For a cell, $$\mathrm{Cu}(\mathrm{s})\left|\mathrm{Cu}^{2+}(0.001 \,\mathrm{M}) \| \mathrm{Ag}^{+}(0.01 \,\mathrm{M})\right| \mathrm{Ag}(\mathrm{s})$$

the cell potential is found to be $0.43 \mathrm{~V}$ at $298 \mathrm{~K}$. The magnitude of standard electrode potential for $\mathrm{Cu}^{2+} / \mathrm{Cu}$ is _________ $\times 10^{-2} \mathrm{~V}$.

[Given : $E_{A{g^ + }/Ag}^\Theta$ = 0.80 V and ${{2.303RT} \over F}$ = 0.06 V]

Anode : $$\mathrm{Cu}(\mathrm{s}) \longrightarrow \mathrm{Cu}^{2+}(\mathrm{aq})+2 \mathrm{e}^{-}$$ <br/><br/> Cathode : $$\left.[\mathrm{Ag}^{+}+\mathrm{e}^{-} \longrightarrow \mathrm{Ag}(\mathrm{s})\right] 2$$<br/><br/> <hr/><br/> Cus(s) $$+2 \mathrm{Ag}^{+}(\mathrm{aq}) \longrightarrow \mathrm{Cu}^{2+}(\mathrm{aq})+2 \mathrm{Ag}(\mathrm{s})$$<br/><br/> $$ \begin{aligned} & E_{\text {cell }}=E_{\text {cell }}^{0}-\frac{0.06}{2} \log \frac{\left[\mathrm{Cu}^{2+}\right]}{\left[\mathrm{Ag}^{+}\right]^{2}} \\ & 0.43=\mathrm{E}_{\text {cell }}^{0}-\frac{0.06}{2} \log \left(\frac{10^{-3}}{\left(10^{-2}\right)^{2}}\right) \\ & 0.43=E_{\text {cell }}^{0}-0.03 \log 10 \\ & \mathrm{E}_{\text {cell }}^{0}=0.46 \mathrm{~V} \\ & \mathrm{E}_{\text {cell }}^{0}=\mathrm{E}_{\mathrm{Ag}^{+} / \mathrm{Ag}}^{0}-\mathrm{E}_{\mathrm{Cu}^{2+} / \mathrm{Cu}}^{0} \\ & \mathrm{E}_{\mathrm{Cu}^{2+} / \mathrm{Cu}}^{0}=(0.80-0.46)=0.34 \mathrm{~V}=34 \times 10^{-2} \end{aligned} $$