually
evolved as bubbles, and the so-called decomposition
point is observed, that is, that point above which water
may be continually decomposed without the aid of
diffusion. The less the diffusion of separated substance
from the immediate neighbourhood of the electrode,
the more marked is the decomposition point, and
indeed often (in the case of metals) the galvanometer
exhibits a clearly defined sudden rise in the strength
of the current.
It has been seen that the decomposition point is
reached when the separated gases are first evolved.
This evolution takes place through the formation of
bubbles at the electrodes. The process may be
likened to the boiling of a liquid, and just as the
ebullition does not occur at a perfectly definite tem-
perature, but may be retarded in different ways, so
also the evoluion of gases as bubbles in the electrolysis
is to be considered within certain limits as accidental.
Some electrodes, through their physical properties,
favour this evolution more than others, and thus the
decomposition point is dependent upon the nature of
the electrode.
Primary Decomposition of Water. The electro-
motive force of the hydrogen -oxygen gas cell is de-
pendent upon the concentrations of the gases, but
nearly independent of the nature of the electrolyte.
This may almost equally well be acid or base. The
electromotive force is the sum of the potential differ-
ences produced at the hydrogen and oxygen electrodes.
That of the former is dependent upon the concentration
of the hydrogen ions, that of the latter upon the con-
centration of the hydroxyl ions. According to the law
260 ELECTROCHEMISTRY CHAP.
of mass action, the product of the concentrations of the
hydrogen and hydroxyl ions is always constant without
regard to other substances present ; therefore, although
the values of the single potential differences may vary
considerably on changing the homogeneous solvent,
their sum always remains the same (p. 230).
Leaving out of account metal salt solutions reducible
by hydrogen, and chlorides, bromides, iodides, etc.,
reducible by oxygen, the ions of water alone take part
in the decomposition, instead of those of the dissolved
electrolyte, so that with the limitations given the law
may be expressed : In electrolysis a primary decomposi-
tion of the water takes place. The actual electrical
conductivity is brought about by all the ions in the
solution, but at the electrode that action takes place
which proceeds most easily, and this is the separation
of the hydrogen and hydroxyl ions. When, for ex-
ample, a solution of potassium sulphate is being
electrolysed, and the current is not too strong, there is
no reason for assuming the separation of potassium and
the S0 4 radical at the electrodes, and the subsequent
or secondary action of these upon the water. This
assumption, though usually made, seems to the author
to introduce an unnecessary complication. What is
actually observed is the separation of hydrogen and
oxygen ; furthermore, it has been seen that the forma-
tion and decomposition of water is a reversible process,
or that in the decomposition there is no unnecessary
loss of work. With the assumption of secondary
decomposition such a loss should occur.
Lack of hydrogen and hydroxyl ions can never
occur, since ions must be immediately generated by the
undissociated water, the product of the two ion con-
centrations always having a definite value. After
vii POLARISATION 261
these remarks the results obtained for the polarisation
when unplatinised electrodes are used may be under-
stood. The substance in presence of which the water
is decomposed will be first considered.
Acids and bases must have the same decomposition
point, because the product of the concentrations of the
hydrogen and hydroxyl ions in the solution, and conse-
quently the sum of the single potential differences,
remains constant. In the electrolysis of salts this
point must be higher, because at that electrode where
hydrogen separates, a base is produced. The accumu-
lation of the OH ions causes the concentration of the
H ions to be reduced ; therefore the potential differ-
ence is increased. Similar considerations apply to the
oxygen electrode, acid being formed, and the concentra-
tion of the hydroxyl ions thereby reduced.
The weaker the tendency to dissociate characterising
the acid or base, the less will be the rise of the
decomposition point, as is actually observed. Since
that ion leaves the solution which requires the lowest
electromotive force for its separation, other ions than
hydrogen and hydroxyl come into account only when
the electromotive force requisite for their continued
separation is less than for these two ions. This ex-
plains the fact that the decomposition points of the
halogen acids, which do not yield oxygen, are lower
than for acids through whose electrolysis oxygen is
evolved. Furthermore, although the decomposition
point of those acids and bases yielding hydrogen and
oxygen is not dependent on the concentration, because
the product of the H and OH ions is constant, with
halogen acids it rises as the concentration diminishes,
owing to simultaneous diminution in the number of
hydrogen and halogen ions. In consequence, the
262 ELECTROCHEMISTRY CHAP.
number of the hydroxyl ions is continually increased,
and with increasing dilution the point is finally
reached where oxygen is more easily evolved than
halogen. At this point the solution exhibits the
decomposition point of water, as is illustrated by
hydrochloric acid (p. 249).
