Question

Match List - I with List - II :
\[ \begin{array}{llcl} & \text{List - I} & & \text{List - II} \\ \text{(Parameter)} & & \text{(Unit)} \\ (a) & \text{Cell constant} & (i) & \text{S cm}^2 \text{ mol}^{-1} \\ (b) & \text{Molar conductivity} & (ii) & \text{Dimensionless} \\ (c) & \text{Conductivity} & (iii) & \text{m}^{-1} \\ (d) & \text{Degree of dissociation of electrolyte} & (iv) & \Omega^{-1} \text{m}^{-1} \\ \end{array} \]
Choose the most appropriate answer from the options given below :

• A. (a)-(ii), (b)-(i), (c)-(iii), (d)-(iv)
• B. (a)-(iii), (b)-(i), (c)-(iv), (d)-(ii)
• C. (a)-(i), (b)-(iv), (c)-(iii), (d)-(ii)
• D. (a)-(iii), (b)-(i), (c)-(ii), (d)-(iv)

Hint:

Conductivity units: \( \Omega^{-1} \) is also called Siemens (S) or Mho. So \( \Omega^{-1} \text{m}^{-1} \) is the same as \( \text{S m}^{-1} \).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
This question involves matching various electrochemical parameters with their respective SI or common units.
Step 2: Key Formula or Approach:
1. Cell Constant (\( G^* \)) = \( \frac{l}{A} \). Unit = \( \text{m} / \text{m}^2 = \text{m}^{-1} \).
2. Molar Conductivity (\( \Lambda_m \)) = \( \frac{\kappa}{C} \). Unit = \( \text{S cm}^2 \text{ mol}^{-1} \).
3. Conductivity (\( \kappa \)) = \( \frac{1}{\rho} = \frac{G^*}{R} \). Unit = \( \Omega^{-1} \text{ m}^{-1} \) or \( \text{S m}^{-1} \).
4. Degree of dissociation (\( \alpha \)) = Ratio of conductivities. Being a ratio of same physical quantities, it is dimensionless.
Step 3: Detailed Explanation:
- (a) Cell constant is the ratio of distance between electrodes to the cross-sectional area. Its unit is \( \text{m}^{-1} \). Match: (a)-(iii).
- (b) Molar conductivity represents the conducting power of all ions produced by dissolving 1 mole of an electrolyte. Its unit is typically expressed as \( \text{S cm}^2 \text{ mol}^{-1} \). Match: (b)-(i).
- (c) Conductivity (specific conductance) is the reciprocal of resistivity. Its unit is \( \Omega^{-1} \text{ m}^{-1} \). Match: (c)-(iv).
- (d) Degree of dissociation is the fraction of total electrolyte that dissociates into ions. It is a pure number. Match: (d)-(ii).
Step 4: Final Answer:
The correct matching is (a)-(iii), (b)-(i), (c)-(iv), (d)-(ii).