Matrix Methods and Normalization Procedures in Chemical Relaxation

Abstract

Two very general methods for dealing with chemical relaxation in solution near equilibrium are developed in detail along parallel lines; in the first of these the normal modes of relaxation are obtained as linear combinations of a set of basic reactions whereas in the second the normal coordinates are obtained as linear combinations of the deviations of the solute concentrations from those at equilibrium. The general procedures described in the literature, differing both in their basic assumptions (some being based on the theory of irreversible thermodynamics, others on kinetic considerations) and also in the concentration units adopted and the normalization procedures used, form special cases of the above two general methods and are considered from this point of view. The two general methods are compared critically and shown to be complementary since each has its own special advantages and disadvantages. In particular, the significance of the normal modes of relaxation corresponding to infinite relaxation times are shown to be entirely different in the two cases; in the first method these modes are “reactionless” and have little significance whereas the “improper” normal modes obtained by the second method show how the concentrations of the various solutes can be changed without disturbing the chemical equilibrium of the system.