Non-equilibrium thermal dissociation of diatomic molecules. I. Extraction of collision-induced rate constants from experimentally measured reaction rates as a function of temperature for ten diatomic molecules dilute in Ar

Abstract

We have solved the master equation for the steady-state low-pressure dissociation of diatomic molecules AB dilute in a bath gas M. Backed by recent a priori calculations we used the truncated harmonic oscillator model with Landau-Teller energy transfer rate constants. No assumptions are made with regards to the values of collision-induced dissociation (CID) rate constants, which we ultimately extract from experimental measurements of non-equilibrium effects available in the literature. An analytical expression for the rate of dissociation takes the form -d[AB]/d t = k d eq[1 + a( T) k m* / k 10] −1[AB][M], where a is a simple temperature-dependent function, k m* is the CID rate constant for dissociation from the most-important (last) level m *, and k 10 is the rate constant for collisional de-excitation from ν = 1 to ν = 0. This expression tests well against a numerical solution of the same master equation in the temperature range from 0 to 10θ vib, where θ vib is the characteristic vibrational temperature ( = hv/k). It also tests well against recent ab initio calculations using rotationally averaged rate constants. It predicts (a) experimental values of activation energies, E a, well for many molecules; and (b) that E a deviates from the bond dissociation energy, D 0, by an amount varying from - hve − u /(1 - e − u ) low temperatures to the high-temperature limiting value of ≈ - D 0/6; and (c) that at high temperatures dissociation rates are determined by energy transfer processes. We deduce the values of CID rate constants for HBr, HCl, HF, H 2, D 2, CO, N 2, NO, O 2, F 2 (all dilute in Ar). We find the activation energies for the hydrides to be all ≈ 4 hv. We review other analytical expressions obtained over the last 30 years, classifying them according to the approximations made and showing their limitations. We also discuss the relationship between our present quantum result and published classical results in terms of an “average energy transferred per collision”, 〈Δ E〉.