NO_x (x = 1 or 2) formed during fuel combustion is harmful to health and to the environment, and therefore there is interest in their effective removal from emissions. One of the most elementary and generally important catalytic reactions of NO_x is the catalytic oxidation of NO to NO₂. Pt-based catalysts are widely used for this catalysis, but to date agreement has not been achieved as to the kinetics or mechanism of the reactions. In this work we use density functional theory calculations to analyze the potential surface intermediates in Pt(111)-catalyzed NO oxidation under relevant reactive conditions. We characterize the energetics, spectroscopy, and reactivity of the surface species in different regimes of oxygen and NO_x coverage and at finite gas phase temperatures and pressures. We find that the thermodynamics of reaction are strong functions of the oxygen coverage, and that the oxygen coverage is a function of the temperature and pressure of the gas phase in equilibrium with the catalyst surface. There is a temperature/pressure window in which NO oxidation to NO₂ is most thermodynamically favored, and it is within this regime that kinetics should be considered.