The dielectric capacity of electrolytes in mixed solvents: ion association in solutions of magnesium sulphate

Abstract

The remarkable achievements of Debye and Hückel, Onsager, and their colleagues in explaining and rationalizing the experimental data upon the behaviour of strong electrolytes in dilute solution have naturally led to much intensive research directed towards the extension of their theories to ranges of greater ionic concentration. From this work the theory of ion association, sponsored by Niels Bjerrum, has emerged with marked success. Assuming that the forces between oppositely charged ions obey the simple Coulomb law, Bjerrum has calculated the probability of such ions being within a distance, q 0 , at which the thermal energy per degree of freedom is but one-quarter of the electrostatic energy holding the ions together. Oppositely charged ions at less than this distance from one another are termed short-range pairs. The true degree of association (1— α *) of an electrolyte, as distinguished from the classical conception of undissociated molecules, is a measure of the number of short-range pairs, and Bjerrum has shown that the law of mass action may be applied to this association to develop a relation which reproduces the activities of electrolytes in more concentrated solution with remarkable fidelity. Onsager (1927) has calculated some approximate values of the true degree of association by consideration of the discrepancies between experimental conductivity data for aqueous solutions and the figures derived from his equation. Similar, and more extensive and more accurate measurements have been made by Davies (1927). In solvents of lower dielectric constant, the increased inter-ionic forces lead to still wider discrepancies, and many workers have shown that electrolytes which are almost completely non-associated in water are appreciably associated in solvents of reduced dielectric capacity. Martin (1928) has shown that the alkali metal halides are incompletely dissociated in benzonitrile and that the association obeys a generalized law of mass action. Fuoss and Kraus (1933 a ) have observed the same effects with the alkali metal nitrates dissolved in ammonia and other solvents of low dielectric constant. The mass-action constants derived from their results are in complete agreement with those predicted by the Bjerrum ion-association theory and, using measurements of the conductivity of tetra iso - amylammonium nitrate in dioxan-water mixtures, the same workers (1933 b ) have succeeded in extending the theory to include higher forms of association. Swift (1938) has confirmed the views of Fuoss and Kraus for ions of small radii by an investigation of the conductivities of solutions of the alkali metal halides in dimethylamine.