Orthonormal chemical reactions and chemical relaxation. Part 1.—Reactions in dilute solution

Abstract

The relaxation times and normal modes of reaction of a chemical system in dilute solution are discussed and compared with the normal frequencies and normal modes of vibration of a polyatomic molecule. The normal modes of reaction are orthogonal and hence can be written as an orthonormal set satisfying ∑νkiνli/text-decoration:overlinemi=δkl, where νki is the stoichiometric coefficient of the ith substance in the kth normal mode of reaction while text-decoration:overlinemi is the number of moles of the ith substance, per mole of solvent, at equilibrium. The use of such an orthonormal set of reactions (not necessarily the normal modes of reaction) simplifies the thermodynamics of the system and facilitates the treatment of the effects of instantaneous temperature and pressure changes (T-jumps and p-jumps). The application of these results to chemical relaxation shows that the use of normalized normal modes of reaction simplifies the usual equations for T-jump, p-jump, and sound-absorption experiments.