On the Velocity Distribution in a Chemically Reacting Gas

The departure of the velocity distribution function from the Maxwellian form and the corresponding correction to the reaction-rate formula have been calculated for a gas undergoing a slow bimolecular reaction. Kinetic theory methods based on the Boltzmann transport equation have been used. This work differs from a previous calculation by Prigogine and Xhrouet in two respects: (1) the energy dependence of the reaction cross section is taken in a form that is consistent with the conventional simple collision theory (in the previous work this was not the case and the results are sensitive to this choice), and (2) a simplified derivation of the important formulas is given, in which we follow the original methods of Chapman based on the equations of change instead of the integral-equation techniques of Enskog. The calculations take into account the effect of the reaction in depleting the tail of the Maxwell distribution, but do not take into account the effects of the heat of reaction. It is found that when kT is one-fifth the activation energy, the reaction rate is 8% less than that predicted by the conventional simple collision theory.