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dissociation of strong solutions, and may be treated by means of the new theory of Jahn and Nernst (p. 79).

If the osmotic pressure of strong solutions were known, it might be used to calculate the electromotive force; but in the present state of our knowledge it is better to reverse the process. This was done by Lehfeldt (loc. cit.), who from electromotive force measurements on ZnCl2 and ZnSO, calculated the osmotic pressure of those salts, and was able to show that it follows a course analogous to that of the gaseous pressure for gases at high densities (i.e. concentrations).

In conclusion, we may summarise the deviation from the simple laws of dilute solutions as follows :-

(a) For great dilution (say millinormal and under) the solutions of electrolytes may be regarded as completely ionised, and as giving osmotic pressure (with change of freezing and boiling-point) and electromotive force in accordance with the simple laws of gases; and the conductivity calculated on the same assumptions together with the rule that the mobility of the ions is independent of their concentration.

(b) For somewhat greater concentrations the degree of ionisation must not be regarded as complete, but must be calculated by the law of mass action in the form of Ostwald's rule, otherwise the laws of dilute solutions still hold.

(c) For the next stage of concentration (deci- to centi-normal in the case of KCl, HCl, etc.), the law of mass action must be applied in the more complex form indicated by the new theory of Jahn and Nernst; hence the logarithmic rule for electromotive force must be given up (as regards strong electrolytes); further, it is probable that the mobility of ions is sensibly affected by concentration, in which case the conductivity is no longer an exact measure of degree of ionisation. The osmotic pressure, however, probably still follows the laws of gases approximately.

(d) Finally, for strong solutions even the last statement no longer holds. The osmotic pressure may still be calculated from the electromotive force, but there is no safe guide to the degree of ionisation.

(vi) CHEMICAL CELLS.

Under the term "chemical cells" may be included all the practical voltaic combinations whose action depends on conversion of the energy of chemical combination-chiefly of solution of metals in acid. Such have, however, already been considered in their general aspect, and will be dealt with individually in succeeding chapters. In the present section the cells treated will be, rather, combinations of theoretical interest in which electromotive force serves as a measure of chemical affinity.

For this purpose the cells may be conveniently classified according to the character of the reaction taking place in them. This may be (a) a transition" in a system of more than one phase, or (b) a reversible reaction in a homogeneous system; and in either case the reaction may be (i.) between the materials of the electrolyte only, or (ii.) may involve the electrodes.

Transition Cells. Of these, which have been studied particularly by van't Hoff and Cohen, we may take the Clark as an example. The reaction in the Clark cell is

Zn+Hg2SO1 = 2Hg + ZnSO

The cell is saturated with zinc sulphate, and the salt occurs in the form ZnSO4.7HO. This hydrate when heated to 39° suffers the transition 1

ZnSO,.7H.OZnSO,.6H2O + H2O

At 39°, then, the two hydrates are equally stable, and can exist in each other's presence indefinitely. If two Clark cells are made, one with heptahydrate, the other with hexahydrate crystals, and kept at 39°, they will possess the same electromotive force; but this is only true at 39°; below that temperature the ordinary cell (with heptahydrate) has a greater E.M.F. than the other, so that if the two be coupled up in series it will drive current through the hexahydrate cell; more heptahydrate will be formed and some hexahydrate will be decomposed by this current, so that indirectly the above transition

1 For transitions in general, see Findlay, Phase Rule, p. 34, in this series.

will be brought about, and the more stable form will gain at the expense of the less. Above 39° the relative stabilities are reversed, and so, too, the electromotive force: the hexahydrate cell becomes the stronger. These facts were brought out by the experiments of Callendar and Barnes,1 shown in Fig. 41, though their explanation on physico-chemical grounds was given subsequently by Jaeger.2 The cell with heptahydrate could be measured up to a temperature of a few degrees above the transition point, but thereafter became uncertain in E.M.F.,

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as the transition takes place of its own accord; the hexahydrate cell was measured down to the freezing-point, for although the hydrate is instable below 39°, it only changes with extreme slowness, on account of the low temperature. It will be noticed that the two curves cross at 39°, and that the larger E.M.F. is shown by the salt that is the more stable, whether below or above that temperature.

Other patterns of cells in which a transition occurs have

1 Proc. Roy. Soc., 62. 117 (1897).

2 Wied. Ann., 63. 354 (1897).

been enumerated by van't Hoff1 and Cohen.2

Amongst these
Thus Cohen

are cases of transition in the electrode material. discovered that ordinary, metallic, white tin undergoes a transition into a grey variety, and is in fact unstable at atmospheric temperature, although the transition, which is always very slow, may be suspended for apparently any length of time. If, then,

a cell be made up with electrodes, one of white, the other of grey tin, it ought to show an electromotive force in such a direction that the resulting current will convert the less into the more stable phase. Accordingly a cell of the type

White tin: solution of SnCl, : grey tin

was set up and found to give a small electromotive force (a few millivolts) in the direction of the arrow at 5°, diminishing steadily to nothing at 20°; the latter temperature is the transition point, and below it, white tin dissolves in the cell and grey is deposited, showing the latter to be the more stable.

Another case is the transition of cadmium amalgam, which affects the behaviour of standard cadmium cells, and is considered below, p. 248.

The theory of chemical transitions has been given by van't Hoff3 in the following way. At the transition temperature the two phases are in equilibrium (like water and ice at o°); neither has any tendency to conversion into the other: the free energy of the two is identical-for the difference in free energy between two systems measures the tendency towards conversion of the one into the other. There is, however, a change in total energy—the latent heat of transition (analogous to latent heat of fusion)—and this is always in such a sense that to convert the phase which is stable at low temperature into the other requires heat to be imparted to it. In the general equation (p. 179) we have

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2 Ibid., 14. 53; 25. 300; 30. 623; 31. 164; 33. 57; 34. 62, 612, 621.

3 Lectures on Theoretical Chemistry, vol. i. p. 181.

E.M.F.

i.e. the temperature coefficient of the electromotive force is proportional to the latent heat. These relations are shown graphically in Fig. 42. The abscissæ represent temperature T being the transition point; ordinates represent electromotive force in the transition cell; this is, of course,

zero at T, and the

rate of change of it

FIG. 42.

T

Temp

is given by the slant line. This line is practically straight near the transition point, for the latent heat is found to be almost independent of temperature, so that for points near

L

together in temperature FT is constant. We see, then, from the figure that the electromotive force of a transition cell is (for a moderate range of temperature) proportional to the diverg ence of the temperature from the transition point: if above the transition point, the E.M.F. is in one sense; if below, in the other. But electromotive force, here as elsewhere, is only one measure of the change in free energy. The rule may therefore be stated in a more general form : the work that can be done (electrically or otherwise) by a transition is zero at the transition temperature, and increases in proportion as the temperature is raised or lowered from that point.

The latent heat of transition of ZnSO4.7 HO into ZnSO4.6HO is about 12,000 joules per equivalent. Hence the temperature coefficient in the transition cell is

L

=

I 2000

FT 96600 X (273 +39)

=0'0003 volts per degree

Cell with Reaction in a Homogeneous System. In the foregoing cases the chemical system yields work (and therefore electromotive force) because it is removed in temperature from the condition of equilibrium; but if it is made up of

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