Q.iv. Equilibrium constant of the reaction, $\mathrm{2Cu^+(aq) \longrightarrow Cu^{2+}(aq) + Cu(s)}$ is 1.2 $\times$ 10$^6$. What is the standard potential of the cell in which the reaction takes place ? (0.36 V)

Electrical work done by a galvanic cell equals charge passed times cell potential, $nFE_{cell}$; Gibbs (1878) identified this with the decrease in Gibbs energy of the cell reaction, giving $\Delta G=-nFE_{cell}$ and, under standard conditions, $\Delta G^0=-nFE^0_{cell}$. Because $\Delta G^0$ is extensive (scales with reaction amount) while $n$ scales identically when the equation is multiplied by any factor, their ratio $E^0_{cell}=-\Delta G^0/nF$ stays constant — proving $E^0_{cell}$ is an intensive property. Since $\Delta G<0$ for spontaneity, $E_{cell}$ must be positive for a spontaneous cell reaction. Combining $\Delta G^0=-nFE^0_{cell}$ with the general thermodynamic relation $\Delta G^0=-RT\ln K$ gives $E^0_{cell}=\dfrac{0.0592}{n …