One important aid in understanding catalysis by gold nanoparticles would be to understand the strength with which they bond to different support materials and the strength with which they bond adsorbed intermediates, and how these strengths depend on nanoparticle size. We present here new measurements of adsorption energies by single crystal adsorption calorimetry, and new analyses of other recent measurements by this technique in our lab, which imply that: (1) small nanoparticles of metals like Au bind much more strongly to supports like titania and iron oxide which are generally observed to be effective in making Au nanoparticles active in catalysis than to supports like MgO which are considered less effective, (2) the thermodynamic stability of adsorbed intermediates for catalytic reactions can either increase strongly or decrease strongly with decreasing metal nanoparticle size below 8 nm, depending on the system, and (3) the reaction to insert O2 into the Au-H bond of adsorbed H on the Au(111) surface to make Au-OOH (O2,g + H(ad) --> OOH(ad)) is exothermic by -80 kJ mol(-1). This adsorbed hydroperoxy species is thought to be a key intermediate in selective oxidation reactions over Au nanoparticle catalysts, but its production by this reaction may also provide a route for O2 activation in less demanding reactions (like CO oxidation) as well. Its stability would be even higher on Au nanoparticles below 3 nm in diameter, but even there it is too unstable to be formed by combining adsorbed OH with an O adatom (OH(ad) + O(ad) --> OOH(ad)), which is estimated to be endothermic by 175 kJ mol(-1). The implications of the stability of metal nanoparticles versus particle size on different supports and of the stability and potential reactions of OOH(ad) in Au catalysis will be discussed.