Question

Sol. [Key Concept: Use $\Delta\ G^{\circ}$ additivity ($\Delta\ G_{3} = \Delta\ G_{2} - \Delta\ G_{1}$): $- 1 \cdot \ F \cdot \ E_{{Fe}^{3 +}/{Fe}^{2 +}}^{\circ} = - 3FY - ( - 2FX)$, giving $E_{{Fe}^{3 +}/{Fe}^{2 +}}^{\circ} = 3Y - 2X$.]

(i) $\overline{{Fe}^{+ 2}(aq) + 2e^{-} \rightarrow Fe(s)\ldots\ldots..\Delta G_{1}\ ^{\circ}}$

(ii) ${Fe}^{+ 3}(aq) + 3e^{-} \rightarrow Fe(s)\ldots\ldots..\Delta G_{2}\ ^{\circ}$

(iii) ${Fe}^{+ 3}(aq) + e^{-} \rightarrow {Fe}^{+ 2}(aq)\ldots\ldots\Delta G_{3}\ ^{\circ}$

iii $=$ ii -i

$${- 1 \times F \times E^{\circ}\ _{{Fe}^{3 +}/{Fe}^{2 +}} = - 3 \times F \times y - ( - 2 \times F \times x) }{E^{\circ}\ _{{Fe}^{3 +}/{Fe}^{2 +}} = 3y - 2x }$$Option (2) is correct