Thermodynamics for chemical equilibria and kinetics in solution at constant volume

Abstract

The relation between isobaric and isochoric equilibrium parameters has been examined from a new viewpoint based on specifically designed partial molar properties at constant temperature and solvent concentration. These are defined by X_B(T, c_A)=(∂X/∂n_B)_{T, cA, n′} and solutes in the corresponding ideal solution conform to A^id_B(T, c_A)=A^°_B(T, c_A)+RTln (r_B/r^°_B) where A is the Helmholtz energy and r_B=n_B/n_A. On this basis, standard equilibrium constants are introduced for reactions at constant T and c_A not involving the solvent stoichiometrically. These equilibrium constants are related to an ideal process consisting of mixing standard solutions containing the reactants, complete transformation of reactants into products and separation to standard solutions containing the products. This ideal process at constant T and c_A is rendered isochoric (in the sense of constant total volume) by an appropriate selection of standard solution compositions. A whole set of standard molar quantities of reaction Δ_rX°(T, c_A) is defined in terms of X^°_B(T, c_A). Exact equations linking Δ_rX°(T, c_A) where X=A, U, S and C_v, with the more usual Δ_r, X°(T, p) quantities where X=G, H, S and C_p, respectively, are derived. Particular attention has been paid to the thermodynamics of the quasi-equilibrium of activation at constant (T, p) and at constant (T, c_A), and to their interrelationship. The results are compared with those of previous approaches and shown to be generally equivalent in the limit of infinitely dilute solutions. This approach is unique in its interpretative capabilities and in giving a rationale of the ‘pressure of activation’. The quantities X_B(T, c_A) and X^id_B(T, c_A) are suitable for studying mineralogically and metallurgically important interstitial solid solutions.