Through liquid metals, such as mercury at ordinary temperatures and
other metals at temperatures above their melting points, the electric
current flows as in solid metals without changing the state of the
conductor, except in so far as heat is developed by the electric
resistance. But another class of liquid conductors exists, and in them
the phenomena are quite different. The conductivity of fused salts, and
of solutions of salts and acids, although less than that of metals, is
very great compared with the traces of conductivity found in so-called
non-conductors. In fused salts and conducting solutions the passage of
the current is always accompanied by definite chemical changes; the
substance of the conductor or electrolyte is decomposed, and the
products of the decomposition appear at the electrodes, i.e. the
metallic plates by means of which the current is led into and out of the
solution. The chemical phenomena are considered in the article
ELECTROLYSIS; we are here concerned solely with the mechanism of this
_electrolytic_ conduction of the current.
To explain the appearance of the products of decomposition at the
electrodes only, while the intervening solution is unaltered, we suppose
that, under the action of the electric forces, the opposite parts of the
electrolyte move in opposite directions through the liquid. These
opposite parts, named ions by Faraday, must therefore be associated with
electric charges, and it is the convective movement of the opposite
streams of ions carrying their charges with them that, on this view,
constitutes the electric current.
In metallic conduction it is found that the current is proportional to
the applied electromotive force--a relation known by the name of Ohm's
law. If we place in a circuit with a small electromotive force an
electrolytic cell consisting of two platinum electrodes and a solution,
the initial current soon dies away, and we shall find that a certain
minimum electromotive force must be applied to the circuit before any
considerable permanent current passes. The chemical changes which are
initiated on the surfaces of the electrodes set up a reverse
electromotive force of polarization, and, until this is overcome, only a
minute current, probably due to the slow but steady removal of the
products of decomposition from the electrodes by a process of diffusion,
will pass through the cell. Thus it is evident that, considering the
electrolytic cell as a whole, the passage of the current through it
cannot conform to Ohm's law. But the polarization is due to chemical
changes, which are confined to the surfaces of the electrodes; and it is
necessary to inquire whether, if the polarization at the electrodes be
eliminated, the passage of the current through the bulk of the solution
itself is proportional to the electromotive force actually applied to
that solution. Rough experiment shows that the current is proportional
to the excess of the electromotive force over a constant value, and thus
verifies the law approximately, the constant electromotive force to be
overcome being a measure of the polarization. A more satisfactory
examination of the question was made by F. Kohlrausch in the years 1873
to 1876. Ohm's law states that the current C is proportional to the
electromotive force E, or C = kR, where k is a constant called the
conductivity of the circuit. The equation may also be written as C =
E/R, where R is a constant, the reciprocal of k, known as the resistance
of the circuit. The essence of the law is the proportionality between C
and E, which means that the ratio E/C is a constant. But E/C = R, and
thus the law may be tested by examining the constancy of the measured
resistance of a conductor when different currents are passing through
it. In this way Ohm's law has been confirmed in the case of metallic
conduction to a very high degree of accuracy. A similar principle was
applied by Kohlrausch to the case of electrolytes, and he was the first
to show that an electrolyte possesses a definite resistance which has a
constant value when measured with different currents and by different
experimental methods.
_Measurement of the Resistance of Electrolytes._--There are two effects
of the passage of an electric current which prevent the possibility of
measuring electrolytic resistance by the ordinary methods with the
direct currents which are used in the case of metals. The products of
the chemical decomposition of the electrolyte appear at the electrodes
and set up the opposing electromotive force of polarization, and unequal
dilution of the solution may occur in the neighbourhood of the two
electrodes. The chemical and electrolytic aspects of these phenomena are
treated in the article ELECTROLYSIS, but from our present point of view
also it is evident that they are again of fundamental importance. The
polarization at the surface of the electrodes will set up an opposing
electromotive force, and the unequal dilution of the solution will turn
the electrolyte into a concentration cell and produce a subsidiary
electromotive force either in the same direction as that applied or in
the reverse according as the anode or the cathode solution becomes the
more dilute. Both effects thus involve internal electromotive forces,
and prevent the application of Ohm's law to the electrolytic cell as a
whole. But the existence of a definite measurable resistance as a
characteristic property of the system depends on the conformity of the
system to Ohm's law, and it is therefore necessary to eliminate both
these effects before attempting to measure the resistance.
