We analyze a thermally activated bimolecular reaction in a dilute gas proceeding with introduction of the Prigogine--Xhrouet model (PX) for the reactive cross section. We use the Shizgal--Karplus perturbation method of solution of the Boltzmann equation for reactions A + A \rightarrow B + B and A + A \rightleftarrows B + B to obtain the analytical expressions for the nonequilibrium temperatures of reagents and for the rate of chemical reaction. We present the results obtained within one and two Sonine polynomials approximations. The rate constant of chemical reaction depends on concentration of products for the first reaction only and for the second reaction is constant. The analytical results for the temperature of the reagent A and its value in the beginning of reaction for the product B are compared with those obtained from the Monte Carlo computer simulations with use of the Bird method. It is shown that the nonequilibrium effects in Shizgal--Karplus temperatures and in decrease of the chemical constant rate are more pronounced than for the lines-of-centers model. For the PX model the rate constant can be decreased even 4 times.

PACS numbers: 05.20.Dd, 82.20.--w, 82.20.Mj, 82.20.Wt