The Significance of the Electromotive Force for
Electrolytic Separations. As already shown, different
decomposition points characterise the various metals,
and from this fact it ought to be possible to quantita-
tively precipitate metals one after another from their
mixed solutions by a gradual increase in the electro-
motive force of the decomposing current. That this
may be done has been shown by Freudenberg. 1
If in a solution containing salts of copper and
cadmium a current be employed whose electromotive
force is insufficient for the continual deposition of the
cadmium, but capable of precipitating the copper, this
metal alone is completely precipitated. When all the
1 Zeitschr. physilc. Chem. xii. 97, 1893. About ten years ago M.
Kiliani called attention to the possibility of electrolytic separations by
a gradation of the electromotive force, and carried out the separation
of silver and copper. He came upon the idea in considering the heat
effects characterising individual metals, and calculated from them the
electrical energy necessary for their precipitation. This method of
calculation has been shown to be inapplicable, for which reason, and
perhaps more especially because of the general uncertainty regarding
polarisation conditions introduced, his work did not receive much
attention. That when the electromotive force is above a certain value
a metal may be continually precipitated from its solution, while below
this point only an analytically negligible or absolutely unweighable
amount precipitates, was not at that time clear. The opinion was then
much more commonly held that even with low electromotive forces
not inconsiderable quantities of the metal were precipitated, accord-
ing to which view the separation of two metals by a proper regulation
of the electromotive force appears as an accident rather than a necessary
result of recognised relations.
vii POLARISATION 263
copper is precipitated the current ceases, it being thus
unnecessary to pay attention to the electrolysis. The
electromotive force necessary for the precipitation of
the copper increases with the dilution of the solution,
according to the formula,
RT. P
TT = In ;
n e Q p
but since an increase in dilution from T ^ to 1OO ^ OOO
normal (the limit of analytical determinations) causes
an increase of less than 0'3 volt for a monovalent and
half as much for a divalent metal, the separation may
usually be made complete.
After the precipitation of the copper the electro-
motive force may be increased and the cadmium pre-
cipitated. In this way a number of separations have
become possible which had not succeeded when atten-
tion was given to changing the current-strength instead
of the electromotive force. In the future this must be
kept in mind in all processes of electrolysis.
Besides the neutral or acid solutions, those of the
double compounds of the metal salt with ammonium
oxalate or potassium cyanide are especially adapted to
such separations. In the latter many metals can be
separated from one another which cannot in acid solution.
Thus in acid solution platinum cannot be separated
from gold, mercury, and silver, i.e. from the metals
with slightly different solution pressures, but is easily
separated in potassium cyanide solution. This depends
upon the formation of the complex salt 2K, Pt(Cy) 6 n ,
whose negative ions are dissociated to an extremely
slight extent into Pt IV and 6Cy. As a result of
the infinitely low concentration of the ions, the plati-
num cannot be precipitated by the electromotive force
264 ELECTROCHEMISTRY CHAP.
sufficient to precipitate the other metals whose ions
are more numerous (see also p. 175).
Previously, in the quantitative separation of the
metals, only the current-strength was altered. In a
mixture of zinc, copper, and silver salts in acid solu-
tion the silver must separate first, since that process
occurs requiring the least expenditure of work, which
is also the case even though the electromotive force be
very high, provided that sufficient silver ions are
present at the electrode. The current must be stopped
at the proper moment, otherwise the second most easily
separated metal will be precipitated. After silver and
copper, hydrogen follows. To precipitate zinc simul-
taneously with the latter from an acid solution the
current -strength must be made so great that the
hydrogen ions present are insufficient to convey all the
electricity from solution to electrode, and zinc ions must
take part in the process. It is evidently more rational
to regulate the electromotive force instead of the
current-strength, and thus do away with the energy
loss involved. Until within the last few years most
electrolytic separations were carried out empirically
without knowledge of these theoretical principles.
Synthesis of Organic Substances. A word may
be said in closing concerning the electrolysis of organic
compounds, especially of the acids. A well-known
example of such an electrolysis is seen in the decom-
position of acetic acid into hydrogen, on the one hand,
and ethane and carbon dioxide, on the other.
2CH 3 COO, 2H = C 2 H 6 + 2C0 2 + H 2 .
The method is now much used for the production of
certain compounds. Crum- Brown and Walker 1 ob-
1 Lieb. Ann. 261, 107, 1891 ; 274, 41, 1893.
vii POLARISATION 265
taiued as principal product of the electrolysis of the
ethyl potassium salt of normal dibasic acids the diethyl
ester of the normal acid of the same homologous series :
.2C H 6 C0 2 (CH 2 ) a .COO =
C 2 H 5 C0 2 (CH 2 ) 2;c e0 2 C 2 H 5 + 2C0 2 .
These syntheses usually take place in concentrated
solutions only, and at high current-strength. In dilute
solutions with not too great current -strength only
hydrogen and oxygen are evolved. This is explicable
from the following consideration : At the anode (to
which the anions migrate) there are OH and acid ions.