The usual and most satisfactory method of measuring the resistance of
electrolytes consists in eliminating the effects of polarization by the
use of alternating currents, that is, currents that are reversed in
direction many times a second.[11] The chemical action produced by the
first current is thus reversed by the second current in the opposite
direction, and the polarization caused by the first current on the
surface of the electrodes is destroyed before it rises to an appreciable
value. The polarization is also diminished in another way. The
electromotive force of polarization is due to the deposition of films of
the products of chemical decomposition on the surface of the electrodes,
and only reaches its full value when a continuous film is formed. If the
current be stopped before such a film is completed, the reverse
electromotive force is less than its full value. A given current flowing
for a given time deposits a definite amount of substance on the
electrodes, and therefore the amount per unit area is inversely
proportional to the area of the electrodes--to the area of contact, that
is, between the electrode and the liquid. Thus, by increasing the area
of the electrodes, the polarization due to a given current is decreased.
Now the area of free surface of a platinum plate can be increased
enormously by coating the plate with platinum black, which is metallic
platinum in a spongy state, and with such a plate as electrode the
effects of polarization are diminished to a very marked extent. The
coating is effected by passing an electric current first one way and
then the other between two platinum plates immersed in a 3% solution of
platinum chloride to which a trace of lead acetate is sometimes added.
The platinized plates thus obtained are quite satisfactory for the
investigation of strong solutions. They have the power, however, of
absorbing a certain amount of salt from the solutions and of giving it
up again when water or more dilute solution is placed in contact with
them. The measurement of very dilute solutions is thus made difficult,
but, if the plates be heated to redness after being platinized, a grey
surface is obtained which possesses sufficient area for use with dilute
solutions and yet does not absorb an appreciable quantity of salt.
Any convenient source of alternating current may be used. The currents
from the secondary circuit of a small induction coil are satisfactory,
or the currents of an alternating electric light supply may be
transformed down to an electromotive force of one or two volts. With
such currents it is necessary to consider the effects of self-induction
in the circuit and of electrostatic capacity. In balancing the
resistance of the electrolyte, resistance coils may be used in which
self-induction and the capacity are reduced to a minimum by winding the
wire of the coil backwards and forwards in alternate layers.
[Illustration: FIG. 1.]
With these arrangements the usual method of measuring resistance by
means of Wheatstone's bridge may be adapted to the case of electrolytes.
With alternating currents, however, it is impossible to use a
galvanometer in the usual way. The galvanometer was therefore replaced
by Kohlrausch by a telephone, which gives a sound when an alternating
current passes through it. The most common plan of the apparatus is
shown diagrammatically in fig. 1. The electrolytic cell and a resistance
box form two arms of the bridge, and the sliding contact is moved along
the metre wire which forms the other two arms till no sound is heard in
the telephone. The resistance of the electrolyte is to that of the box
as that of the right-hand end of the wire is to that of the left-hand
end. A more accurate method of using alternating currents, and one more
pleasant to use, gets rid of the telephone (_Phil. Trans._, 1900, 194,
p. 321). The current from one or two voltaic cells is led to an ebonite
drum turned by a motor or a hand-wheel and cord. On the drum are fixed
brass strips with wire brushes touching them in such a manner that the
current from the brushes is reversed several times in each revolution of
the drum. The wires from the brushes are connected with the Wheatstone's
bridge. A moving coil galvanometer is used as indicator, its connexions
being reversed in time with those of the battery by a slightly narrower
set of brass strips fixed on the other end of the ebonite commutator.
Thus any residual current through the galvanometer is direct and not
alternating. The high moment of inertia of the coil makes the period of
swing slow compared with the period of alternation of the current, and
the slight periodic disturbances are thus prevented from affecting the
galvanometer. When the measured resistance is not altered by increasing
the speed of the commutator or changing the ratio of the arms of the
bridge, the disturbing effects may be considered to be eliminated.
[Illustration: FIG. 2.]
[Illustration: FIG. 3.]
