Within the recently proposed asymptotic method for solving the Boltzmann equation for chemically reacting gas mixture, the equations for a dissociating diatomic gas have been derived assuming two-temperature (translational-rotational + vibrational) approximation. Corresponding expressions for the reaction and relaxation rates, determined by the quasi-stationary vibrational distributions, have been obtained under assumption of dissociation from the highest vibrational level. Cut-off harmonic oscillator approximation for the diatomic molecules is assumed. It is shown that all reaction rates are the complex functions of the species densities. Analysis of a flow behind a shock wave is performed in a wide range of the flow parameters. It is shown that under strong non-equilibrium condition the dissociation rate is determined not by the dissociation probability, but by the vibration probability, since the excitation of highest vibrational levels is the bottleneck of dissociation process. This means that the procedure of obtaining the data on dissociation rates needs the accurate revision.