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Methane oxidation rates uncorrupted by nonchemical effects of transport, taken together with stoichiometric oxygen uptake (oxidation cycle) and evolution (decomposition cycle) data, are used to establish for the first time a set of conditions required for true thermodynamic equilibrium during metal-to-oxide interconversions in small Pd clusters (1.8−8.8 nm). These conditions allow us to assess the intrinsic thermodynamics of small Pd clusters and their catalytic effects in CH 4 oxidation. PdO decomposition in the absence of CH 4 deviates from equilibrium, as this step is limited by the nucleation of an oxygen vacancy ensemble on oxide domains. The nucleation bottleneck is removed by CH 4 during its catalytic sojourns, when CH 4 pressure and the related rates exceed a critical value, because CH 4 effectively removes the oxygen adatoms near an oxygen vacancy site via C−H bond activation on an oxygen−oxygen vacancy site pair that converts the O* adatom to a hydroxyl intermediate, which desorbs as H 2 O in sequential steps. CH 4 oxidation turnovers promote the nucleation of oxygen vacancy ensembles at conditions that maintain the global oxygen equilibration, as confirmed from the absence of CH 4 oxidation rate hysteresis in both Pd oxidation and PdO decomposition cycles and from coincidence of rate and oxygen content profiles during Pd oxidation. A theoretical construction decoupling the inherent cluster size variance from cluster diameter effects shows marked effects of size on bulk phase transition. The bulk phase transition occurs at lower oxygen chemical potentials for the smaller clusters, which confirm their more negative Gibbs free energy for PdO formation than the large structures. The bulk phase transition converts O*−O* adatom sites to Pd 2+ −O 2− ion pairs that are more effective for the kinetically relevant C−H bond activation in CH 4 . These effects of size on the thermodynamics and reactivities of small clusters illustrated in this study are general and extend beyond the Pd−PdO system.

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Density functional theory (DFT) and dihydrogen chemisorption uptakes at temperatures relevant to catalysis are used to determine and interpret adsorption enthalpies and entropies over a broad range of chemisorbed hydrogen (H*) coverages (0.1 ML to saturation) on Pt nanoparticles (1.6, 3.0, and 9.1 nm mean diameters) and Pt(111) surfaces. Heats of adsorption decrease by 30 kJ mol −1 as H 2 coverage increases from nearly bare (0.1 ML) to saturated (∼1 ML) surfaces, because of the preferential saturation of lowcoordination surface atoms by H* at low coverages. Such surface nonuniformity also leads to stronger binding on small Pt particles at all coverages (e.g., 47 kJ mol −1 on 1.6 nm, 40 kJ mol −1 on 3.0 nm, and 37 kJ mol −1 on 9.1 nm particles all at 0.5 ML), because their surfaces expose a larger fraction of low-coordination atoms. As H* approaches monolayer coverages, H*−H* repulsion leads to a sharp decrease in binding energies on all Pt particles. Measured H* entropies decrease with increasing H* coverage and decreasing particle size, but their values (35−65 J mol −1 K −1 ) are much larger than for immobile H* species at all coverages and particle sizes. Two-dimensional gas models in which mobile H* adsorbates move rapidly across uniform (ideal), excluded-area, or DFT-predicted nonuniform potential energy surfaces all give H* entropies ≥30 J mol −1 K −1 , qualitatively consistent with measured values. Larger H* entropies are predicted for uniform (ideal) PES while smaller H* entropies are predicted using nonuniform PES. DFT-derived barriers for H* diffusion between hcp and fcc 3-fold sites on Pt( 111) surface are about 6 kJ mol −1 , a value similar to thermal energies (kT) at temperatures of catalytic relevance, consistent with fast diffusion in the time scale of adsorption−desorption events and isotherm measurements. Mobile adsorbate entropy models are therefore essential for accurate estimates of adsorbate coverages, particularly because vibrational frequencies analyzed by harmonic oscillator approximations lead to large underpredictions of entropies, resulting in DFT-predicted adsorption free energies that are too large to result in high coverageseven at conditions where H* is known to cover the surface. The nonuniformity of Pt surfaces, repulsion among coadsorbates, and high adsorbate mobility starkly contrast with the requirements for Langmuirian descriptions of binding and reactions at surfaces, despite the ubiquitous use and success in practice of the resulting equations in describing adsorption isotherms and reaction rates on surfaces. Such fortuitous agreement is a likely consequence of the versatility of their functional form, taken together with the limited range in pressure and temperature in adsorption and kinetic measurements. The adsorption and kinetic constants derived from such data, however, would differ significantly from theoretical estimates that rigorously account for surface coordination, adsorbate mobility, and coadsorbate repulsion.