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conductivity; normal ZnSO4, 23 per cent.; but the latter of these numbers, at any rate, may be many per cent. different from the truth, on account of uncertainty in the reasoning by which it is arrived at. A solution of zinc sulphate normal with respect to the ions-i.e. containing 32.5 grams of Zn" per litre—is not obtainable, so that these numbers involve a certain imaginary extrapolation.

Taking the meaning of electro-affinity in accordance with current usage, however, the following table' contains the most important results :-

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The convention" as to sign adopted in the preceding table is as follows:

A cation electrode is called positive when it is positive to a normal solution of its ion (e.g. Ag, Cu). Such metals have a strong tendency to come out of the ionic form, or, in other words, are easily deposited electrolytically, and indeed can do work whilst so depositing. When a metal ion is deposited it conveys its positive charge to the electrode, and so makes that positive to the solution; so in a solution of copper sulphate

1

1 N. T. M. Wilsmore and W. Ostwald, Zeitschr. phys. Chem., 36. 92 (1901).

2 This is for an oxygen electrode in a solution normal with respect to the hydrogen ion.

3 The German writers disagree as to this unavoidable convention : see Lorenz, Elektrochemisches Prakticum, p. 169.

with copper electrodes, we may suppose that incipient electrolysis takes place, and the electrode gets charged electrostatically till its potential is about 0·606 volts above that of the solution; to charge it any further would require more work than the ions are capable of doing, and so the process ceases, unless the charge on the electrode is led away by some means; if this be done as, for example, in the Daniell cell, by a wire leading to the zinc-then more electrolysis occurs, and so on, indefinitely. On the other hand, if a metal has a strong tendency to form ions, it will do so to a certain extent, and leave the electrode depleted of positive electricity, i.e. negatively charged; this is the case with zinc, and still more with the alkali metals. Their electro-affinity is accordingly described as negative.

An anion electrode is called positive when it is positive. to a normal solution of its ion (e.g. Cl). Such a substance has a strong tendency to form ions, or, in other words, is hard to liberate by electrolysis, and work needs to be done on it in order to obtain it in the gaseous (or solid) form. But since such a substance carries a negative charge, its tendency to form ions leaves the electrode depleted of negative electricity, i.e. positively charged: hence the convention.

0493 and

If a cell (electrolytic or voltaic) be made of electrodes reversible with respect to any ions, its electromotive force (for normal concentration) is simply the algebraic difference between the electro-affinities of the two ions. Eg. the E.M.F. of the Daniell is, as we have already seen, the difference between 0'606, i.e. 1099 volts, the copper being the positive. It is a voltaic cell as ordinarily used; that is, current is allowed to flow out of it, from the copper through the external circuit to the zinc, so that the cell affords 1'099 volts to drive the current in this direction. If current be forced through it the opposite way it will be an electrolytic cell, with a back electromotive force of 1'099, i.e. work will have to be done to drive the current through. Again, if a zinc electrode be combined with a chlorine electrode, the voltage obtained is the difference between -0'493 and +1694, i.e. 2*187 volts; and, though this would not make a practically useful voltaic

cell, it shows what is the voltage required to decompose ZnCl2.

In the last instance, treated as a case of electrolysis, work is needed both to deprive the Zn" and the Cl' of their charges; hence the high total. If, on the other hand, CuCl, be electrolysed (between unalterable, e.g. platinum electrodes), while work represented by 1694 volts is needed to take the charge from the chlorine, no work is required to take that from the copper; on the contrary, the copper ion gives up its charge so readily as to help by work equivalent to o'606 volt. Hence there only needs to be supplied from outside 1.694 + 0'606 = 1'088.

To take an extreme case, in a solution of AgI the silver would have such a strong tendency to deposit, it would overpower that of the iodine to go into solution by o‘251 volt, and the solution would therefore break up spontaneously. This is, perhaps, an indication of the reason why AgI is a practically insoluble substance-although there are other factors in insolubility, for the above reasoning would not apply to salts like BaSO,.

