A model of gas-surface reactivity is developed based on the ideas that (a) adsorbate chemistry is a local phenomenon, (b) the active system energy of an adsorbed molecule and a few immediately adjacent surface atoms suffices to fix microcanonical rate constants for surface kinetic processes such as desorption and dissociation, and (c) energy exchange between the local adsorbate-surface complexes and the surrounding substrate can be modeled via a Master equation to describe the system/heat reservoir coupling. The resulting microcanonical unimolecular rate theory (MURT) for analyzing and predicting both thermal equilibrium and nonequilibrium kinetics for surface reactions is applied to the dissociative chemisorption of methane on Pt(111). Energy exchange due to phonon-mediated energy transfer between the local adsorbate-surface complexes and the surface is explored and estimated to be insignificant for the reactive experimental conditions investigated here. Simulations of experimental molecular beam data indicate that the apparent threshold energy for CH4 dissociative chemisorption on Pt(111) is E-0=0.61 eV (over a C-H stretch reaction coordinate), the local adsorbate-surface complex includes three surface oscillators, and the pooled energy from 16 active degrees of freedom is available to help surmount the dissociation barrier. For nonequilibrium molecular beam experiments, predictions are made for the initial methane dissociative sticking coefficient as a function of isotope, normal translational energy, molecular beam nozzle temperature, and surface temperature. MURT analysis of the thermal programmed desorption of CH4 physisorbed on Pt(111) finds the physisorption well depth is 0.16 eV. Thermal equilibrium dissociative sticking coefficients for methane on Pt(111) are predicted for the temperature range from 250-2000 K. Tolman relations for the activation energy under thermal equilibrium conditions and for a variety of "effective activation energies" under nonequilibrium conditions are derived. Expressions for the efficacy of sticking with respect to normal translational energy and vibrational energy are found. Fractional energy uptakes, f(j), defined as the fraction of the mean energy of the complexes undergoing reaction that derives from the jth degrees of freedom of the reactants (e.g., molecular translation, vibration, etc.) are calculated for thermal equilibrium and nonequilibrium dissociative chemisorption. The fractional energy uptakes are found to vary with the relative availability of energy of different types under the specific experimental conditions. For thermal dissociative chemisorption at 500 K the fractional energy uptakes are predicted to be f(t)=13%, f(r)=18%, f(v)=33%, and f(s)=36%. For this equilibrium scenario relevant to catalysis, the incident gas molecules supply the preponderance of energy used to surmount the barrier to chemisorption, f(g)=f(t)+f(v)+f(r)=64%, but the surface contribution at f(s)=36% remains significant. (C) 2003 American Institute of Physics.