The Quantum Mechanics of Chemical Kinetics of Homogeneous Gas Phase Reactions II. Approximations for Displacement Reaction between an Atom and a Diatomic Molecule

Abstract

The quantum mechanics of a displacement reaction: AB+C→A+BC, has been considered and the results have been applied to the reaction: H₂+Br→H+HBr at 500°K. The potential energy of the reacting system is based upon the London approximation as modified by Eyring and Polanyi. The absolute rate has been found to be a sensitive function of the coulombic energy fraction; when this fraction is taken to be 30 percent, the absolute rate is in essential agreement with the observed value. This agreement can only be regarded as fortuitous, however. Several results have been derived which are not sensitive to the fraction of coulombic energy and furnish, therefore, a more stringent test of the present formulation. It has been found that the variation of the absolute rate with temperature, as calculated at 500°K, compares favorably with the observed variation. Approximately 95 percent of the rate comes from hydrogen molecules in the first excited vibrational state. The contribution from hydrogen molecules in various rotational states is given. The distribution of the initially formed hydrogen bromide molecules has been found to be representable by a pseudo‐canonical distribution function of the rotational quantum number, in which the ``rotational temperature'' is approximately one‐half the initial temperature.