Oxygen equilibrium isotope effects (O-18 EIEs) upon the formation of metal superoxide and peroxide structures from natural abundance O-2 are reported. The O-18 EIEs determined over a range of temperatures are compared to those calculated on the basis of vibrational frequencies. Considering all vibrational modes in a "full frequency model" is found to reproduce the empirical results better than "cut-off" models which consider only the most isotopically sensitive modes. Theoretically, the full frequency model predicts that O-18 EIEs arise from competing enthalpic and entropic influences resulting in nonlinear variations with temperature. Experimental evidence is provided for an increase in the magnitude of the EIE, in some instances implicating a change from inverse to normal values, as the temperature is raised. This finding is not easily reconciled with the common intuition that O-18 EIEs arise from a reduction of the O-O force constant and attendant changes in zero point energy level splitting. Instead a dominant entropic effect, as described here, is expected to characterize isotope effects upon reversible binding of small molecules to metal centers in enzymes and inorganic compounds.