If the rules given above as to sign be considered, it will be seen that in the case of a positive ion the work done by it on deposition is expressed by the electro-affinity; but in the case of a negative ion, the work done by it on deposition would be expressed by the electro-affinity with reversed sign in both cases the work is calculated for so much of the substance as corresponds to a coulomb, i.e. 600 gram-equivalent.

1

:

§ 4. INFLUENCE OF CONCENTRATION

We have now to find how these numbers are modified by a change in concentration of the solution. Here the analogy between a solution and a gas helps. It is well known that a gas when allowed to expand and consequently fall in pressure, is capable of doing work; and that conversely, to compress it, work must be done on it. The corresponding changes in the case of a solution are its dilution and concentration. It is true that when water is mixed with a strong solution in the ordinary

T. P. C.

M

water.

way, no work is gained; but work may be gained if the process of dilution be proceeded with in the right manner. To show this, suppose we have a vessel of salt solution and one of water side by side, at the same temperature: then, it is well known, the vapour pressure of the solution is less than that of the pure Provide the pair of vessels with a mechanism like that of a steam-engine, treating the water vessel as the boiler, the other as the condenser. Let some water evaporate under the piston in the cylinder; cut off; expand down to the vapour pressure of the solution; and condense the vapour on to the solution. In this series of processes work will have been done by the steam, and the result is to make the salt solution more dilute than it was to start with.1

It is of no consequence that the mechanism described is an almost impracticable one. The sole purpose of it is to help in finding out what the properties of solutions are; and we find that a strong solution is more capable of doing work than a dilute one. This is sometimes expressed by saying that the strong solution possesses a greater "free energy" than the other, and that the work which it is capable of doing on dilution represents the loss of free energy. We shall return to this aspect of the matter later. Its application to the question

at issue is as follows:

For a cation the electrode potential in a normal solution (electro-affinity) is the work that the ion can do on deposition. But if the solution is more concentrated it is capable of doing more work; therefore the electrode potential is higher, and increases with the concentration.

For an anion the electrode potential in a normal solution (electro-affinity) is the negative of the work that the ion can do on deposition. But if the solution is more concentrated it is capable of doing more work; therefore the electrode potential is lower, and decreases with increase of concentration.

If the solution be assumed to be completely dissociated, and to follow precisely the laws of gases, it is easy to calculate An alternative method of argument is to consider the osmotic pressure of the solution and the work it can do by means of a semi-permeable membrane.

the change of free energy on dilution.

This was done by

Nernst, who obtained the well-known and important logarithmic formula, which may be written—

where

Here

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E = electrode potential for ionic concentration C;

E electro-affinity;

=

C = concentration in gram-equivalents per litre of the ion given off by the electrode ;

R

=

the gas constant (8°32 joules per degree);

T = absolute temperature (= temp. Centigrade + 273) ; 1 = valency of the ion ;

F = one faraday (96600 coulombs).

is to be taken with a positive or negative sign according as the ion is positively or negatively charged; so that rF is the charge in coulombs associated with one "gram-ion" of the substance. With this convention the formula is equally applicable to cations and anions.

2 3026 is the factor required to convert common to natural logarithms.

If the temperature of the cell be 18° cent. (= 291 abs.)— an average atmospheric temperature, the equation becomes-

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Accordingly, a change of tenfold in the concentration would cause a change of o'058 volt in the electrode potential for a univalent ion, o‘029 for a divalent, or o‘0193 for a trivalent.

This result is probably strictly true for extremely dilute solutions, and has been satisfactorily verified in many cases. It is unfortunately less applicable to solutions of ordinary strength, as these-say from decinormal upwards-show very marked deviations from the laws of gases.

The meaning of the logarithmic formula may be conveniently illustrated by a diagram (Fig. 30) in which the electrode potential is represented by one axis, concentration

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