Chemistry - Electrochemistry Question with Solution | TestHub

The relationship between standard Gibbs free energy change and standard cell potential is given by:

$\Delta G^{\circ }=-nF{E}_{\text{cell}}^{\circ }$

The relationship between standard Gibbs free energy change and equilibrium constant is:

$\Delta G^{\circ }=-2.303RT{\log }_{10}K$

Equating the two expressions for $\Delta G^{\circ }$:

$-nF{E}_{\text{cell}}^{\circ }=-2.303RT{\log }_{10}K$

$E_{\text{cell}}^{\circ }=\frac{2.303RT}{nF}{\log }_{10}K$

At standard temperature $T=298\text{ K}$, substituting $R=8.314{\text{ J K}}^{-1}{\text{ mol}}^{-1}$ and $F=96500{\text{ C mol}}^{-1}$:

$\frac{2.303\times 8.314\times 298}{96500}\approx 0.0592\text{ V}$

Therefore, the equation becomes:

$E_{\text{cell}}^{\circ }=\frac{0.0592}{n}{\log }_{10}K$

Answer: ${\mathrm{E}}_{\text{cell }}^{\circ }=\frac{0.0592}{\mathrm{n}}{\log }_{10}\mathrm{K}$