Question

\(0.5\) molal aqueous solution of a weak acid (HX) is \(20\%\) ionized. If \(K_{f}\) for water is \(1.86\ \text{K kg mol}^{-1}\) Calculate the lowering in freezing point of the solution.

• A. \(0.56\ \text{K}\)
• B. \(1.12\ \text{K}\)
• C. \(-0.56\ \text{K}\)
• D. \(-1.12\ \text{K}\)

Hint:

Find the van't Hoff factor from the degree of ionisation, then use delta Tf = i Kf m.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
For a weak acid, \(\text{HX}\rightleftharpoons\text{H}^{+}+\text{X}^{-}\), the van't Hoff factor is \(i = 1+\alpha\).

Step 2: Van't Hoff factor
With \(\alpha = 0.20\), \(i = 1.20\).

Step 3: Calculation
\(\Delta T_{f} = i\,K_{f}\,m = 1.20\times1.86\times0.5 = 1.116 \approx 1.12\ \text{K}\).

Final Answer:
The lowering in freezing point is about 1.12 K. \[ \boxed{\text{(B) }1.12\ \text{K}} \]