The reactivity of sp(2) carbon materials is studied using the adsorption and dissociation of O2 on graphene and graphene oxide as model systems. The reactions on the basal plane, zigzag and armchair edges of graphene and graphene oxide with different oxygen-containing groups are calculated using first principles calculations. Two Brønsted-Evans-Polanyi relationships are identified and an electron delocalization model is suggested to understand the general trend of reactivity for sp(2) carbon materials.