Calculate the cryoscopic constant of solvent when 2.5 gram solute is dissolved in 35 gram solvent lowers its…

Calculate the cryoscopic constant of solvent when 2.5 gram solute is dissolved in 35 gram solvent lowers its freezing point by 3 K . (molar mass of solute is $117 \mathrm{~g} \mathrm{~mol}^{-1}$ )
  1. $3.11 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$
  2. $3.56 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$
  3. $5.52 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$
  4. $\quad 4.91 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$

Solution

$\begin{aligned} & \Delta \mathrm{T}_{\mathrm{f}}=\frac{1000 \mathrm{~K}_{\mathrm{f}} \mathrm{~W}_2}{\mathrm{M}_2 \mathrm{~W}_1} \\ & \mathrm{~K}_{\mathrm{f}}=\frac{\Delta \mathrm{T}_{\mathrm{f}} \times \mathrm{M}_2 \times \mathrm{W}_{\mathrm{i}}}{1000 \times \mathrm{W}_2} \\ & =\frac{3 \mathrm{~K} \times 117 \mathrm{~g} \mathrm{~mol}^{-1} \times 35 \mathrm{~g}}{1000 \mathrm{gkg}^{-1} \times 2.5 \mathrm{~g}} \\ & =4.91 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1} \end{aligned}$

Asked in: MHT CET 2024 (09 May Shift 1)

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