Question

Cell constant is equal to:

• A. Conductivity \(\times\) Resistance
• B. Conductivity / Resistance
• C. \(\frac{1}{A}\)
• D. (A) and (C) both

Hint:

For cell constant:
- \(G^* = \frac{l}{A}\), measured in \(\mathrm{cm}^{-1}\).
- Relates to conductivity via \(G^* = \kappa \cdot R\).
- Check units to verify relationships.

Answer 1

The Correct Option is A

The cell constant (\(G^*\)) of an electrolytic cell is defined as the ratio of the distance between electrodes (\(l\)) to the cross-sectional area of the electrodes (\(A\)): \[ G^* = \frac{l}{A} \] It has units of \(\mathrm{cm}^{-1}\) or \(\mathrm{m}^{-1}\).
Step 1: Relate to conductivity and resistance
- Conductivity (\(\kappa\)): Measures a solution’s ability to conduct electricity (\(\mathrm{S \, cm}^{-1}\)).
- Resistance (\(R\)): Measured in ohms (\(\Omega\)).
- Conductance (\(G\)): Inverse of resistance, \(G = \frac{1}{R}\), in siemens (\(\mathrm{S}\)).
The relationship is: \[ \kappa = G \cdot \frac{l}{A} = \frac{1}{R} \cdot G^* \] \[ G^* = \kappa \cdot R \] Thus, cell constant equals conductivity times resistance.
Step 2: Analyze options
- (A) Conductivity \(\times\) Resistance: Correct, as \(G^* = \kappa \cdot R\).
- (B) Conductivity / Resistance: Incorrect, as \(\kappa / R = \frac{\kappa}{R}\), which has different units.
- (C) \(\frac{1}{A}\): Incorrect, as \(G^* = \frac{l}{A}\), not \(\frac{1}{A}\).
- (D) (A) and (C): Incorrect, as (C) is wrong.
Step 3: Conclusion
Option (A) is correct, but since the question implies a single correct answer and option (D) incorrectly pairs (A) and (C), we note that (A) is the most accurate.