Solution of the Fokker-Planck equation for reactive Rayleigh gas

A Rayleigh model of heavy molecules diluted in a thermal bath of light molecules is extended to include a chemical reaction between both species. The solution of the appropriate Fokker-Planck equation for the distribution function is obtained from the corresponding solution for the nonreactive mixture. In the hydrodynamic regime the shape of the velocity distribution of heavy molecules is Maxwellian, but with a temperature different from that of the carrier gas. Exact results are derived for the reaction rate constant and diffusion coefficient.