THE COMPENSATING-MIXTURE MODEL FOR MULTICOMPONENT SYSTEMS AND ITS APPLICATION TO ION-EXCHANGE

The term "compensating mixture" is introduced to specify a mixture of components that belong to the same compensation class. A compensation class is defined as a group of similar experimental systems described by the same compensation temperature: Tc = ΔH/ΔS, where the enthalpy and entropy changes refer to a phase equilibrium. The sufficient conditions for systems to belong to the same compensation class, obtained from a statistical analysis, are stated. Various expressions for thermodynamic properties of compensating mixtures are derived. Experimental data pertain to the ion-exchange equilibrium of alkali-metal ions between an aqueous solution and a solid exchanger. Experimental results for the isosteric enthalpy and entropy of exchange as a function of composition are compared with calculated values. A good agreement is observed. Other treatments of multicomponent mixtures (viz., ideal- and regular-solution models) are shown to yield results that do not agree with experiment. For a binary mixture, an equation of state is derived, illustrating the physical significance of the compensation temperature of a class. © 1990 American Chemical Society.