Question

Calculate the dissociation constant of a weak monobasic acid if it is 0.04% dissociated in a 0.01M solution.

• A. \(2.4\times 10^{-9}\)
• B. \(1.2\times 10^{-9}\)
• C. \(2.0\times 10^{-9}\)
• D. \(1.6\times 10^{-9}\)

Hint:

Convert the percentage dissociation to a fraction and use Ostwald's dilution law, K = C times alpha squared.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept
For a weak acid with small dissociation, Ostwald's dilution law gives \(K_{a} = C\alpha^{2}\).

Step 2: Find alpha
\(\alpha = \dfrac{0.04}{100} = 4\times 10^{-4}\).

Step 3: Calculation
\(K_{a} = 0.01\times (4\times 10^{-4})^{2} = 0.01\times 1.6\times 10^{-7} = 1.6\times 10^{-9}\).

Final Answer:
The dissociation constant is 1.6 times 10 to the power minus 9. \[ \boxed{\text{(D) }1.6\times 10^{-9}} \]