Question

What is the relationship between the degree of dissociation of a weak base and its concentration?

• A. The degree of dissociation of a weak base is directly proportional to square root of its concentration.
• B. The degree of dissociation of a weak base is inversely proportional to square root of its concentration.
• C. The degree of dissociation of a weak base doesn't depend on concentration.
• D. The degree of dissociation of a weak base is directly proportional to its concentration

Hint:

Use Ostwald dilution law: the degree of dissociation varies as the inverse square root of concentration.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
A weak base only partly ionises. How far it ionises depends on its concentration. The more dilute the solution, the larger the fraction of ionised molecules.

Step 2: Key Formula or Approach:
Ostwald dilution law for a weak base BOH of concentration \(C\):
\[ K_b = \frac{C\alpha^2}{1-\alpha} \approx C\alpha^2 \quad (\alpha \ll 1) \]

Step 3: Detailed Explanation:
Solve for \(\alpha\):
\[ \alpha = \sqrt{\frac{K_b}{C}} \]
So \(\alpha \propto \dfrac{1}{\sqrt{C}}\). If the concentration becomes 4 times, \(\alpha\) halves.

Step 4: Why the other options are wrong.
(A) says directly proportional to \(\sqrt{C}\), which is the opposite trend. (C) is wrong because \(\alpha\) clearly changes with dilution. (D) says directly proportional to \(C\), again the wrong direction.

Final Answer:
The degree of dissociation is inversely proportional to the square root of concentration, option (B). \[ \boxed{\alpha \propto \frac{1}{\sqrt{C}}} \]