For a $\mathrm{Mg}\left|\mathrm{Mg}^{2+}(\mathrm{aq}) \| \mathrm{Ag}^{+}(\mathrm{aq})\right| \mathrm{Ag}$ the correct Nernst Equation is :

(B) $\mathrm{E}_{\text {cell }}=\mathrm{E}_{\text {cell }}^{\mathrm{o}}+\frac{\mathrm{RT}}{2 \mathrm{~F}} \ln \frac{\left[\mathrm{Ag}^{+}\right]^{2}}{\left[\mathrm{Mg}^{2+}\right]}$

(A) $\mathrm{E}_{\text {cell }}=\mathrm{E}_{\text {cell }}^{\mathrm{o}}-\frac{\mathrm{RT}}{2 \mathrm{~F}} \ln \frac{\left[\mathrm{Ag}^{+}\right]}{\left[\mathrm{Mg}^{2+}\right]}$

(C) $\mathrm{E}_{\text {cell }}=\mathrm{E}_{\text {cell }}^{\mathrm{o}}-\frac{\mathrm{RT}}{2 \mathrm{~F}} \ln \frac{\left[\mathrm{Mg}^{2+}\right]}{\left[\mathrm{Ag}^{+}\right]}$

(D) $\mathrm{E}_{\text {cell }}=\mathrm{E}_{\text {cell }}^{\mathrm{o}}-\frac{\mathrm{RT}}{2 \mathrm{~F}} \ln \frac{\left[\mathrm{Ag}^{+}\right]^{2}}{\left[\mathrm{Mg}^{2+}\right]}$

JEE Main · 2025 · 29 Jan 2025 · Shift 1 · Redox Reactions and Electrochemistry

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For a

Mg Mg^{2 +} (aq) ∥ Ag^{+} (aq) Ag

the correct Nernst Equation is :

(A) $E_{cell} = E_{cell}^{o} - \frac{RT}{2 F} ln \frac{[ Ag ^{+} ]}{[ Mg ^{2 +} ]}$
(B) $E_{cell} = E_{cell}^{o} + \frac{RT}{2 F} ln \frac{[ Ag ^{+} ] ^{2}}{[ Mg ^{2 +} ]}$ ✓ Correct
(C) $E_{cell} = E_{cell}^{o} - \frac{RT}{2 F} ln \frac{[ Mg ^{2 +} ]}{[ Ag ^{+} ]}$
(D) $E_{cell} = E_{cell}^{o} - \frac{RT}{2 F} ln \frac{[ Ag ^{+} ] ^{2}}{[ Mg ^{2 +} ]}$

Answer: (B)

Solution

The cell

Mg ∣ Mg^{2 +} (a q) ∥ Ag^{+} (a q) ∣ Ag

runs the overall reaction

Mg_{(s)} + 2 Ag_{(a q)}^{+} \to Mg_{(a q)}^{2 +} + 2 Ag_{(s)}

with

n = 2

electrons transferred. The Nernst equation reads

E_{cell} = E_{cell}^{\circ} - \frac{R T}{2 F} ln \frac{[ Mg ^{2 +} ]}{[ Ag ^{+} ] ^{2}}

which, on flipping the ratio inside the logarithm, is the same as

E_{cell} = E_{cell}^{\circ} + \frac{R T}{2 F} ln \frac{[ Ag ^{+} ] ^{2}}{[ Mg ^{2 +} ]}

JEE Main · 2025 · 29 Jan 2025 · Shift 1 · Single correct option

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JEE Main · 2025 · 29 Jan 2025 · Shift 1 · Redox Reactions and Electrochemistry

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