Standard electrode potentials for a few half cells are mentioned below : $\begin{aligned} &…

Standard electrode potentials for a few half cells are mentioned below :
$\begin{aligned}
& \mathrm{E}_{\mathrm{Cu}^{2+} / \mathrm{Cu}}^{\circ}=0.34 \mathrm{~V}, \mathrm{E}_{\mathrm{Zn}^{2+} / \mathrm{Zn}}^{\circ}=-0.76 \mathrm{~V} \\
& \mathrm{E}_{\mathrm{Ag}^{+} / \mathrm{Ag}}^{\circ}=0.80 \mathrm{~V}, \mathrm{E}_{\mathrm{Mg}^{2+} / \mathrm{Mg}}^{\circ}=-2.37 \mathrm{~V}
\end{aligned}$
Which one of the following cells gives the most negative value of $\Delta \mathrm{G}^{\circ}$ ?
  1. $\mathrm{Zn}\left|\mathrm{Zn}^{2+}(1 \mathrm{M})\right|\left|\mathrm{Ag}^{+}(1 \mathrm{M})\right| \mathrm{Ag}$
  2. $\mathrm{Zn}\left|\mathrm{Zn}^{2+}(1 \mathrm{M})\right|\left|\mathrm{Mg}^{2+}(1 \mathrm{M})\right| \mathrm{Mg}$
  3. $\mathrm{Ag}\left|\mathrm{Ag}^{+}(1 \mathrm{M})\right|\left|\mathrm{Mg}^{2+}(1 \mathrm{M})\right| \mathrm{Mg}$
  4. $\mathrm{Cu}\left|\mathrm{Cu}^{2+}(1 \mathrm{M}) \| \mathrm{Ag}^{+}(1 \mathrm{M})\right| \mathrm{Ag}$

Solution

$\begin{gathered}\because \Delta \mathrm{G}^{\circ}=-\mathrm{nFE}^{\circ} \\ \text { Option }(1) \mathrm{E}^{\circ}=0.8+0.76 \\ =1.56 \mathrm{~V} \\ \therefore \Delta \mathrm{G}^{\circ}=-2 \times \mathrm{F} \times 1.56 \\ =-3.12 \mathrm{~V} \\ \text { Option (2) } \mathrm{E}^{\circ}=-2.37+0.76 \\ =-1.61 \mathrm{~V} \\ \therefore \Delta \mathrm{G}^{\circ}=-2 \times \mathrm{F} \times(-1.61) \\ =+3.22 \mathrm{~V} \\ \text { Option (3) } \mathrm{E}^{\circ}=-2.37-0.8 \\ =-3.17 \mathrm{~V} \\ \left.\begin{array}{c}\Delta \mathrm{G}^{\circ}=-2\end{array}\right) \times \mathrm{F} \times(-3.17) \\ =+6.34 \\ \text { Option }(4) \mathrm{E}^{\circ}=0.8-0.34 \\ =0.46 \mathrm{~V} \\ \Delta \mathrm{G}^{\circ}=-2 \times \mathrm{F} \times 0.46 \\ =-0.92 \mathrm{~V}\end{gathered}$

Asked in: JEE Main 2025 (23 Jan Shift 2)

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