A statistical model of activated dissociative adsorption is developed using microcanonical, unimolecular rate theory. Dissociation is treated as occurring through energy randomizing collisions between incident molecules and local clusters of surface atoms. The predictions of the statistical model are found to be in remarkable accord with existent experimental data for methane dissociative adsorption and the thermal hydrogenation of methyl radicals on Pt(111). Perhaps surprisingly, the "over the barrer" statistical model adequately describes the known kinetics of these reactions without any explicit provision for quantum tunneling.