As the decomposition point for the OH ions is the
lower, oxygen is evolved, new OH ions are formed
from the water, but this process is not infinitely rapid ;
therefore, if the current be too great, insufficient OH
ions are produced and the acid ions partially take their
place. Increasing the concentration of the solution
has the same effect as increasing the current-strength.
The osmotic pressure of the acid ions being increased
with increasing concentration, their change into the
neutral condition is facilitated. The potassium salt is
chosen instead of the free acid because of its greater
Conductivity.
Conceptions of Water Decomposition. It may
be here repeated that the assumption often made, in
accordance with which those ions primarily separated
at the electrodes axe brought there in the conductivity,
and that these act secondarily upon the water or other
material present, does not appear to the author to
accord with the facts. That the conductivity of the
current through the solution and the decomposition
at the electrodes do not at all stand in that close
relation usually accredited to them is shown by simple
266 ELECTROCHEMISTRY CHAP.
consideration of the fact that in the electrolysis of any
electrolyte at either electrode more ions leave the
solution than migrate to the electrode through it (p.
68). Thus in every case a part of the ions originally
at the electrode must be precipitated without having
migrated through the solution.
The following conception is much to be preferred :
Conductivity and separation at the electrode are not
closely connected phenomena. All ions in the solution
share in the electrical conductivity, while at the
electrode those ions leave the solution which demand
for their separation the least consumption of work.
Therefore it happens, for example, that the ions of
water which scarcely take a measurable part in the
actual conductivity play the most important role in
the separation at the electrodes. The assumption of
secondary reactions is usually entirely unnecessary.
The following example well illustrates the simplicity
of the new conception as compared with the old.
Suppose a fairly concentrated aqueous solution of salts
of potassium, cadmium, copper, and silver to be electro-
lysed between platinum electrodes through application
of a not too strong current. The ions K, Cd 11 , H, Cii 11 ,
and Ag simultaneously come to the negative electrode.
The experimental result is that only metallic silver is
deposited at first. After some time, the number of
silver ions at the electrode being no longer sufficient
for the current density, copper also precipitates, then
hydrogen, and finally cadmium. Is not the simplest
conceivable expression of the results of the experiment
contained in the following sentence ? Those ions which
give up their electrical charges most easily are first
precipitated through primary action, each other metal
remaining until those preceding it in the series are
vii POLARISATION 267
removed. The process as thus explained becomes
simple and clear.
What of the other explanation ? This necessitates
the simultaneous precipitation of the cadmium, copper,
potassium, and silver. The potassium can now act
upon the water producing hydrogen, precipitate copper
from the copper salts, cadmium from the cadmium
salts, and silver from the silver salts. (It cannot be
assumed that a silver particle is always in the im-
mediate neighbourhood of the potassium, but the latter
would precipitate whatever metal presented itself.) The
deposited cadmium can precipitate hydrogen from the
water, copper from the copper salts, and silver from the
silver salts ; the hydrogen can precipitate copper from
the copper and silver from the silver salts, and, finally,
the copper must precipitate the silver from the silver
salt. This conception of the process cannot be called
simple, and why the assumption of all these secondary
reactions which no one has observed, and which are in
no sense necessary !
CHAPTER VIII
THE ORDINARY GALVANIC ELEMENTS AND ACCUMULATORS
THE chemical processes taking place in galvanic
elements may now be briefly considered. It will be
assumed that the remarks in the chapters on electro-
motive force and polarisation, especially the influence
of dilution (p. 230), are understood.
Constant Elements. --Besides the Daniell, the
Helmholtz, Clark, and Weston elements are used as
so-called normal elements (p. 128). These are:
Helmholtz: Zinc zinc 'MilpliifcU, mercurous chloride,
mercury.
Clark : Zinc zinc sulphate, mercurous sulphate,
mercury.
Weston : Cadmium cadmium sulphate, mercurous
sulphate, mercury.
They have the advantage over the Daniell element
of remaining unaltered for an indefinite time, and may
be transported without incurring changes affecting the
electromotive force, while the Daniell is preferably
made shortly before use, because of the disturbing
effects due to the diffusion of the solutions into each
other. In these normal elements amalgams containing
about 1 per cent of the metals, zinc or cadmium, may
advantageously be used instead of the pure metal.
CH. vin GALVANIC ELEMENTS AND ACCUMULATORS 269
An H tube, into which two platinum wires are fused
below (Fig. 33), is advantageously used. The amalgam
is placed in one limb and mercury
in the other. Some solid mercurous
sulphate or chloride is placed upon
the mercury, and the tube, being filled
with the zinc or cadmium sulphate
solution, is closed with corks covered
with paraffin.