The form of vessel chosen to contain the electrolyte depends on the
order of resistance to be measured. For dilute solutions the shape of
cell shown in fig. 2 will be found convenient, while for more
concentrated solutions, that indicated in fig. 3 is suitable. The
absolute resistances of certain solutions have been determined by
Kohlrausch by comparison with mercury, and, by using one of these
solutions in any cell, the constant of that cell may be found once for
all. From the observed resistance of any given solution in the cell the
resistance of a centimetre cube--the so-called specific resistance--may
be calculated. The reciprocal of this, or the conductivity, is a more
generally useful constant; it is conveniently expressed in terms of a
unit equal to the reciprocal of an ohm. Thus Kohlrausch found that a
solution of potassium chloride, containing one-tenth of a gram
equivalent (7.46 grams) per litre, has at 18 deg. C. a specific
resistance of 89.37 ohms per centimetre cube, or a conductivity of 1.119
X 10^-2 mhos or 1.119 X 10^-11 C.G.S. units. As the temperature
variation of conductivity is large, usually about 2% per degree, it is
necessary to place the resistance cell in a paraffin or water bath, and
to observe its temperature with some accuracy.
Another way of eliminating the effects of polarization and of dilution
has been used by W. Stroud and J. B. Henderson (_Phil. Mag._, 1897 [5],
43, p. 19). Two of the arms of a Wheatstone's bridge are composed of
narrow tubes filled with the solution, the tubes being of equal diameter
but of different length. The other two arms are made of coils of wire of
equal resistance, and metallic resistance is added to the shorter tube
till the bridge is balanced. Direct currents of somewhat high
electromotive force are used to work the bridge. Equal currents then
flow through the two tubes; the effects of polarization and dilution
must be the same in each, and the resistance added to the shorter tube
must be equal to the resistance of a column of liquid the length of
which is equal to the difference in length of the two tubes.
A somewhat different principle was adopted by E. Bouty in 1884. If a
current be passed through two resistances in series by means of an
applied electromotive force, the electric potential falls from one end
of the resistances to the other, and, if we apply Ohm's law to each
resistance in succession, we see that, since for each of them E = CR,
and C the current is the same through both, E the electromotive force or
fall of potential between the ends of each resistance must be
proportional to the resistance between them. Thus by measuring the
potential difference between the ends of the two resistances
successively, we may compare their resistances. If, on the other hand,
we can measure the potential difference in some known units, and
similarly measure the current flowing, we can determine the resistance
of a single electrolyte. The details of the apparatus may vary, but its
principle is illustrated in the following description. A narrow glass
tube is fixed horizontally into side openings in two glass vessels, and
an electric current passed through it by means of platinum electrodes
and a battery of considerable electromotive force. In this way a steady
fall of electric potential is set up along the length of the tube. To
measure the potential difference between the ends of the tube, tapping
electrodes are constructed, e.g. by placing zinc rods in vessels with
zinc sulphate solution and connecting these vessels (by means of thin
siphon tubes also filled with solution) with the vessels at the ends of
the long tube which contains the electrolyte to be examined. Whatever be
the contact potential difference between zinc and its solution, it is
the same at both ends, and thus the potential difference between the
zinc rods is equal to that between the liquid at the two ends of the
tube. This potential difference may be measured without passing any
appreciable current through the tapping electrodes, and thus the
resistance of the liquid deduced.
_Equivalent Conductivity of Solutions._--As is the case in the other
properties of solutions, the phenomena are much more simple when the
concentration is small than when it is great, and a study of dilute
solutions is therefore the best way of getting an insight into the
essential principles of the subject. The foundation of our knowledge was
laid by Kohlrausch when he had developed the method of measuring
electrolyte resistance described above. He expressed his results in
terms of "equivalent conductivity," that is, the conductivity (k) of the
solution divided by the number (m) of gram-equivalents of electrolyte
per litre. He finds that, as the concentration diminishes, the value of
k/m approaches a limit, and eventually becomes constant, that is to say,
at great dilution the conductivity is proportional to the concentration.
