New approach to sensitivity analysis of multiple equilibria in solutions

Abstract

We consider multiple equilibria in solutions in which the interaction of n chemical species is described by means of m stoichiometrically independent reactions (SIRs). For the study of certain thermodynamic properties of such system. in particular, for sensitivity analysis, it is important to know the determinant Δ of the Hessian matrix of the Gibbs energy, as a function of the extent of the SIRs. Any linear combination of SIRs, in which (at least)m– 1 species are not involved, is called a Hessian response reaction (HR): Several properties of the HRs are pointed out, in particular, the equivalence of Δ to the sum of contributions origintaing from each HR. The effect of temperature and pressure on chemical equilibria in ideal solutions is analysed. It is shown that the sensitivity coefficient of a chemical species A_i may be presented as a sum of contributions coming from all HRs in which A_i is involved. Each of these contributions is a product of the stoichiometric coefficient of A_i, the enthalpy or volume change of the respective HR, and a concentration-dependent term which is always positive. It is also shown that the relaxation contribution to the heat capacity is a sum of contributions over all HRs.