JEE Main 2026 Apr 8 Shift 2, Chemistry Q6: Electrochemical Cell And Nernst Equation

Standard potentials are not additive across half-reactions with different electron counts — but the associated Gibbs energies $\Delta G^{\circ }=-nF{E}^{\circ }$ are.

Label the three half-reactions:

(i) ${\mathrm{Fe}}^{2+}+2e^{-}\to \mathrm{Fe}$, $\Delta G_1^{\circ }=-2FX$.

(ii) ${\mathrm{Fe}}^{3+}+3e^{-}\to \mathrm{Fe}$, $\Delta G_2^{\circ }=-3FY$.

(iii) ${\mathrm{Fe}}^{3+}+e^{-}\to {\mathrm{Fe}}^{2+}$, $\Delta G_3^{\circ }=-1\cdot F\cdot E_{{\mathrm{Fe}}^{3+}/{\mathrm{Fe}}^{2+}}^{\circ }$.

Reaction (iii) = (ii) − (i), so $\Delta G_3^{\circ }=\Delta G_2^{\circ }-\Delta G_1^{\circ }$.

$-F\cdot E_{{\mathrm{Fe}}^{3+}/{\mathrm{Fe}}^{2+}}^{\circ }=-3FY-(-2FX)=-3FY+2FX$

$\therefore$ $E_{{\mathrm{Fe}}^{3+}/{\mathrm{Fe}}^{2+}}^{\circ }=3Y-2X$.