Kohlrausch first prepared very pure water by repeated distillation and
found that its resistance continually increased as the process of
purification proceeded. The conductivity of the water, and of the slight
impurities which must always remain, was subtracted from that of the
solution made with it, and the result, divided by m, gave the equivalent
conductivity of the substance dissolved. This procedure appears
justifiable, for as long as conductivity is proportional to
concentration it is evident that each part of the dissolved matter
produces its own independent effect, so that the total conductivity is
the sum of the conductivities of the parts; when this ceases to hold,
the concentration of the solution has in general become so great that
the conductivity of the solvent may be neglected. The general result of
these experiments can be represented graphically by plotting k/m as
ordinates and [root 3]m as abscissae, [root 3]m being a number
proportional to the reciprocal of the average distance between the
molecules, to which it seems likely that the molecular conductivity may
be related. The general types of curve for a simple neutral salt like
potassium or sodium chloride and for a caustic alkali or acid are shown
in fig. 4. The curve for the neutral salt comes to a limiting value;
that for the acid attains a maximum at a certain very small
concentration, and falls again when the dilution is carried farther. It
has usually been considered that this destruction of conductivity is due
to chemical action between the acid and the residual impurities in the
water. At such great dilution these impurities are present in quantities
comparable with the amount of acid which they convert into a less highly
conducting neutral salt. In the case of acids, then, the maximum must be
taken as the limiting value. The decrease in equivalent conductivity at
great dilution is, however, so constant that this explanation seems
insufficient. The true cause of the phenomenon may perhaps be connected
with the fact that the bodies in which it occurs, acids and alkalis,
contain the ions, hydrogen in the one case, hydroxyl in the other, which
are present in the solvent, water, and have, perhaps because of this
relation, velocities higher than those of any other ions. The values of
the molecular conductivities of all neutral salts are, at great
dilution, of the same order of magnitude, while those of acids at their
maxima are about three times as large. The influence of increasing
concentration is greater in the case of salts containing divalent ions,
and greatest of all in such cases as solutions of ammonia and acetic
acid, which are substances of very low conductivity.
[Illustration: FIG. 4.]
_Theory of Moving Ions._--Kohlrausch found that, when the polarization
at the electrodes was eliminated, the resistance of a solution was
constant however determined, and thus established Ohm's Law for
electrolytes. The law was confirmed in the case of strong currents by G.
F. Fitzgerald and F. T. Trouton (_B.A. Report_, 1886, p. 312). Now,
Ohm's Law implies that no work is done by the current in overcoming
reversible electromotive forces such as those of polarization. Thus the
molecular interchange of ions, which must occur in order that the
products may be able to work their way through the liquid and appear at
the electrodes, continues throughout the solution whether a current is
flowing or not. The influence of the current on the ions is merely
directive, and, when it flows, streams of electrified ions travel in
opposite directions, and, if the applied electromotive force is enough
to overcome the local polarization, give up their charges to the
electrodes. We may therefore represent the facts by considering the
process of electrolysis to be a kind of convection. Faraday's classical
experiments proved that when a current flows through an electrolyte the
quantity of substance liberated at each electrode is proportional to its
chemical equivalent weight, and to the total amount of electricity
passed. Accurate determinations have since shown that the mass of an ion
deposited by one electromagnetic unit of electricity, i.e. its
electro-chemical equivalent, is 1.036 X 10^-4 X its chemical equivalent
weight. Thus the amount of electricity associated with one
gram-equivalent of any ion is 10^4/1.036 = 9653 units. Each monovalent
ion must therefore be associated with a certain definite charge, which
we may take to be a natural unit of electricity; a divalent ion carries
two such units, and so on. A cation, i.e. an ion giving up its charge at
the cathode, as the electrode at which the current leaves the solution
is called, carries a positive charge of electricity; an anion,
travelling in the opposite direction, carries a negative charge. It will
now be seen that the quantity of electricity flowing per second, i.e.
the current through the solution, depends on (1) the number of the ions
concerned, (2) the charge on each ion, and (3) the velocity with which
the ions travel past each other. Now, the number of ions is given by the
concentration of the solution, for even if all the ions are not actively
engaged in carrying the current at the same instant, they must, on any
dynamical idea of chemical equilibrium, be all active in turn. The
charge on each, as we have seen, can be expressed in absolute units, and
therefore the velocity with which they move past each other can be
calculated. This was first done by Kohlrausch (_Gottingen Nachrichten_,
1876, p. 213, and _Das Leitvermogen der Elektrolyte_, Leipzig, 1898)
about 1879.
In order to develop Kohlrausch's theory, let us take, as an example,
the case of an aqueous solution of potassium chloride, of
concentration n gram-equivalents per cubic centimetre. There will then
be n gram-equivalents of potassium ions and the same number of
chlorine ions in this volume. Let us suppose that on each
gram-equivalent of potassium there reside +e units of electricity, and
on each gram-equivalent of chlorine ions -e units. If u denotes the
average velocity of the potassium ion, the positive charge carried per
second across unit area normal to the flow is n e u. Similarly, if v
be the average velocity of the chlorine ions, the negative charge
carried in the opposite direction is n e v. But positive electricity
moving in one direction is equivalent to negative electricity moving
in the other, so that, before changes in concentration sensibly
supervene, the total current, C, is ne(u + v). Now let us consider the
amounts of potassium and chlorine liberated at the electrodes by this
current. At the cathode, if the chlorine ions were at rest, the excess
of potassium ions would be simply those arriving in one second,
namely, nu. But since the chlorine ions move also, a further
separation occurs, and nv potassium ions are left without partners.
