Question

A weak monobasic acid is \(4\%\) dissociated in \(0.05\) M solution. What is percent dissociation in \(0.1\) M solution ?

• A. \(5.715\%\)
• B. \(8.516\%\)
• C. \(2.828\%\)
• D. \(4.620\%\)

Hint:

Ostwald dilution law: degree of dissociation varies as the square root of 1/c.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
For a weak monobasic acid the degree of dissociation \(\alpha\) is small, so Ostwald's dilution law applies: \(K_a = c\alpha^2\).

Step 2: Key Approach:
\(K_a\) is constant at a given temperature, so \(c_1\alpha_1^2 = c_2\alpha_2^2\), which gives \(\alpha_2 = \alpha_1\sqrt{c_1/c_2}\).

Step 3: Detailed Explanation:
Given \(\alpha_1 = 4\%\) at \(c_1 = 0.05\) M, and the new concentration is \(c_2 = 0.1\) M.
\[ \alpha_2 = 4 \times \sqrt{\frac{0.05}{0.1}} = 4 \times \sqrt{0.5} = 4 \times 0.7071 \]
\[ \alpha_2 = 2.828\% \]
The solution became more concentrated, so the percent dissociation falls.

Step 4: Why the other options are wrong.
Values 5.715%, 8.516% and 4.620% are all larger than or close to 4%. Dissociation of a weak acid decreases when concentration increases, so a higher value like 5.715% or 8.516% cannot be right.

Final Answer:
The percent dissociation becomes \(2.828\%\), option (C). \[ \boxed{2.828\%} \]