Find the depression in freezing point of solution when 3.2 gram non volatile solute with molar mass $128…

Find the depression in freezing point of solution when 3.2 gram non volatile solute with molar mass $128 \mathrm{gram} \mathrm{mol}^{-1}$ is dissolved in 80 gram solvent if cryoscopic constant of solvent is $4.8 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$.
  1. $3.0 \mathrm{~K}$
  2. $1.5 \mathrm{~K}$
  3. $2.0 \mathrm{~K}$
  4. $2.5 \mathrm{~K}$

Solution

$\begin{aligned} \Delta \mathrm{T}_{\mathrm{f}} & =\frac{1000 \mathrm{~K}_{\mathrm{f}} \mathrm{W}_2}{\mathrm{M}_2 \mathrm{~W}_1} \\ & =\frac{1000 \mathrm{~g} \mathrm{~kg}^{-1} \times 4.8 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1} \times 3.2 \mathrm{~g}}{128 \mathrm{~g} \mathrm{~mol}^{-1} \times 80 \mathrm{~g}} \\ & =1.5 \mathrm{~K}\end{aligned}$

Asked in: MHT CET 2023 (10 May Shift 1)

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