Question

Calculate the molality of the solution of nonvolatile solute if it freezes at $-0.36^{\circ}\text{C}$. [$K_{f}$ for solvent $=1.86\text{ K kg mol}^{-1}$]}

• A. 0.218 $\text{mol kg}^{-1}$
• B. 0.193 $\text{mol kg}^{-1}$
• C. 0.401 $\text{mol kg}^{-1}$
• D. 0.520 $\text{mol kg}^{-1}$

Hint:

Depression in freezing point ($\Delta T_f$) is always a positive magnitude! Just drop the negative sign from the solution's freezing point when plugging it into the equation.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Freezing point depression ($\Delta T_f$) is a colligative property directly proportional to the molality ($m$) of the solution.

Step 2: Formula Application:
$\Delta T_f = K_f \times m$

Step 3: Explanation:
Given: Freezing point of solution = $-0.36^\circ\text{C}$. Assuming solvent is water (f.p. $0^\circ\text{C}$), $\Delta T_f = 0 - (-0.36) = 0.36 \text{ K}$. $0.36 = 1.86 \times m$ $m = \frac{0.36}{1.86} \approx 0.1935 \text{ mol kg}^{-1}$.

Step 4: Final Answer:
The molality is approximately 0.193 mol kg$^{-1}$.