The chemical reaction taking place
when these elements are active con-
sists in the passage of the positive F
zinc (or cadmium) ions into the
solution and the deposition of ions as metal from the
solid mercurous salt at the other electrode. These
elements differ from the Daniell in that they can
only produce very feeble currents. On account of
the difficult solubility of the mercurous salts used, the
quantity of mercurous ions is very small, and the
replacement of these ions by the dissolving of more
mercurous salt takes place but slowly. On this
account the electromotive force of the element rapidly
diminishes when too much is required of it. The
simultaneous supersaturation of the positive ions at
the negative electrode also tends to reduce the electro-
motive force. If the element be allowed to stand, the
original condition is again attained, or the element
recovers.
In the Clark or the Weston ' element, where the
zinc or cadmium solution as well as that of the mer-
curous salt is saturated, the conditions before and after,
normal activity differ in that the quantity of amalgam
is slightly smaller, while the solid zinc or cadmium
sulphate is slightly greater, the mercurous sulphate
270 ELECTROCHEMISTRY CHAP.
being diminished in amount and the quantity of pure
mercury somewhat augmented. Practically, then, the
zinc or cadmium ions entering the solution receive an
equivalent amount of S0 4 n ions through the solution
of the solid mercury salt, and solid zinc or cadmium
salt is found. The zinc or cadmium and the mercury
ions remain unaltered in concentration so long as
amalgam and solid mercurous salt are present ; there-
fore the cells are strictly constant. The same applies
to the Daniell element when saturated solutions in
contact with the solid salts are used. In the Helm-
holtz cell, on the contrary, the zinc chloride solution
7 increases in concentration when used, and thereby a
change, though practically an inconsiderable one, takes
place in its electromotive force.
The changes of electromotive force with the
temperature must finally be considered. The com-
position of the solutions remaining unaltered, the tem-
perature coefficient of an element is practically the
sum of the coefficients of the potential differences at
the two electrodes. In these elements, where saturated
solutions containing also an excess of the solid salt are
employed, the change of the solubility of the salt with
the temperature plays an important part. The rela-
tively high temperature coefficient of the Clark element
is principally due to the fact that with rising tempera-
ture the solubility of the zinc sulphate greatly
increases, that is, the concentration of the zinc ions
becomes greater. The solubility of cadmium sulphate
is only slightly influenced by the temperature, and the
temperature coefficient of the Weston element is nearly
zero.
Inconstant Elements. In the elements just de-
scribed the constancy of the electromotive force only
vni GALVANIC ELEMENTS AND ACCUMULATORS 271
was of importance, the height of this and the cheap-
ness of the materials being of very secondary import-
ance. With the elements necessary for the ordinary
electrical work in the laboratory these relations are
nearly reversed. High electromotive force combined
with economical processes is here more important than
great constancy. The number of different kinds of
galvanic elements in use is very great; three of them
may be profitably studied here.
Formerly the cell containing zinc, ammonium
chloride solution, bleaching powder solution, carbon,
was much used. The ammonium or sodium chloride
solution is separated from that of the bleaching powder
by a porous earthenware cell.
Through the action of this element, zinc ions come
into existence at the negative electrode and chlorine
at the positive. The bleaching powder supplies the
chlorine ions and the carbon acts as conductor. The
electromotive force is at first very considerable, because
the concentration of zinc ions in the chloride solution
is extremely small, while the solution pressure of the
chlorine in the bleaching powder is great. When the
element is being used the concentration of the zinc, as
well as of the chlorine ions, increases, and both changes
reduce the electromotive force. The solution pressure
of the chlorine remains constant so long as any of the
solid bleaching powder remains.
If the porous cell and the bleaching powder of this
element be removed, and the carbon be replaced by a
mixture of carbon and manganese dioxide, the much-
used Leclanch^ element results. Distinction must
here be made between the action of the dioxide and of
the carbon ; for the present the former will be left out
of account. If the element be closed, zinc goes into
272 ELECTROCHEMISTRY CHAP.
solution, and hydrogen ions, being more easily deposited
than the NH 4 ions, which participate in the conduct-
ivity, separate at the carbon electrode. Carbon has a
considerable solvent action upon gases, and rapidly
conducts the separating hydrogen into the air, thus
preventing the accumulation of hydrogen dissolved in
the water. An accumulation of the gas at the elec-
trode, by rendering difficult the separation of more
hydrogen ions, would cause a reduction of the electro-
motive force. This, in fact, occurs when the element
is allowed to Work too rapidly, the ability of the carbon
to remove the hydrogen being overtaxed. If the
element be allowed to stand inactive a short time it
recovers.
The manganese dioxide aids the carbon, as is evident
from the following considerations. Since every sub-
stance has a certain solubility, such must be ascribed
to the dioxide, and Mn lv , together with the correspond-
ing OH ions, may be considered present in the solution.
The quadrivalent manganese ions tend to give positive
electricity to the electrode and become bivalent.
