The cell emf depends on:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Temperature
The emf of a cell is given by the Nernst equation. For a cell reaction with reaction quotient Q:
\( \displaystyle E_{\text{cell}} = E^{\circ}_{\text{cell}} - \frac{2.303\,RT}{nF}\log Q \)
The emf therefore depends on the nature of the electrodes and the reaction (through \( E^{\circ}_{\text{cell}} \) and n), on the concentrations of the ions (through Q) and on the temperature, which appears directly in the equation (and \( E^{\circ} \) itself changes with temperature). Emf is an intensive property: it does not depend on how much material the cell contains. So of the options, the emf depends on temperature.
Why the other options are incorrect
Option (1) Size of anode — Incorrect. A larger anode can supply current for longer (more capacity), but the potential difference stays the same.
Option (2) Size of cathode — Incorrect. For the same reason, the size of the cathode changes only the amount of reaction possible, not the emf.
Option (4) Volume of electrolytic solution — Incorrect. A larger volume at the same concentration gives the same Q, so the emf is unchanged; only the concentration enters the Nernst equation.