Standard electrode potentials for a few half cells are mentioned below:
$\begin{array}{l} E_{{Cu}^{2 +} / Cu}^{0} = 0.34 V, E_{{Zn}^{2 +} / Zn}^{0} = - 0.76 V \\ E_{{Ag}^{\circ} / Ag}^{\circ} = 0.80 V, E_{{Mg}^{2 +} / Mg}^{\circ} = - 2.37 V \end{array}$
Which one of the following cells gives the most negative value of $Δ G^{o}$ ?

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$Zn |{Zn}^{2 +} (1 M) ‖ {Ag}^{+} (1 M)| Ag$

$Zn |{Zn}^{2 +} (1 M)| {Mg}^{2 +} (1 M) ∣ Mg$

$Cu |{Cu}^{2 +} (1 M) ‖ {Ag}^{+} (1 M)| Ag$

$Ag |{Ag}^{+} (1 M)| |{Mg}^{2 +} (1 M)| Mg$

answer is A.

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Detailed Solution

$\begin{array}{l} ∵ {ΔG}^{\circ} = - {nFE}^{\circ} \\ Option (1) E^{\circ} = 0.8 + 0.76 \\ = 1.56 V \\ ∴ {ΔG}^{\circ} = - 2 \times F \times 1.56 \\ = - 3.12 V \\ \begin{array}{l} Option (2) E^{\circ} = - 2.37 + 0.76 \\ = - 1.61 V \\ ∴ {ΔG}^{\circ} = - 2 \times F \times (- 1.61) \\ = + 3.22 V \\ Option (3) E^{\circ} = - 2.37 - 0.8 \\ = - 3.17 V \\ ∴ {ΔG}^{\circ} = - 2 \times F \times (- 3.17) \\ = + 6.34 \\ \begin{array}{l} Option (4) E^{\circ} = 0.8 - 0.34 \\ = 0.46 V \\ {ΔG}^{\circ} = - 2 \times F \times 0.46 \\ = - 0.92 V \end{array} \end{array} \end{array}$