Cathodic reaction : \(2{H^ + } \to {H_2}({P_2})\)

\({E_{cathode}} = - \frac{{RT}}{{2F}}\ln \frac{{{P_2}}}{{{{[{H^ + }]}^2}}}\) ;\({E_{{\rm{anode}}}} = - \frac{{RT}}{{2F}}\ln \frac{{{{[{H^ + }]}^2}}}{{{P_1}}}\)

\({E_{\inf }} = {E_{anode}} + {E_{cathode}}\)\( = - \frac{{RT}}{{2F}}\ln \frac{{{{({H^ + })}^2}}}{{{P_1}}} - \frac{{RT}}{{2F}}\ln \frac{{{P_2}}}{{{{({H^ + })}^2}}}\)

\(= - \frac{{RT}}{{2F}}\ln \frac{{{P_2}}}{{{P_1}}} = \frac{{RT}}{{2F}}\ln \frac{{{P_1}}}{{{P_2}}}\).