Oxy-fuel combustion technology holds a great promise in both increasing the efficiency of the energy conversion and reducing environmental impact. However, effects of the higher pressures and replacement of the nitrogen with carbon dioxide diluent are not well understood at present. The title reaction is one of the most important processes in combustion. Despite numerous studies, the effects of supercritical carbon dioxide environment did not receive much attention in the past. Here we report the results of boxed molecular dynamics simulations of these effects at QM/MM theory level with periodical boundary conditions. The free energy barriers for HOCO intermediate formation and decomposition were tabulated in a wide range of pressures (1-1000 atm) and temperatures (400-1600 K). Pressure dependence of calculated rate constants for these reaction steps and overall reaction were analyzed. We found that the CO2 environment may increase these rate constants up to a factor of 25, at near critical conditions. At higher temperatures, this effect weakens significantly. Numerical values for parameters of extended Arrhenius equation, suitable for combustion kinetic modeling are reported.