The cell potential for the following cell  $\text{Pt}\left|{\mathrm{H}}_2\right(\mathrm{g}\left)\right|{\mathrm{H}}^{+}\left(\mathrm{aq}\right)\parallel {\mathrm{Cu}}^{2+}\left(0.01\mathrm{M}\right)\mid \mathrm{Cu}\left(\mathrm{s}\right)$ is 0.576 V at 298 K. The pH of the solution is ___. (Nearest integer)

 

by using nernst equation $$\begin{gathered} \text{Anode}:{\mathrm{H}}_2\to 2{\mathrm{H}}^{+}+2{\mathrm{e}}^{-} \\ \mathrm{Cathode} : {\mathrm{Cu}}^{2+}+2{\mathrm{e}}^{-}\to \mathrm{Cu} \\ {\mathrm{Cu}}^{2+}+{\mathrm{H}}_2\to 2{\mathrm{H}}^{+}+\mathrm{Cu} \\ {\mathrm{E}}_{\text{cell }}={\mathrm{E}}_{\text{cell }}^0-\frac{0.06}{2}\log \frac{{\left[{\mathrm{H}}^{+}\right]}^2}{\left[{\mathrm{Cu}}^{2+}\right]} \\ 0.576=0.34-\frac{0.06}{2}\log \left\{\frac{{\left[{\mathrm{H}}^{+}\right]}^2}{\left(0.01\right)}\right\} \\ +3.93-\log \left({\mathrm{H}}^{+}\right)+\log 0.1\Rightarrow \mathrm{pH}=4.93\simeq 5 \end{gathered}$$