Kinetic theory of a chemically reacting gas with inelastic transitions

The problem of a gas mixture of four multilevel molecules undergoing a reversible bimolecular chemical reaction plus mechanical encounters, leading to elastic or inelastic scattering, is addressed in the frame of extended kinetic theory. When elastic scattering is the dominant microscopic interaction, an approximate closed set of moment equations is derived for the evolution of the macroscopic observables in a suitable asymptotic limit. It is shown that the resulting set of PDE's describes correctly the main features of the original integrodifferential kinetic equations, namely conservation equations, equilibria (mass action law), and H-theorem.