In electrochemistry, the standard hydrogen electrode (abbreviated SHE), is a redox electrode which forms the basis of the thermodynamic scale of oxidation-reduction potentials. Its absolute electrode potential is estimated to be 4.44 ± 0.02 V at 25 °C, but to form a basis for comparison with all other electrochemical reactions, hydrogen's standard electrode potential (E°) is declared to be zero volts at any temperature. Potentials of all other electrodes are compared with that of the standard hydrogen electrode at the same temperature.
Nernst equation for SHE
The hydrogen electrode is based on the redox half cell corresponding to the reduction of two hydrated protons, 2 H+(aq), into one gaseous hydrogen molecule, H2(g). General equation for a reduction reaction:
(oxidant) ox + z e − ↽ − − ⇀ (reductant) red {\displaystyle {\underset {\text{ox}}{\text{(oxidant)}}}+z{\ce {e- <=>}}\ {\underset {\text{red}}{\text{(reductant)}}}}
The reaction quotient (Qr) of the half-reaction is the ratio between the chemical activities (a) of the reduced form (the reductant, ared) and the oxidized form (the oxidant, aox).
Q r = a red a ox {\displaystyle Q_{r}={\frac {a_{\text{red}}}{a_{\text{ox}}}}}
Considering the 2 H+ / H2 redox couple:
2 H ( aq ) + + 2 e − ↽ − − ⇀ H 2 ( g ) {\displaystyle {\ce {2H_{(aq)}+ + 2e- <=> H2_{(g)}}}}
at chemical equilibrium, the ratio Qr of the reaction products by the reagents is equal to the equilibrium constant K of the half-reaction:
K = a red a ox = a H 2 a H + 2 = p H 2 / p 0 a H + 2 = x H 2 p / p 0 a H + 2 {\displaystyle K={\frac {a_{\text{red}}}{a_{\text{ox}}}}={\frac {a_{\mathrm {H_{2}} }}{a_{\mathrm {H^{+}} }^{2}}}={\frac {p_{\mathrm {H_{2}} }/p^{0}}{a_{\mathrm {H^{+}} }^{2}}}={\frac {x_{\mathrm {H_{2}} }p/p^{0}}{a_{\mathrm {H^{+}} }^{2}}}}
where
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