The standard equilibrium constant of the reaction

$2{\mathrm{Cu}}^{+}\left(\mathrm{aq}\right)\rightleftharpoons {\mathrm{Cu}}^{2+}\left(\mathrm{aq}\right)+\mathrm{Cu}\left(\mathrm{s}\right)$

is about [Given: $\left.E^{\circ }\left({\mathrm{Cu}}^{+}\mid \mathrm{Cu}\right)=0.53\mathrm{V}\text{ and }{E}^{\circ }\left({\mathrm{Cu}}^{2+}\mid \mathrm{Cu}\right)=0.34\mathrm{V}\right]$

Consider the cell

$\mathrm{Cu}\left(\mathrm{s}\right)\left|{\mathrm{Cu}}^{2+}\left(1\mathrm{M}\right)\right|\left|{\mathrm{Cu}}^{+}\left(1\mathrm{M}\right)\right|\mathrm{Cu}$

The cell reaction is

$\begin{array}{l}\text{ RHC }\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}{\mathrm{Cu}}^{+}+{\mathrm{e}}^{-}\to \mathrm{Cu}\\ LHC\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\mathrm{Cu}\to {\mathrm{Cu}}^{2+}+2{\mathrm{e}}^{-}\\ \text{Cell reaction }\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}2{\mathrm{Cu}}^{+}\to \mathrm{Cu}+{\mathrm{Cu}}^{2+}\\ \text{ Cell potential }\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}{E}_{\mathrm{cell}}^{\circ }=E^{\circ }{\mathrm{Cu}}^{+}\mid {\mathrm{Cu}}^{-}-E_{{\mathrm{Cu}}^{2+}\mid \mathrm{Cu}}^{\circ }\end{array}$

Thus  $E_{\mathrm{cell}}^{\circ }=E_{{\mathrm{Cu}}^{+}\mid \mathrm{Cu}}^{\circ }-E_{{\mathrm{Cu}}^2\mid \mathrm{Cu}}^{\circ }=0.53\mathrm{V}-0.34\mathrm{V}=0.19\mathrm{V}$

$\text{ Finally }-nF{E}_{\mathrm{cell}}^{\circ }=-RT\ln K_{\mathrm{eq}}^{\circ }\text{ or }\log K_{\mathrm{eq}}^{\circ }=\frac{n{E}_{\mathrm{cell}}^{\circ }}{2.303(RT/F)}$

or $\log K_{\mathrm{eq}}^{\circ }=\frac{\left(2\right)\left(0.19\mathrm{V}\right)}{\left(0.059\mathrm{V}\right)}=6.44$

$K_{\text{eq }}^{\circ }={10}^{6.44}=2.76\times {10}^6$