Application of irreversible thermodynamics to transport in self-complexing electrolytes

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Abstract
The study of transport in self-complexed aqueous electrolytes, particularly those of the metal halides, has been pursued since the middle of last century. In 1859 Hittorf observed negative transport numbers for cadmium in concentrated solutions of cadmium chloride and cadmium iodide and for zinc in concentrated solutions of zinc chloride and zinc iodide. These results have been verified by subsequent work. Arrhenius, in 1902, noted the requirement of negative complexes of cadmium to explain such effects and expected a number of such to exist in solution. McBain, surveying the effects of complexes and hydrolysis in 1907, concluded that the concentrations of simple uncomplexed ions would be negligibly small when such anomalous transport phenomena were observed. The effect of complexing is less dramatic for electrical conductance and diffusivity of these salts, but both are lower than would be expected if the salts were dissociated. This paper is concerned with the more quantitative explanation and prediction of such data, using as a basis the theory of irreversible thermodynamics. Any predictive treatment will require a knowledge of the concentrations of free ions and complexes in solution, together with their corresponding mobilities. The theory of irreversible thermodynamics requires in addition that kinetic coupling interactions between these species be recognised. The Onsager mobility coefficients of the binary electrolyte have been determined experimentally for a number of these self-complexed salts. These are shown to be functions of the more fundamental direct mobilities of the free ions and complexes, together with their coupling coefficients, one with another, in all possible combinations. The experimentally derived binary coefficients are shown to have an anomalous concentration dependence, varying in degree according to the degree of complexation of the salt. Choosing aqueous cadmium iodide, which is the most complexed of the group IIB halides, predictive calculations have been made which reproduce the observed concentration dependencies of the binary coefficients, electrical conductance, transport number and salt diffusivity. The method employs Pikal's restatement of Onsager limiting law theory in macroscopic irreversible thermodynamic terms. Additional data on cadmium isotopic diffusion in cadmium iodide are presented. There too, anomalous behaviour is observed, particularly an initial maximum in diffusion coefficient. An extension of the theoretical method to include isotopic experiments is presented and once more, using Pikal's basic treatment these isotopic diffusion features are reproduced. In both cases the predictive capability of theory is limited by the concentration limits for Onsager theory.

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