NEW APPROACH TO SENSITIVITY ANALYSIS OF MULTIPLE EQUILIBRIA IN SOLUTIONS

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 systems, in particular, for sensitivity analysis, it is important to know the determinant DELTA 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 DELTA to the sum of contributions originating 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.