Page:A history of the theories of aether and electricity. Whittacker E.T. (1910).pdf/405

ascribed to a blue copper cation. A striking instance of the same kind is afforded by ferric sulphocyanide; here the strong solution shows a deep red colour, due to the salt itself; but on dilution the colour disappears, the ions being colourless.

If it be granted that ions can have any kind of permanent existence in a salt solution, it may be shown from thermodynamical considerations that the degree of dissociation must increase as te dilution increases, and that at infinite dilution there must be complete dissociation. For the available energy of a dilute solution of volume V, containing n₁, gramme-molecules of one substance, n₂ gramme-molecules of another, and so on, is (as may be shown by an obvious extension of the reasoning already employed in connexion with concentration-cells)^[1]

$\sum _{r}n_{r}\phi _{r}(T)+RT\sum _{r}n_{r}\log(n_{r}/V)+{\text{ the available energy}}$

possessed by the solvent before the introduction of the solutes, where φ_r(T) depends on T and on the nature of the r^th solute, but not on V, and R denotes the constant which occurs in the equation of state of perfect gases. When the system is in equilibrium, the proportions of the reacting substances will be so adjusted that the available energy has a stationary value for small virtual alterations ∂n₁, ∂n₂, …… of the proportions; and therefore

$0=\sum _{r}\delta n_{r}.\phi _{r}(T)+RT\sum _{r}\delta n_{r}.\log(n_{r}/V)+RT\sum \delta n_{r}$.

Applying this to the case of an electrolyte in which the disappearance of one molecule of salt indicated by the suffix ₁) gives rise to one cation (indicated by the suffix ₂) and one anion (indicated by the suffix ₃), we have ∂n₁ = -∂n₂ = -∂n₃; so the equation becomes

$0=\phi _{1}(T)-\phi _{2}(T)-\phi _{3}(T)+RT\log(n_{1}V/n_{2}n_{3})-RT$,

or

$n_{1}V/n_{2}n_{3}={\text{ a function of }}T{\text{ only}}$.

1. Cf. pp. 382-383.

2 C