Question

If the concentration of an electrolyte solution decreases, the molar conductivity \( \Lambda_m \) will:

• A. Decrease
• B. Increase
• C. Remain same
• D. Become zero

Hint:

Remember:

• Conductivity \( (\kappa) \) usually \textbf{decreases} on dilution.
• Molar conductivity \( (\Lambda_m) \) \textbf{increases} on dilution.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The question asks about the effect of decreasing the concentration of an electrolyte solution (i.e., dilution) on its molar conductivity (\( \Lambda_m \)).
Step 2: Key Formula or Approach:
We can analyze this from two perspectives: the mathematical formula and the physical behavior of ions in the solution.
The formula is: \( \Lambda_m = \frac{\kappa \times 1000}{C} \).
The physical concept involves ion mobility and the degree of dissociation.
Step 3: Detailed Explanation:
Mathematical Perspective:
The formula \( \Lambda_m \propto \frac{\kappa}{C} \) shows that molar conductivity is inversely related to concentration \( C \). When the solution is diluted, \( C \) decreases. Simultaneously, the conductivity \( \kappa \) (number of ions per unit volume) also decreases. However, the decrease in concentration \( C \) is more pronounced than the decrease in conductivity \( \kappa \), leading to an overall increase in the ratio \( \kappa/C \). Therefore, \( \Lambda_m \) increases.
Physical Perspective:
Molar conductivity is the conducting power of all the ions produced by one mole of an electrolyte.
When we decrease the concentration by adding more solvent (dilution), two main effects occur:
1. Increased Ionic Mobility: The ions in the solution become farther apart. This reduces the inter-ionic forces of attraction, allowing the ions to move more freely towards the electrodes when a voltage is applied. This increased mobility leads to higher molar conductivity.
2. Increased Degree of Dissociation (for weak electrolytes): According to Ostwald's dilution law, the degree of dissociation (\(\alpha\)) of a weak electrolyte increases upon dilution. This means more ions are formed from each mole of the electrolyte, which significantly increases the molar conductivity.
Both effects contribute to an increase in \( \Lambda_m \) as the concentration decreases.
Step 4: Final Answer:
When the concentration of an electrolyte solution decreases, its molar conductivity increases.