On the thermodynamic framework of solutions (with special reference to aqueous electrolyte solutions)

Thermodynamic consistency relations arising from the properties of equations that are homogeneous in the sense of Euler are examined, and alternative minimum tests for demonstrating full consistency of semi-empirical model equations for activity coefficients are established. Inconsistencies of this type can be avoided by the open-quotes differentiate downclose quotes approach in which an expression is postulated for the excess Gibbs energy, and expression for activity coefficients follow by the application of appropriate partial differential equations. A problem peculiar to aqueous solutions is the usage in the literature of two distinct definitions of thermodynamic ideality: one consistent with the notion of unit mole fraction or rational activity coefficients, the other with the notion of unit molal activity parts of the thermodynamic framework, notably the partial differential equations for obtaining activity coefficients, have forms that are specific to each ideality. Combination of an equation specific to one ideality with an equation specific to the other generates an inconsistency. The development of solution thermodynamics in this paper is non-traditional in two ways: the focus on condensed solutions leads to a direct definition of the thermodynamic activity, and the calculus of limits is used instead of the calculus of infinitesimals