in which -SO3*, [H + ]Solution, -[SO3H]Nafion and * represent an adsorbed sulfonate group, a proton in the liquid electrolyte, a sulfonate group in Nafion and an unoccupied surface Pt site, respectively. The need to include [H + ]Solution in Eq. 1 stems from the electroneutrality requirement in the Nafion phase during the electron transfer. Thermodynamic derivations (Supplementary Note 2) show that at a given coverage of sulfonate and temperature, the electrode potential on the SHE scale could be expressed as: