Question

Calculate the cryoscopic constant of solvent if depression in freezing point of 0.4 m solution of nonvolatile solute is 1.8 K .

• A. \( 4.0\text{ K kg mol}^{-1} \)
• B. \( 4.5\text{ K kg mol}^{-1} \)
• C. \( 5.1\text{ K kg mol}^{-1} \)
• D. \( 5.7\text{ K kg mol}^{-1} \)

Hint:

$K_f = \Delta T_f / m$. Cryoscopic constant is independent of the solute type, only dependent on the solvent.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
Cryoscopic constant (\( K_{f} \)) is the proportionality constant in the equation for depression in freezing point (\( \Delta T_{f} \)).
Step 2: Key Formula or Approach:
\[ \Delta T_{f} = K_{f} \cdot m \]
Where \( m \) is the molality of the solution.
Step 3: Detailed Explanation:
Given:
\( \Delta T_{f} = 1.8 \text{ K} \)
\( m = 0.4 \text{ m} \) (molal)
Rearranging the formula to find \( K_{f} \):
\[ K_{f} = \frac{\Delta T_{f}}{m} \]
\[ K_{f} = \frac{1.8}{0.4} \]
\[ K_{f} = \frac{18}{4} = 4.5 \text{ K kg mol}^{-1} \]
Step 4: Final Answer:
The cryoscopic constant of the solvent is \( 4.5\text{ K kg mol}^{-1} \).