The kinetics of the oxidation of NO by O-2 was studied on 1 cm diameter single crystals, Pt(111) and Pt(321), at atmospheric pressure. The surface of the (321) crystal is composed of 20% kink, 20% step, and 60% terrace atoms and simulates small 1-3 nm size Pt particles on supported catalysts, while the (111) surface simulates the most stable plane found on large, > 5 nm, particles. The turnover rates (TORs), that is, rate normalized by the exposed platinum, on the two single crystals differ by less than a factor of 2 over the range of conditions studied and are also similar to the TOR on a supported catalyst with an average particle size of 9 nm. Both surfaces show a dynamic kinetic behavior as evidenced by a change in the apparent activation energy and reaction orders as a function of reaction conditions. The oxygen coverage after initial rate experiments on Pt(111) was 0.6 monolayer (ML) on average which is similar to that measured previously by in situ X-ray photoelectron spectroscopy (XPS) under similar conditions. This oxygen overlayer, which is likely controlled by the relative presence of NO and NO2, inhibits O-2 dissociation but lowers the binding energy of reactants enough to allow the catalysis. Long-term stability studies on Pt(111) correlate catalyst deactivation with irreversibly bound oxygen on the surface at coverages over 1 ML, as measured after reaction. Ex situ Auger electron spectroscopy (AES) and XPS results suggest that the surface defect sites on Pt(321) begin to oxidize relative to atoms on the (111) plane at lower NO2 to NO ratios.