What is cryoscopic constant of water if $5 \mathrm{~g}$ of glucose in $100 \mathrm{~g}$ of water has…

What is cryoscopic constant of water if $5 \mathrm{~g}$ of glucose in $100 \mathrm{~g}$ of water has depression in freezing point $2.15 \mathrm{~K}$ ? (Molar mass of glucose $=180$ )
  1. $7.74 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$
  2. $0.52 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$
  3. $1.32 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$
  4. $3.86 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$

Solution

$\begin{aligned} & \Delta \mathrm{T}_{\mathrm{f}}=\mathrm{kf} \cdot \mathrm{m} \\ & \mathrm{m}(\text { molality })=\frac{\text { moles of glucose }}{\text { massof water }(\mathrm{kg})} \\ & \mathrm{m}=\frac{5 / 180}{0.1 \mathrm{~kg}}=\frac{5}{18} \mathrm{~mol} / \mathrm{kg} \\ & \Delta \mathrm{T}_{\mathrm{f}}=2.15 \mathrm{~K} \\ & 2.15=\mathrm{K}_{\mathrm{f}} \cdot \frac{5}{18} \\ & \mathrm{~K}_{\mathrm{f}}=7.74 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}\end{aligned}$

Asked in: MHT CET 2021 (20 Sep Shift 1)

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