Derive an equation for the equilibrium constant $K_C$ of any galvanic cell (redox reaction) and also state its uses.

(N/A) According to the Nernst equation,for any redox reaction at equilibrium,the cell potential $E_{\text{cell}}$ becomes $0.0 \ V$ and the reaction quotient $Q$ becomes equal to the equilibrium constant $K_C$.
The Nernst equation is given by:
$E_{\text{cell}} = E_{\text{cell}}^{o} - \frac{0.059}{n} \log Q$
At equilibrium,$E_{\text{cell}} = 0$ and $Q = K_C$,so:
$0 = E_{\text{cell}}^{o} - \frac{0.059}{n} \log K_C$
Rearranging for $E_{\text{cell}}^{o}$:
$E_{\text{cell}}^{o} = \frac{0.059}{n} \log K_C$
Solving for $\log K_C$:
$\log K_C = \frac{n \times E_{\text{cell}}^{o}}{0.059}$
Thus,$K_C = \text{antilog} \left( \frac{n \times E_{\text{cell}}^{o}}{0.059} \right)$
Where $n$ is the number of electrons exchanged and $E_{\text{cell}}^{o} = E_{\text{cathode}}^{o} - E_{\text{anode}}^{o}$.
Uses:
$(i)$ The equilibrium constant $K_C$ can be calculated by measuring the standard cell potential.
$(ii)$ The magnitude of $K_C$ indicates the extent of the reaction; a high value of $K_C$ implies that the forward reaction is favored,resulting in a higher yield of products.