If the pressure of H₂ gas is increased from 1 atm to 100 atm keeping H⁺ concentration constant at 1 M, the change in reduction potential of hydrogen half-cell at 25°C will be

0.059 V

The half-cell reaction for hydrogen half-cell  acting as cathode is

\(2H^+  +   2e^-  \rightarrow  H_2\)

\(E_{H^+|H_2} = E^0_{H^+|H_2} − \frac{0.059}{2}log\frac{p_{H_2}}{[H^+]^2}\)

Now, when the pressure of of \(H_2\) gas is changed to 100atm without changing \([H^+]\), the reduction potential becomes

\(E^´_{H^+|H_2} = − \frac{0.0591}{2}log\frac{100}{[H^+]^2}\)

∴ Change in reduction potential =

\(E_{H^+|H_2} − E^´_{H^+|H_2} = \frac{0.0591}{2}log\frac{100}{[H^+]^2} × \frac{[H^+]^2}{1}= 0.059 V\)