The heterogeneous reactions (1) and ( ) are considered to be occurring at the planar cathode surface in the CO 2 ER process, where the protons are provided by water. For simplicity, we base our calculations on CO producing catalysts such as Ag and Au but the analysis can be easily extended to catalysts producing a wider range of CO 2 reduction products. We do not assume a Faradaic current due to the consumption of H + in our base-case. A comparison of the base-case with the scenario where a maximum of 10% of the bulk concentration of H + is present at the OHP (limiting H + current case) can be found in the supplimentary information (SI).