Therefore, while zinc ions are formed at the negative,
the corresponding amount of manganese ions change
their valency from four to two, and manganous chloride
is formed at the positive electrode, the Mn lv ions being
replaced from the solid Mn0 2 . Which of the processes
described predominates in the element depends upon
the composition of the mixture of carbon and di-
oxide. By long-continued use the electromotive force
diminishes, principally because of the accumulation of
zinc ions. This may be remedied by renewing the
ammonium chloride solution.
Another frequently used element having a high
electromotive force is the so-called bichromate
vni GALVANIC ELEMENTS AND ACCUMULATORS 273
element, containing zinc chromic acid (or sodium
bichromate with sulphuric acid) carbon. Zinc
ions are formed at the negative pole as usual, but
the reaction taking place at the other electrode is
more complicated. It may be assumed that the ions
Cr 2 7 n are present, the chromium being sexivalent. As
in the case of the compound H 2 PtCl 6 it was assumed
that the negative ions PtCl 6 " were slightly dissociated
into the quadrivalent platinum and univalent chlorine
ions (p. 175), so also here the Cr 2 7 n ions may yield
a minimum quantity of sexivalent chromium and the
corresponding quantity of univalent OH ions. The
chromium ions of high valency tend to change into
ions of lower valency, probably trivalent, and the high
electromotive force, with the exception of the potential
difference at the zinc electrode, depends upon this
change. The number of zinc as well as trivalent
chromium ions increases with the time, while the con-
centration of the sexivalent chromium ions decreases,
and each of the three changes should cause a reduction
of the electromotive force. The electromotive force of
the active bichromate element does actually diminish
rapidly.
ACCUMULATOES
Accumulators are arrangements in which electrical
may be stored as chemical energy, and whence it may
again be obtained at wish in the form of electrical
energy. Any reversible cell may be used as an
accumulator. If a current be sent through a used
Daniell element in the direction from copper to zinc,
copper is dissolved and zinc precipitated in other words,
electrical energy is stored up in the form of chemical.
In practice lead accumulators are used almost exclu-
T
274 ELECTROCHEMISTRY CHAP.
sively. 1 The electrodes consist of lead plates coated
with a specially prepared layer of lead oxide or sulphate,
and the electrolyte is 20 per cent sulphuric acid.
When a current is sent through this arrangement, lead
superoxide (or a corresponding hydrate) is formed on
that electrode at which the positive electricity enters
the acid, while at the other electrode metallic lead in
spongy form is produced. The accumulator is thus
charged after the conduction of sufficient electricity
through it. In the discharge both the superoxide and
the metallic lead return to sulphate. The chemical
process on charging is then essentially the change of
lead sulphate to lead at one electrode, and to superoxide
at the other, while the discharge is simply the return
of these substances to lead sulphate. The correspond-
ing heat of reaction is given by Streintz 2 as follows :
Pb0 2 + 2H 2 S0 4 aq + Pb = 2PbS0 4 + aq + 87000 cal,
If the electromotive force of the accumulator be
calculated from the known heat of reaction, assuming
complete transformation into electrical energy, 1*885
volt is obtained. This agrees very well with the
experimentally determined value for dilute sulphuric
acid of 1*900 volt. From this agreement it also
follows that the electromotive force of the accumulator
is nearly independent of the temperature (p. 142), and
this has also been demonstrated by Streintz. It is
therefore very probable that the reaction takes place
as represented above.
The process as yet has not been explained on the
1 For particulars concerning the making and use of accumulators
attention is called to the work of Heim, Die Accumulatoren, Leipzig,
Oskar Leiner, and that of Elbs, Die Accumulatoren, Leipzig, Johann
Ambrosius Barth.
2 Wien. Akad. Ber. 103, Jan. 1894.
viii GALVANIC ELEMENTS AND ACCUMULATORS 275
basis of the ion theory ; the following is an attempt in
this direction.
The accumulator being charged and ready for use,
the positive electrode is coated with superoxide of lead
and the negative with the spongy metal ; between the
two is sulphuric acid. It was lately pointed out that
in the Leclanche element the manganese dioxide in
contact with the water produces quadrivalent manganese
and the corresponding OH ions. Analogously quadri-
valent Pb IV ions must be formed at the positive elec-
trode of the accumulator, and just as the quadrivalent
manganese ions in the Leclanche element are changed
to bivalent, so here the quadrivalent lead ions also
change into bivalent. This process is the principal
source of the electromotive force of the accumulator. The
quadrivalent lead ions disappearing are continually
supplied by the solid superoxide. The bivalent lead
ions formed, instead of remaining in the solution,
combine with the S0 4 n ions to form solid lead
sulphate, since this is difficultly soluble, that is, the
value of the concentration product of Pb n and S0 4 n
ions is small.
