JEE Advanced 2022 — Paper 1 — Question 36

(i) $\mathrm{MnO}_{4}^{-}($aq $)+8 \mathrm{H}^{+}+7 \mathrm{e}^{-} \longrightarrow \mathrm{Mn}(\mathrm{s})+4 \mathrm{H}_{2} \mathrm{O}(\ell) ; \Delta \mathrm{G}_{1}^{\circ}=-7 \times \mathrm{F} \times \mathrm{E}_{1}^{\circ}$

(ii) $\mathrm{MnO}_{4}^{-}+4 \mathrm{H}^{+}+3 \mathrm{e}^{-} \longrightarrow \mathrm{MnO}_{2}(\mathrm{~s})+2 \mathrm{H}_{2} \mathrm{O}(\ell) ; \Delta \mathrm{G}_{2}^{\circ}=-3 \times \mathrm{F} \times 1.68$

(iii) $\mathrm{MnO}_{2}(\mathrm{~s})+4 \mathrm{H}^{+}+2 \mathrm{e}^{-} \longrightarrow \mathrm{Mn}^{2+}(\mathrm{aq})+2 \mathrm{H}_{2} \mathrm{O}(\ell) ; \Delta \mathrm{G}_{3}^{\circ}=-2 \times \mathrm{F} \times 1.21$

(iv) $\mathrm{Mn}^{2+}(\mathrm{aq})+2 \mathrm{e}^{-} \longrightarrow \mathrm{Mn}(\mathrm{s}) ; \Delta \mathrm{G}_{4}^{\circ}=-2 \times \mathrm{F} \times(-1.03)$ Now, (i) $=($ ii $)+($ iii $)+(i v)$

$\Delta \mathrm{G}_{1}^{\circ}=\Delta \mathrm{G}_{2}^{\circ}+\Delta \mathrm{G}_{3}^{\circ}+\Delta \mathrm{G}_{4}^{\circ}$

$-7 \times \mathrm{F} \times \mathrm{E}_{1}^{\circ}=-3 \times \mathrm{F} \times 1.68--2 \times \mathrm{F} \times 1.21+2 \times \mathrm{F} \times 1.03$

$-7 \mathrm{E}_{1}^{\circ}=3 \times 1.68+2 \times 1.21-2 \times 1.03$

$\mathrm{E}_{1}^{\circ}=\frac{3 \times 1.68+2 \times 1.21-2 \times 1.03}{7}$

$\mathrm{E}_{1}^{\circ}=\frac{5.04+2.42-2.06}{7}$

$=0.7714$ $=0.77 \mathrm{~V}$