Standard cell potential and equilibrium constant

The relation between the standard Gibbs energy change of a cell reaction and the standard cell potential is given by Eq. (5.28): $-\Delta G^0 = nFE^0_{cell}$.

The relation between the standard Gibbs energy change of a chemical reaction and its equilibrium constant, as given in thermodynamics, is

Combining Eq. (5.28) and Eq. (5.29), we have $-nFE^0_{cell} = -RT\,\ln K$, or

$E^0_{cell} = \frac{RT}{nF}\,\ln K = \frac{2.303\,RT}{nF}\,\log_{10}K = \frac{0.0592}{n}\,\log_{10}K \;\;\text{at } 25\,^0\mathrm{C} \qquad \text{...(5.29)}$ …