At the negative pole metallic lead changes into
bivalent ions, a process taking place without producing
any considerable potential difference. Here also in-
soluble lead sulphate is formed from the Pb 11 and
S0 4 n ions.
Moreover, the ion theory not only renders clear the
changes of superoxide and metallic lead into sulphate,
but explains the gradual diminution of the electro-
motive force of the accumulator in action. The
magnitude of the potential at the positive electrode
depends upon the concentration of the quadrivalent
and bivalent lead ions in the presence of excess of
276 ELECTROCHEMISTRY CHAP.
metallic lead. The concentration of the quadrivalent
ions decreases with time, and that of the bivalent
increases, as may be seen from the following. At the
superoxide electrode there is a saturated solution of
this compound that is, the product of the concentra-
tion of Pb IV and the fourth power l of the concentra-
tion of the OH ions is a constant. On the other hand,
there must be definite relations between these concen-
trations and those of the sulphuric acid ions. The
product of the concentration of the H and OH ions in
the solution must have a constant value equal to that
of water. It has been seen, in the first place, that
during the discharge of the accumulator, lead sulphate
is formed at the superoxide electrode, and in the
second, that newly formed OH ions produced by the
superoxide cannot exist as such, but must combine with
the H ions of the acid to form water. There is thus
a continual removal of H and S0 4 n ions taking place.
The removal of the former allows of an increase in the
concentration of the OH ions, and therefore causes a
reduction in that of the quadrivalent lead ions. The
removal of S0 4 n ions allows of an increase in the con-
centration of the Pb " ions, since the solution is
saturated with lead sulphate. This latter process also
takes place at the negative electrode. When the
supply of superoxide is exhausted, the electromotive
force falls very rapidly to an exceedingly low value.
After the accumulator has been discharged there
is lead sulphate on both electrodes, consequently
bivalent lead ions are present. The process of
charging consists simply in the change of bivalent lead
ions to quadrivalent at that electrode at which the
positive electricity enters the solution, and to metallic
1 Because four OH ions correspond to one of the lead ions.
viii GALVANIC ELEMENTS AND ACCUMULATORS 277
lead at the other electrode. The Pb " ions used are
replaced from the solid lead sulphate. The Pb lv ions
and the OH ions present, having reached that concen-
tration in the solution determined by the dissociation
constant for superoxide of lead, combine to form this
oxide (or a hydrate). Thus the lead sulphate at one
electrode gradually changes into superoxide, and into
metallic lead at the other. The opposing electromotive
force of the accumulator increases during the charging,
because the processes described as taking place during
discharge are reversed. The concentration of the
bivalent lead ions at both electrodes diminishes with
time, while that of the SOJ 1 ions is continually in-
creasing. The concentration of the Pb IV ions increases
with the increase of H ions formed with equivalent
quantities of OH ions from the undissociated water.
The OH ions continually combine with the Pb IV to
form superoxide, and their concentration must diminish
as that of the hydrogen ions increases. The lower the
concentration of the OH ions the greater is that of the
Pb IV ions. If no more bivalent lead ions are present,
the hydrogen ions separate at one electrode and
hydroxyl ions at the other. Thus the rapid generation
of hydrogen and oxygen at the electrodes in charging
shows that the accumulator is overcharged. In order
to cause a considerable generation of hydrogen and
oxygen in the accumulator, a somewhat higher electro-
motive force is required than is necessary to charge it,
since the separating gases can accumulate to a high
degree of concentration, owing to the existing conditions;
otherwise the charging of the accumulator could only
be brought about with a great loss of electrical energy.
