This report deals with a theoretical study of chemical reaction rates and transport processes in non-equilibrium reacting gas flows and the influence of gas mixture compressibility on the reaction rates. A self-consistent model based on the kinetic theory methods is developed taking into account strongly non-equilibrium chemical kinetics in a flow. Tempered reaction regime is studied in the frame of the one-temperature approximation. Gas mixtures with bimolecular reactions, dissociation and recombination are considered. A closed set of non-equilibrium gas dynamic equations coupled to the equations of chemical kinetics in a flow is derived, and distribution functions in the zero and first-order approximations and corresponding expressions for the transport and source terms are obtained. The algorithms for the calculation of transport and reaction rate coefficients are elaborated, allowing to reduce integral equations to the linear algebraic equations. Relations of the reaction rate coefficients to the bulk viscosity coefficient and chemical-reaction contribution to the normal mean stress are established. An alternative problem formulation relating reaction rates and reaction contribution to the normal mean stress to the chemical reaction affinities is proposed, and cross effects between reaction rates and diagonal elements of the viscous stress tensor are found. Thus a consistency of the kinetic theory results with the ones given by linear irreversible thermodynamics is shown.