Question

When metallic copper is shaken with a solution of a copper salt, the reaction $Cu+{Cu}^{2+}\to 2{Cu}^{+}$ proceeds. When equilibrium is established at $298K$, $\left[{Cu}^{2+}\right]/{\left[{Cu}^{+}\right]}^2=1.66\times {10}^6$ ${\left(mol{dm}^{-3}\right)}^{-1}$. If the standard potential of the ${Cu}^{2+}|Cu$ half-cell is $+0.337V$, what is the standard (reduction) potential of ${Cu}^{+}|Cu$ half cell.

Answer 1

Given reaction

$Cu+C{u}^{+2}\to 2C{u}^{+}$

$K_C=\frac{[C{u}^{+}{]}^2}{\left[C{u}^{+2}\right]}=\frac{1}{2\times {10}^6}=0.5\times {10}^{-6}mold{m}^{-3}$

According to Nernst equation

$E=E_0-\frac{0.059}{n}ln{K}_C$

Where n is the number of electrons

$E=E_0-\frac{0.059}{n}ln{K}_C$

$E=E_0-\frac{0.059}{2}ln(0.5\times {10}^{-6})$

$E=0.337-\frac{0.059}{2}(ln0.5+ln{10}^{-6})$

$E=0.337-(\frac{0.059\times (-0.69)}{2}-\frac{6\times 0.059}{2})$

$E=0.337+0.02+0.15=0.507$V