A solution of nonvolatile solute is obtained by dissolving $15 \mathrm{~g}$ in $200 \mathrm{~mL}$ water has…

A solution of nonvolatile solute is obtained by dissolving $15 \mathrm{~g}$ in $200 \mathrm{~mL}$ water has depression in freezing point $0.75 \mathrm{~K}$. Calculate the molar mass of solute if cryoscopic constant of water is $1.86 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$.
  1. $160 \mathrm{~g} \mathrm{~mol}^{-1}$
  2. $172 \mathrm{~g} \mathrm{~mol}^{-1}$
  3. $186 \mathrm{~g} \mathrm{~mol}^{-1}$
  4. $198 \mathrm{~g} \mathrm{~mol}^{-1}$

Solution

$\begin{aligned} \mathrm{M}_2 & =\frac{1000 \mathrm{~K}_{\mathrm{f}} \mathrm{W}_2}{\Delta \mathrm{T}_{\mathrm{f}} \mathrm{W}_1} \\ & =\frac{1000 \times 1.86 \times 15}{0.75 \times 200} \\ & =186 \mathrm{~g} \mathrm{~mol}^{-1}\end{aligned}$

Asked in: MHT CET 2023 (14 May Shift 2)

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