Kinetic and isotopic data and density functional 1 theory treatments provide evidence for the elementary steps and the active site requirements involved in the four distinct kinetic regimes observed during CH4, oxidation reactions using O-2, H2O, or CO2 as oxidants on Pt clusters. These four regimes exhibit distinct rate equations because of the involvement of different kinetically relevant steps, predominant adsorbed species, and rate and equilibrium constants for different elementary steps. Transitions among 3 regimes occur as chemisorbed oxygen (O*) coverages change on Pt clusters. O* coverages are given, in turn, by a virtual O-2 pressure, which represents the pressure that would give the prevalent steady-state O* coverages if their adsorption-desorption equilibrium was maintained. The virtual O-2 pressure acts as a surrogate for oxygen chemical potentials at catalytic surfaces and reflects the kinetic coupling between C H and O=O activation steps. O* coverages and virtual pressures depend on O-2 pressure when O-2 activation is equilibrated and on O-2/CH4 ratios when this step becomes irreversible as a result of fast scavenging of O* by CH4-derived intermediates. In three of these kinetic regimes, C H bond activation is the sole kinetically relevant step, but occurs on different active sites, which evolve from oxygen oxygen (O*-O*), to oxygen oxygen vacancy (O*-*), and to vacancy vacancy (*-*) site pairs as O* coverages decrease. On O*-saturated cluster surfaces, O*-O* site pairs activate C-H bonds in CH4, via homolytic hydrogen abstraction steps that form CH3 groups with significant radical character and weak interactions with the surface at the transition state. In this regime, rates depend linearly on CH4, pressure but are independent of O-2 pressure. The observed normal CH4/CD4 kinetic isotope effects are consistent with the kinetic-relevance of C-H bond activation; identical O-16(2)-O-18(2) isotopic exchange rates in the presence or absence of CH4, show that O-2 activation steps are quasi-equilibrated during catalysis. Measured and DFT-derived C-H. bond activation barriers are large, because of the weak stabilization of the CH3 fragments at transition states, but are compensated by the high entropy of these radical-like species. Turnover rates in this regime decrease with increasing Pt dispersion, because low-coordination exposed Pt atoms on small clusters bind O* more strongly than those that reside at low-index facets on large clusters, thus making O* less effective in H-abstraction. As vacancies (*, also exposed Pt atoms) become available on O*-covered surfaces, O*-* site pairs activate C-H bonds via concerted oxidative addition and H-abstraction in transition states effectively stabilized by CH3 interactions with the vacancies, which lead to much higher turnover rates than on O*-O* pairs. In this regime, O-2 activation becomes irreversible, because fast C-H bond activation steps scavenge O* as it forms. Thus, O* coverages are set by the prevalent O-2/CH4 ratios instead of the O-2 pressures. CH4/CD4 kinetic isotope effects are much larger for turnovers mediated by O*-* than by O*-O* site pairs, because C-H (and C-D) activation steps are required to form the * sites involved in C-H bond activation. Turnove rates for CH4-O-2 reactions mediated by O*-* pairs decrease with increasing Pt dispersion, as in the case of O*-O* active structures, because stronger O* binding on small clusters leads not only to less reactive O* atoms, but also to lower vacancy concentrations at cluster surfaces. As O-2/CH4 ratios and O* coverages become smaller, O-2 activation on bare Pt clusters becomes the sole kinetically relevant step; turnover rates are proportional to O-2 pressures and independent of CH4, pressure and no CH4/CD4 kinetic isotope effects are observed. In this regime, turnover rates become nearly independent of Pt dispersion, because the O-2 activation step is essentially barrierless. In the absence of O-2, alternate weaker oxidants, such as H2O or CO2, lead to a final kinetic regime in which C-H bond dissociation on *-* pairs at bare cluster surfaces limit CH, conversion rates. Rates become first-order in CH4, and independent of coreactant and normal CH4/CD4 kinetic isotope effects are observed. In this case, turnover rates increase with increasing dispersion, because low-coordination Pt atoms stabilize the C-H bond activation transition states more effectively via stronger binding to CH3 and H fragments. These findings and their mechanistic interpretations are consistent with all rate and isotopic data and with theoretical estimates of activation barriers and of cluster size effects on transition states. They serve to demonstrate the essential role of the coverage and reactivity of chemisorbed oxygen in determining the type and effectiveness of surface structures in CH4, oxidation reactions using O-2, H2O, or CO2 as oxidants, as well as the diversity of rate dependencies, activation energies and entropies, and cluster size effects that prevail in these reactions. These results also show how theory and experiments can unravel complex surface chemistries on realistic catalysts under practical conditions and provide through the resulting mechanistic insights specific predictions for the effects of cluster size and surface coordination on turnover rates, the trends and magnitude of which depend sensitively on the nature of the predominant adsorbed intermediates and the kinetically relevant steps.