The total number of gram-equivalents liberated is therefore n(u + v).
By Faraday's law, the number of grams liberated is equal to the
product of the current and the electro-chemical equivalent of the ion;
the number of gram-equivalents therefore must be equal to [eta]C,
where [eta] denotes the electro-chemical equivalent of hydrogen in
C.G.S. units. Thus we get
n(u + v) = [eta]C = [eta]ne(u + v),
and it follows that the charge, e, on 1 gram-equivalent of each kind
of ion is equal to 1/[eta]. We know that Ohm's Law holds good for
electrolytes, so that the current C is also given by k.dP/dx, where k
denotes the conductivity of the solution, and dP/dx the potential
gradient, i.e. the change in potential per unit length along the lines
of current flow. Thus
n
-----(u + v) = kdP/dx;
[eta]
therefore
k dP
u + v = [eta] - --.
n dx
Now [eta] is 1.036 X 10^-4, and the concentration of a solution is
usually expressed in terms of the number, m, of gram-equivalents per
litre instead of per cubic centimetre. Therefore
k dP
u + v = 1.036 X 10^-1 - -- --.
m dx
When the potential gradient is one volt (10^8 C.G.S. units) per
centimetre this becomes
u + v = 1.036 X 10^-7 X k/m.
Thus by measuring the value of k/m, which is known as the equivalent
conductivity of the solution, we can find u + v, the velocity of the
ions relative to each other. For instance, the equivalent conductivity
of a solution of potassium chloride containing one-tenth of a
gram-equivalent per litre is 1119 X 10^-13 C.G.S. units at 18 deg. C.
Therefore
u + v = 1.036 X 10^7 X 1119 X 10^-13
= 1.159 X 10^-3 = 0.001159 cm. per sec.
In order to obtain the absolute velocities u and v, we must find some
other relation between them. Let us resolve u into 1/2(u + v) in one
direction, say to the right, and 1/2(u - v) to the left. Similarly v
can be resolved into 1/2(v+u) to the left and 1/2(v-u) to the right.
On pairing these velocities we have a combined movement of the ions to
the right, with a speed of 1/2(u - v) and a drift right and left, past
each other, each ion travelling with a speed of 1/2(u + v),
constituting the electrolytic separation. If u is greater than v, the
combined movement involves a concentration of salt at the cathode, and
a corresponding dilution at the anode, and _vice versa_. The rate at
which salt is electrolysed, and thus removed from the solution at each
electrode, is 1/2(u + v). Thus the total loss of salt at the cathode
is 1/2(u + v) - 1/2(u - v) or v, and at the anode, 1/2(v + u) - 1/2(v
- u), or u. Therefore, as is explained in the article ELECTROLYSIS, by
measuring the dilution of the liquid round the electrodes when a
current passed, W. Hittorf (_Pogg. Ann._, 1853-1859, 89, p. 177; 98,
p. 1; 103, p. 1; 106, pp. 337 and 513) was able to deduce the ratio of
the two velocities, for simple salts when no complex ions are present,
and many further experiments have been made on the subject (see _Das
Leitvermogen der Elektrolyte_).
By combining the results thus obtained with the sum of the velocities,
as determined from the conductivities, Kohlrausch calculated the
absolute velocities of different ions under stated conditions. Thus,
in the case of the solution of potassium chloride considered above,
Hittorf's experiments show us that the ratio of the velocity of the
anion to that of the cation in this solution is .51 : .49. The
absolute velocity of the potassium ion under unit potential gradient
is therefore 0.000567 cm. per sec., and that of the chlorine ion
0.000592 cm. per sec. Similar calculations can be made for solutions
of other concentrations, and of different substances.
Table IX. shows Kohlrausch's values for the ionic velocities of three
chlorides of alkali metals at 18 deg. C, calculated for a potential
gradient of 1 volt per cm.; the numbers are in terms of a unit equal to
10^-6 cm. per sec.:--