The free energy change (ΔG) is related to the emf of the cell (E) by the relation
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( \Delta G=-nFE_{\mathrm{cell}} \)
In a galvanic cell, the chemical energy released by the reaction is converted into electrical work. The maximum electrical work equals the charge passed × the emf:
If n moles of electrons flow, the charge is nF (F = 96500 C mol−1).
Electrical work done by the cell = nFEcell.
This useful work equals the decrease in Gibbs energy, −ΔG.
\( \displaystyle -\Delta G=nFE_{\mathrm{cell}}\quad\Rightarrow\quad\Delta G=-nFE_{\mathrm{cell}} \)
A positive Ecell gives a negative ΔG, i.e. a spontaneous cell reaction. Under standard conditions the same relation reads ΔG° = −nFE°cell.
Why the other options are incorrect
Option (1) \( \Delta G=-2.303nFE_{\mathrm{cell}}^{\circ} \) — Incorrect. The factor 2.303 appears only when ln is converted to log (as in the Nernst equation); it has no place in ΔG = −nFE.
Option (3) \( \Delta G=-RT\ln E \) — Incorrect. The logarithmic relation is ΔG° = −RT ln K, which uses the equilibrium constant K, not the emf.
Option (4) \( \Delta G=\frac{-nF}{RT\ln E} \) — Incorrect. ΔG is directly proportional to E (ΔG = −nFE); this expression puts E inside a logarithm in the denominator, which has no basis.
NCERT (2026-27 edition):
Electrochemical Cell and Gibbs Energy of the Reaction
