Question

A weak monobasic acid is 10 percent dissociated in 0.05 M solution. What is percent dissociation in 0.15 M solution?

Hint:

For weak electrolytes, dilution increases dissociation but percent dissociation decreases with higher concentration due to \( K_a \) constancy.

Answer 1

For a weak monobasic acid \( HA \rightleftharpoons H^+ + A^- \), the dissociation constant \( K_a = \frac{\alpha^2 C}{1 - \alpha} \), where \( \alpha \) is the degree of dissociation, and \( C \) is concentration.
Step 1: For 0.05 M, \( \alpha = 0.1 \): \[ K_a = \frac{(0.1)^2 \cdot 0.05}{1 - 0.1} = \frac{0.01 \cdot 0.05}{0.9} = \frac{0.0005}{0.9} \approx 5.5556 \times 10^{-4}. \]
Step 2: For 0.15 M, use \( K_a \): \[ 5.5556 \times 10^{-4} = \frac{\alpha^2 \cdot 0.15}{1 - \alpha}. \] Since \( \alpha \) is small, approximate \( 1 - \alpha \approx 1 \): \[ \alpha^2 \cdot 0.15 \approx 5.5556 \times 10^{-4}, \quad \alpha^2 \approx \frac{5.5556 \times 10^{-4}}{0.15} \approx 3.7037 \times 10^{-3}. \] \[ \alpha \approx \sqrt{3.7037 \times 10^{-3}} \approx 0.06086. \] Percent dissociation = \( 0.06086 \times 100 \approx 6.09% \).