Question

Calculate cryoscopic constant of solvent if depression in freezing point of 0.18 m solution of nonvolatile solute is 0.2 K

• A. 1.73 K $kg~mol^{-1}$
• B. 1.50 K $kg~mol^{-1}$
• C. 1.11 K $kg~mol^{-1}$
• D. 1.92 K $kg~mol^{-1}$

Hint:

Cryoscopic constant ($K_f$) is the depression in freezing point for 1 molal solution.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The question asks for the cryoscopic constant (\( K_f \)) using the formula for freezing point depression.

Step 2: Key Formula or Approach:
\[ \Delta T_f = K_f \times m \]
where \( \Delta T_f \) is the freezing point depression and \( m \) is molality.

Step 3: Detailed Explanation:
Given: \( \Delta T_f = 0.2 \text{ K} \) and \( m = 0.18 \text{ m} \).
\[ K_f = \frac{\Delta T_f}{m} = \frac{0.2}{0.18} \]
\[ K_f = \frac{20}{18} = \frac{10}{9} \approx 1.111 \text{ K kg mol}^{-1} . \]

Step 4: Final Answer:
The cryoscopic constant is \( 1.11 \text{ K kg mol}^{-1} \).