A statistical mechanical analysis of the solvation effects on the kinetic rate constants of reactions in near and supercritical solvents is presented to understand the experimental findings regarding the thermodynamic pressure effects. This is an extension of the solvation formalism of Chialvo and Cummings to the analysis of the microscopic basis for the macroscopic pressure and temperature effects on the kinetic rate constants of reactions conducted in the compressible region of the solvent phase diagram. This analysis is illustrated with integral equations calculations involving Lennard-Jones infinitely dilute quaternary systems to describe the species in solution during the reaction of triplet benzophenone ((BP)-B-3) with a cosolvent (either O-2 or 1,4-cyclohexadiene) in supercritical CO2 along the supercritical isotherms T-r = 1.01 and 1.06. The role of the species molecular asymmetries and consequently their solvation behavior in determining the thermodynamic pressure and temperature effects on the kinetic rate constant of reactions at near-critical conditions are discussed.