Q18 / 150 · MHT CET 2026 (13 April Shift 1) · Chemistry
What is the relationship between the degree of dissociation of a weak base and its concentration?
- AThe degree of dissociation of a weak base is directly proportional to square root of its concentration.
- Correct answerBThe degree of dissociation of a weak base is inversely proportional to square root of its concentration.
- CThe degree of dissociation of a weak base doesn't depend on concentration.
- DThe degree of dissociation of a weak base is directly proportional to its concentration
Solution
For a weak base $BOH$, the dissociation reaction is $BOH \rightleftharpoons B^+ + OH^-$.
Let the initial concentration be $C$ and the degree of dissociation be $\alpha$.
At equilibrium, the concentrations are $[BOH] = C(1-\alpha)$, $[B^+] = C\alpha$, and $[OH^-] = C\alpha$.
The base dissociation constant $K_b$ is given by $K_b = \dfrac{[B^+][OH^-]}{[BOH]} = \dfrac{C\alpha \cdot C\alpha}{C(1-\alpha)} = \dfrac{C\alpha^2}{1-\alpha}$.
For a weak base, $\alpha$ is very small compared to $1$, so $1-\alpha \approx 1$.
Thus, $K_b \approx C\alpha^2 \Rightarrow \alpha = \sqrt{\dfrac{K_b}{C}}$.
Therefore, the degree of dissociation of a weak base is inversely proportional to the square root of its concentration.
Answer: The degree of dissociation of a weak base is inversely proportional to square root of its concentration.
Let the initial concentration be $C$ and the degree of dissociation be $\alpha$.
At equilibrium, the concentrations are $[BOH] = C(1-\alpha)$, $[B^+] = C\alpha$, and $[OH^-] = C\alpha$.
The base dissociation constant $K_b$ is given by $K_b = \dfrac{[B^+][OH^-]}{[BOH]} = \dfrac{C\alpha \cdot C\alpha}{C(1-\alpha)} = \dfrac{C\alpha^2}{1-\alpha}$.
For a weak base, $\alpha$ is very small compared to $1$, so $1-\alpha \approx 1$.
Thus, $K_b \approx C\alpha^2 \Rightarrow \alpha = \sqrt{\dfrac{K_b}{C}}$.
Therefore, the degree of dissociation of a weak base is inversely proportional to the square root of its concentration.
Answer: The degree of dissociation of a weak base is inversely proportional to square root of its concentration.
Hence, the correct answer is option: 'B'.