In hydrogen gas electrode on increasing $[H^+]$ concentration,then (at $P_{H_2}=1atm)$

Question

$\begin{array}{1 1}(a)\;E_{H^+/H_2}\;decreases&(b)\;E_{H^+/H_2}\;increases\\(c)\;E_{H^+/H_2}\;constant&(d)\;None\end{array}$

Answer 1

By Nernst equation

$E_{H^+/H_2}=E^o_{H^+/H_2}-\large\frac{0.0591}{1}$$\log\large\frac{ \sqrt{P_{H_2}}}{[H^+]}$

Since cell reaction is

$H^+e^-\rightarrow \large\frac{1}{2}$$H_2(g)$

$P_{H_2}=1$atm

$E^o_{H^+/H_2}=0$

Standard hydrogen electrode as reference electrode

$E_{H^+/H_2}=-0.059\log \large\frac{1}{[H^+]}$

$E_{H^+/H_2}=-0.059\times P_H$

If we increase $[H^+]$ then $P_H$ increases to $E_{H^+/H_2}$ increases

Hence (b) is the correct answer.