A microbial fuel cell (MFC) is a sustainable technology which commonly uses graphite as cathode for the production of hydrogen peroxide. Besides, water formation through four‐electron oxygen reduction mechanism is a commonly observed product. Determining the selectivity of H2O2/H2O reaction through experimental means is time consuming because of the slow kinetics of oxygen reduction reaction. Therefore, quantum chemical approaches are essential to comprehend the molecular nature of this process. Thus, density functional theory (DFT) was employed and quantum chemical calculations were performed to predict the chemical reactivity, stability, and thermodynamic properties of molecules participating in oxygen reduction reaction at graphite cathode. The calculations showed that graphene with higher value of “highest occupied molecular orbital” (HOMO), i.e., −4.544 eV has a higher tendency to donate electron for oxygen reduction reaction Furthermore, with an aim of predicting the most favorable conditions for H2O2 production, two different points, i.e., at the edge and middle of graphene plane were investigated. Calculated values showed that oxygen adsorption with the lowest energy requirement of 43.638 kcal/mol is energetically favorable at the edge of graphene plane. Nevertheless, oxygen complexes (O2*, HOO*, and HO*) characterized by high HOMO values −4.96, −4.37, and −4.34 eV are highly polarizable in the middle of the graphene plane. Furthermore, thermodynamic feasibility analysis showed that oxygen reduction required for hydrogen peroxide production had lower ΔG values of −90.94 (edge) and −98.44 (middle) kcal/mole than that of water synthesis (i.e., ΔG = −48.37(edge), −48.97 (middle) kcal/mole) at two‐electron reduction step. Therefore, it was concluded that H2O2 which followed the lowest energy pathway would be more thermodynamically feasible compared to water synthesis. © 2017 American Institute of Chemical Engineers Environ Prog, 37: 1291–1304, 2018