The standard potential of the cell $(E_{cell}^θ)$ is related to the equilibrium constant ($K_C$) as

$E_{cell}^θ=\frac{2.303\,RT}{nF}\log K_C$

The correct answer is Option (4) → $E_{cell}^θ=\frac{2.303\,RT}{nF}\log K_C$

The relation between standard cell potential (E°cell) and equilibrium constant (Kc) is derived from the Nernst equation at equilibrium:

$\Delta G^\circ = -RT \ln K_c \quad \text{and} \quad \Delta G^\circ = -n F E^\circ_\text{cell}$

$-n F E^\circ_\text{cell} = -RT \ln K_c$

$E^\circ_\text{cell} = \frac{RT}{nF} \ln K_c$

Converting $\ln$ to $\log_{10}$​:

$E^\circ_\text{cell} = \frac{2.303 RT}{nF} \log K_c$