SUBJECT INDEX
ABNORMAL freezing-point reduc-
tions, 59
Absolute electromotive series, 229
velocity of ions, 120
Accumulators, 273
Acid-alkali cell, 189
Acids, decomposition points of, 248
Activity coefficient, 58
Additivity of conductivity, 83
Affinity coefficient, 58, 87
Alloys, E.M.P. due to, 159
Amalgams as electrodes, 156, 234
Ampere, 9
Anions, 42
Anode, 42
Arrangement of batteries, 26, 27
Arrhenius theory, 52
Atmospheric electricity, 30
BASES, decomposition points of,
248
Basicity of acids from conductivity,
107
Batteries, see Elements
Becquerel element, 189
Bichromate element, 240, 273
Bleaching powder element, 271
CADMIUM element, 129, 268
Calculation of E.M.F., 196, 197
of potential difference, 153
Calomel element, 128, 182
Calorie, 3
Capacity, electrical, 18
Capillary electrometer, 127, 212
Carbon electrodes, 257
Cathions, 42
Cathode, 42
Cells, see Elements
Charges of ions, 60
Chemical activity versus dissocia-
tion, 87
cells, 205
constitution and dissociation con-
stants, 102
effect of electrical current, 33
versus electrical energy, 49, 131
Chromic acid element, 273
Clark element, 129, 268
Clausius theory, 48
Coefficient of activity, 59
Concentration and liquid cells, 198
cells, 156, 167
changes at electrodes, 68
changes in cells, 230
double cells, 182
Conditions for electric current, 240
Conductivity and basicity, 107
at infinite dilution, 97
changes with temperature, 111,
113
equivalent, 82
in solutions, 65, 83
method of measurement, 91
molecular, 81
of fused salts, 119
of isomers, 103
of mixed solutions, 115
of water, 109
Conductors, classes of, 32
Constant elements, 268
of resistance capacity, 96
Corresponding solutions, 115
Coulomb, 11
Current- strength defined, 8
determination of, 10
280
ELECTROCHEMISTRY
DANIELL element, 49, 205
Decomposition of water, 256, 265
point of acids, 248, 261
point of solutions, 259
values of E.M.F., 246
Degree of dissociation, 117
Depolariser, 257
Determination of degree of dissocia-
tion, 87, 88
of single potential differences,
210, 217
Dielectric constants, 117
Dielectrics, 117
Direction of electric current, 21,
221
Dissociating power of solvents, 117,
Dissociation constants, 88, 90
constants versus chemical con-
stitution, 102
constants versus activity, 118
degree of, 87, 117
in solution, 57
of water, 109, 180
theory, 52
Doppelschicht, 148
Double layer, 148
Drop electrodes, 215
Dyne, 2
ELECTRIC charges of ions, 60
current, direction of, 6, 21
current, properties of, 6
derivation of word, 28
Electrical capacity, 19
decomposition of water, 259
energy measured, 144
equivalent of heat, 17
units, 9
versus chemical energy, 131
Electricitas spontanea, 29
Electricity, atmospheric, 30
frictional, 28
Electrochemical theory of Berzelius,
39
theory of Davy, 38
Electrode, 42
Electrodes of second order, 174
Electrolysis, 42, 43
Electrolyte, 42
Electrolytic process, 43
separations, 262
solution pressure, 145, 228
Electrolytic solution tension, 145
Electrometer, 23, 212
Electrometric measurements, 22
Electromotive force, 8, 124
force, calculation of, 196
force, determination of, 10
force of alloys, 159
force of cell, 219, 221
force of polarisation, 244
force versus potential difference,
11
series, 32, 201
series, absolute, 229
Elements, common, 205, 270
normal, 128, 268
Empirical rules of migration, 106
Energy, forms of, 1
laws of, 132
units, 2
Entropy, 141
Equivalent conductivity, 79, 82
Erg, 2, 18
Expansion of gas, work of, 135
External resistance, 15
FACTORS of electrical energy, 6
of volume energy, 5
Fall of potential, 13, 16
Farad, 19
Faraday's law, 40, 62
First law of energetics, 132
Frictional electricity, 29
Frog's legs experiment, 30
Fused salts, conductivity of, 119
GALVANIC element, 6
Galvani's experiments, 29
Gas cell, 254
cell's electromotive force, 165
electrodes, 163
equation, 53
laws applied to electrolytes, 89
Gold leaf electrometer, 33
Graphic representation of potential
fall, 223-225
Grotthus theory, 43
HEAT generated in element, 145
of dissociation, 114
of ionisation, 232
of reaction versus electrical
energy, 142
SUBJECT INDEX
281
Helmholtz normal element, 128,
268
Henry's law, 152
Hydrogen cell, 179
Hydrogen-oxygen cell, 254
INACCURACY of E.M.F. calculations,
200
Inconstant elements, 270
Influence of composition on velocity
of ions, 105
Intensity factor, 5
of current, 8
Internal pressure of liquids, 54
resistance, 15
International ohm, 129
lonisation heat, 232
Ions, 42, 45, 60
Irreversible cells, 129
