Calculate the depression in freezing point of solution when $4 \mathrm{~g}$ nonvolatile solute of molar mass…

Calculate the depression in freezing point of solution when $4 \mathrm{~g}$ nonvolatile solute of molar mass $126 \mathrm{~g} \mathrm{~mol}^{-1}$ dissolved in $80 \mathrm{~mL}$ water. $\left[\right.$ Cryoscopic constant of water $\left.=1.86 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\right]$
  1. $0.55 \mathrm{~K}$
  2. $0.74 \mathrm{~K}$
  3. $0.86 \mathrm{~K}$
  4. $0.96 \mathrm{~K}$

Solution

$\begin{aligned} & 80 \mathrm{~mL} \text { water }=80 \mathrm{~g} \text { water (Density of water }= \\ & 1 \mathrm{~g} / \mathrm{mL} \text { ) } \\ & \Delta \mathrm{T}_{\mathrm{f}}=\frac{1000 \mathrm{~K}_{\mathrm{f}} \mathrm{W}_2}{\mathrm{M}_2 \mathrm{~W}_1} \\ & =\frac{1000 \mathrm{~g} \mathrm{~kg}^{-1} \times 1.86 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1} \times 4 \mathrm{~g}}{126 \mathrm{~g} \mathrm{~mol}^{-1} \times 80 \mathrm{~g}} \\ & =0.74 \mathrm{~K} \\ & \end{aligned}$

Asked in: MHT CET 2023 (14 May Shift 1)

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