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

(A) $\mathrm{Zn}|\mathrm{Zn}^{2+}(1\,\mathrm{M})||\mathrm{Ag}^{+}(1\,\mathrm{M})|\mathrm{Ag}$

(B) $\mathrm{Zn}|\mathrm{Zn}^{2+}(1\,\mathrm{M})||\mathrm{Mg}^{2+}(1\,\mathrm{M})|\mathrm{Mg}$

(C) $\mathrm{Ag}|\mathrm{Ag}^{+}(1\,\mathrm{M})||\mathrm{Mg}^{2+}(1\,\mathrm{M})|\mathrm{Mg}$

(D) $\mathrm{Cu}|\mathrm{Cu}^{2+}(1\,\mathrm{M})||\mathrm{Ag}^{+}(1\,\mathrm{M})|\mathrm{Ag}$

JEE Main · 2025 · 23 Jan 2025 · Shift 2 · Redox Reactions and Electrochemistry

Standard electrode potentials for a few half cells are mentioned below:

E_{Cu^{2 +} / Cu}^{o} = 0.34 V, E_{Zn^{2 +} / Zn}^{o} = - 0.76 V

E_{Ag^{+} / Ag}^{o} = 0.80 V, E_{Mg^{2 +} / Mg}^{o} = - 2.37 V

Which one of the following cells gives the most negative value of

Δ G^{\circ}

Answer: (A)

For a cell reaction,

Δ G^{\circ} = - n F E_{ce l l}^{\circ}

, so for the same number of electrons transferred, the most negative

Δ G^{\circ}

belongs to the cell with the largest positive

E_{ce l l}^{\circ}

. Pairing

Zn

as anode with

Ag X^{+} / Ag

as cathode gives

E_{ce l l}^{\circ} = 0.80 - (- 0.76) = 1.56 V

, with

n = 2

, so

Δ G^{\circ} = - 2 F (1.56) = - 3.12 F

. The

Zn

–

Mg

cell gives

E^{\circ} = - 1.61 V

(non-spontaneous as written), the

Ag

–

Mg

cell gives

E^{\circ} = - 3.17 V

(also non-spontaneous), and the

Cu

–

Ag

cell gives

E^{\circ} = 0.46 V

Δ G^{\circ} = - 0.92 F

. The cell

Zn ∣ Zn X^{2 +} (1 M) ∣∣ Ag X^{+} (1 M) ∣ Ag

delivers the most negative

Δ G^{\circ}

of the four.

JEE Main · 2025 · 23 Jan 2025 · Shift 2 · Single correct option