Isohydric solutions, 115
Isohydrism, 116
JOULE, 18
Joule's law, 18
KOHLRAUSCH law, 82, 85
LECLANCH element, 271
Legal ohm, 129
Lippmann's electrometer, 127, 212
Liquid cells, 189
MASS, 2
Maximum of conductivity, 82
Measurement, electrometric, 22
Measurements of electromotive
force, 125
Mechanical energy units, 2
equivalent of electricity, 17
equivalent of heat, 3
Mercury concentration cells, 159,
162
dropping electrode, 216
unit of resistance, 80
Method of measuring polarisation,
244
Migration of ions, 62, 69, 70, 75,
86, 104
Molecular conductivity, 79, 81
NEGATIVE potential differences, 209
Normal electrode, 218
elements, 128, 268
OHM, 9, 80
international, 129
legal, 129
Ohm's law, 9
Ordinary galvanic elements, 271
Organic synthesis, 264
Osmotic pressure, 53, 54
Oxidation and reduction cells, 235,
238
Oxidising agents, 234
PILE, voltaic, 33
Platinised versus plain electrodes,
164, 257
Polarisation, 243
current, 244
measurement of, 244
of mercury, 210
Positive and negative electricity,
19
potential difference, 209
Potential difference between metals,
131, 204, 234
difference, calculation of, 153
difference, solid versus liquid
metal, 242
difference, source of, 148
fall illustrated, 223
versus electromotive force, 11
Precipitation of metals, 262
Primary decomposition of water,
259
Process in accumulators, 270
Production of electricity, 21
QUANTITY of electricity, 42
RATES of migration of ions, 66
Reaction, acid and base, 117
Reactive power of electrolytes, 117
Reducing agent, 239
Reduction and oxidation, 235, 238
Relation, chemical versus electrical
energy, 131
dissociation constant and chemi-
cal constitution, 102
Resinous electricity, 29
Resistance, 7
box, 125
capacity, 94
capacity, measurement of, 10
Reversible cells, 129
282
ELECTROCHEMISTRY
SEAT of potential difference, 155
Secondary reactions in electrolysis,
260
Second law of energetics, 40, 132
order electrodes, 174
Separation of metals, 263
Shares of transport, 71, 74
Siemens unit, 80
Silver chloride electrode, 172
concentration cells, 178
Single potential differences, 210
Solubility determination from
E.M.F., 172, 176
determination from conductivity,
123
Solution of gold, platinum, etc.,
241
pressure, 145, 228
Source of electrical energy, 206
of potential difference, 155
Specific conductivity, 79
resistance, 80
Storage batteries, see Accumu-
lators
Strength of acids and bases, 87
Structure of ions and their velocity,
106-
Supersaturated solutions, 111
Surface tension and polarisation of
mercury, 210
Synthesis of organic compounds,
264
TEMPEKATURE coefficient of con-
ductivity, 111
Thales' experiments, 28
Theory of polarisation, 251
Thermochemical data, 232
Thermoelements, 201
Transference numbers, see Shares of
transport
Transformation of energy, 4, 5,
133
UNITS of electricity, 9
of energy, 2, 3
of mass, 2
of mechanical energy, 2
VELOCITY of migration of ions, 86,
104, 106
Vitreous electricity, 29
Volt, 9
Voltaic pile, 33
Volta's theory, 31
Volume energy, 4, 5
WATER, conductivity of, 109
decomposition of, 205
dissociation of, 109
Watt, 18
Weight, 2
Weston element, 129, 268
LIST OF AUTHOKS' NAMES
ABBOT, see Noyes
Arrhenius, 49, 52, 59, 87
BANCROFT, 237
Becquerel, 189
Berzelius, 39
Braun, 50
Bredig, 104, 108
Budde, 120
CARLISLE, see Nicholson
Clausius, 47, 132
Crum-Brown and Walker, 264
DANIELL, 44
Davy, 36
Des Coudres, 152, 162
Dufay, 29
ERMANN, 34
FARADAY, 40
Franklin, 29
Freudenberg, 262
GALVANI, 29
Gibbs, 50
Gilbert, 28
Goodwin, 184
Graetz, 120
Grotthus, 43
HELMHOLTZ, 50, 143, 215
Henry, 152
Hisinger, 38
Hittorf, 45, 63
Hoff, van't, 52
Hollemann, 123
JAHN, 143
Joule, 18
KILIANI, 262
Kohlrausch, 45, 77, 82, 86, 110,
120, 123
Konig, 215
LE BLANC, 164, 247, 250
Lippraann, 127, 210
; Lodge, 122
Loeb, see Nernst
MEYER, 157
Moser, 171
NERNST, 117, 132, 170, 179, 190,
202
and Loeb, 72
Neumann, 225
Nicholson and Carlisle, 34
Noyes and Abbot, 107
OBERBECK, 252
Ostwald, 88, 98, 125, 178, 215,
233, 239
PPEFFER, 54
Planck, 57
Poggendorf, 125
Poincare, 119
RAOULT, 56
Ritter, 32
Rose, 123
Rqthmund, 253
284
SCHILLER, 152
Smale, 254
Streintz, 274
THALES, 28
ELECTROCHEMISTRY
VOLTA, 31
WALKER, see Crura-Browii
Warburg, 210
Whetham, 122
Wilke, 29
THE END
Printed by R. & R. CLARK, LIMITED, Edinburgh
r -
-p
uu
P
CO &
H -P
3 O
O CD
01
3 CM
H O
H
C^ r ^ CO
o> HS -P
H H
0)
a
University of Toronto
Library
DO NOT
REMOVE
THE
CARD
FROM
THIS
POCKET
Acme Library Card Pocket
Under Pat. "Rel. Index File"
Made by LIBRARY BUREAU
