The influence of non-equilibrium transient effects on measurements of vibrational relaxation times and of dissociation rate constants

Abstract

A semi-empirical analysis based on a rate law for vibrational relaxation of dissociating simple harmonic oscillators allows for a detailed study of measurements of vibrational relaxation times τ and of steady dissociation rate coefficients k0. It is shown that non-equilibrium populations of vibrational energy levels prevent attainment of the thermodynamically expected equilibrium energy. Even under near-isothermal and mild conditions, [Formula: see text], serious experimental errors result when the Bethe–Teller relaxation rate law is used. Closed form expressions are given which permit evaluation of these errors. Measurements should be analyzed using the rate law[Formula: see text]where ε is the vibrational energy per molecule, τ the relaxation time, kd the non-equilibrium rate coefficient, ετ the thermodynamically expected vibrational energy at temperature T, and (ε* + hv) the energy just above the dissociation limit. It is also shown that if[Formula: see text]a local minimum and maximum are predicted for measured density gradients in shock tube dissociations of diatomic molecules, where tine is the incubation time, D′ the effective dissociation energy, and x0 the mole fraction of dissociating molecules in an inert diluent. Expressions are given for extracting incubation times and rate constants from such studies when [Formula: see text]. Analysis of experimental data actually showing such phenomena (J. Chem Phys. 55, 4017 (1971)) is carried out. There are indications that any analysis which does not explicitly account for transient effects could result in errors in measured k0's of factors of 2 or more.