The application of the cage theory of liquids to the problem of ion mobilities

When applying the cage theory of liquids to ions in solution it appears that the cage is much smaller for ions than for the solvent molecules themselves. This suggests that the walls of the cage are to be identified with the so-called hydration layer. Further, the dimensions of the cage are such that classical and quantum mechanics apply equally well (or equally badly for that matter). An expression for the frequency of oscillation in the cage is proposed. On the basis of this expression it is possible to relate the ion mobility to its temperature coefficient. The agreement with experimental data is very satisfactory. The exceptionally high mobility of the hydrogen ions is easily explained by its dimensions compared with the dimensions of the smallest cage possible. Finally, it is shown that the effect of tunnelling through the walls of the cage is inappreciable.