For the cell \( \mathrm{Zn(s)|Zn^{2+}(aq)||Ag^{+}(aq)|Ag(s)} \), the correct Nernst equation is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( \displaystyle \mathrm{E_{cell}=E^{o}_{cell}+\frac{RT}{2F}\ln\frac{[Ag^{+}]^{2}}{[Zn^{2+}]}} \)
For a cell reaction, the Nernst equation is written from the balanced equation, with the reaction quotient Q = [products]/[reactants] (solids are taken as 1):
\( \displaystyle E_{cell}=E^{o}_{cell}-\frac{RT}{nF}\ln Q \)
Each concentration is raised to the power of its coefficient.
In this cell zinc is the anode and silver the cathode:
\( \displaystyle \text{Anode: }\ce{Zn -> Zn^2+ + 2e^-} \)
\( \displaystyle \text{Cathode: }\ce{2Ag^+ + 2e^- -> 2Ag} \)
\( \displaystyle \text{Cell: }\ce{Zn + 2Ag^+ -> Zn^2+ + 2Ag},\quad n=2 \)
So:
\( \displaystyle E_{cell}=E^{o}_{cell}-\frac{RT}{2F}\ln\frac{[\ce{Zn^2+}]}{[\ce{Ag^+}]^2} \)
Since −ln(a/b) = +ln(b/a), this is the same as:
\( \displaystyle E_{cell}=E^{o}_{cell}+\frac{RT}{2F}\ln\frac{[\ce{Ag^+}]^2}{[\ce{Zn^2+}]} \)
This is Option (2).
Why the other options are incorrect
Option (1) — Incorrect. The ratio is the right way up for a minus sign, but \( \ce{[Ag^{+}]} \) is not squared. Two \( \ce{Ag^{+}} \) ions take part in the balanced reaction.
Option (3) — Incorrect. With a minus sign the ratio must be products over reactants; here it is inverted, and the square on \( \ce{[Ag^{+}]} \) is also missing.
Option (4) — Incorrect. The square is correct, but the ratio [Ag+]2/\( \ce{[Zn^{2+}]} \) needs a plus sign. With a minus sign, Ecell would wrongly fall when \( \ce{[Ag^{+}]} \) increases.
NCERT (2026-27 edition):
Nernst Equation – …
Note: The same/similar question has been asked in different years by NTA as per the details given below:
| 2026 | 2025 | 2024 | 2023 | 2022 |
|---|---|---|---|---|
| 14-05 S2 | 21-05 S1 | – | – | – |