Relationships between Kinetics and Acoustic Phenomena in Equilibrium Systems

Abstract

In a reacting (one-phase, one-reaction) system close to equilibrium, each variable (for example, composition, volume, temperature) approaches its equilibrium value at a rate proportional to its displacement from equilibrium. All the first-order rate constants in a particular state are identical. One can therefore characterize any system at equilibrium by a single relaxation time. When the relaxation of a chemical reaction gives rise to absorption and dispersion of sound, the thermal and dilatational contributions to the relaxational compressibility are necessarily in phase with each other and with the chemical reaction. A known but hitherto limited equation for the propagation of sound has been generalized to combine all such contributions for any system, irrespective of reaction mechanism, so that the propagation of sound may be described in terms of the instantaneous compressibility, the static compressibility, and the relaxation time. The relaxation time is a rather simple function of composition, temperature, and the rate laws for the forward and reverse reactions; it can be expressed for any postulated pair of rate laws. Therefore, measurement of the relaxation time of a (single) chemical reaction at different equilibrium compositions and temperatures yields kinetic information. The relationships derived here may be applied under certain conditions to acoustic studies of very fast reactions