We combine reactivity studies with infrared reflection absorption spectroscopy to provide molecular-scale insights into the oxidation of two cyclic alcohols, cyclohexanol and 2-cyclohexen-1-ol, by atomic oxygen adsorbed on Au(111). The two alcohols share common features in their reaction pathways: they are both activated by Brønsted acid-base reactions with adsorbed oxygen. Cyclic ketones, cyclohexanone and 2-cyclohexen-1-one, are the major products, formed from cyclohexanol and 2-cyclohexen-1-ol, respectively. These ketones also undergo secondary ring C-H bond activation. The product distributions reflect a substantial difference in the secondary reactions for these two ketones, which correlate with their gas-phase acidity. The allylic alcohol (2-cylohexen-1-ol) has a greater degree of ring C-H activation, yielding the diketone (2-cyclohexene-1,4-dione) and phenol. Our results provide clear evidence for the importance of C═C functionalities in determining the reactivity of molecules in heterogeneous oxidative transformations promoted on Au-based materials.