Q16 / 75 · JEE Main 2025 (28 Jan Shift 1) · Chemistry

What is the freezing point depression constant of a solvent, 50 g of which contain 1 g non volatile solute (molar mass $256 \mathrm{~g} \mathrm{~mol}^{-1}$ ) and the decrease in freezing point is 0.40 K ?

  • A
    $3.72 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$
  • B
    $1.86 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$
  • C
    $4.43 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$
  • Correct answer
    D
    $5.12 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$

Solution

$\begin{aligned} \Delta \mathrm{T}_{\mathrm{f}} & =\mathrm{K}_{\mathrm{b}} \cdot \mathrm{m} \\ 0.4 & =\mathrm{K}_{\mathrm{b}} \frac{\frac{1}{256}}{50 \times 10^{-3}} \\ \mathrm{~K}_{\mathrm{b}} & =5.12 \mathrm{~K} \mathrm{~kg} / \mathrm{mol}\end{aligned}$

Hence, the correct answer is option: 'D'.

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