For a cell with the reaction, 2Ag+ + Cu → 2Ag + Cu2+ the standard cell potential is +0.46 V at 25°C. The value of standard Gibbs energy is
(F = 96500 C mol−1)
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → −89 kJ mol−1
The standard Gibbs energy of a cell reaction is related to its standard cell potential by:
\( \displaystyle \Delta G^{\circ}=-nFE^{\circ}_{\mathrm{cell}} \)
Here n is the number of electrons transferred in the balanced cell reaction and F is the Faraday constant. A positive E° gives a negative ΔG°, so the reaction is spontaneous.
In \( \ce{2Ag^{+}} \) + Cu → 2Ag + \( \ce{Cu^{2+}} \), copper goes from 0 to +2 and loses 2 electrons, which are taken up by the two \( \ce{Ag^{+}} \) ions (one each). So n = 2.
\( \displaystyle \Delta G^{\circ}=-2\times96500\times0.46 \)
\( \displaystyle \Delta G^{\circ}=-88780\ \mathrm{J\,mol^{-1}}=-88.78\ \mathrm{kJ\,mol^{-1}}\approx-89\ \mathrm{kJ\,mol^{-1}} \)
Shortcut: E° is positive, so ΔG° must be negative, which removes Option (3). Then 2 × 96.5 × 0.46 ≈ 89.