A solution of $5.6 \mathrm{~g}$ nonvolatile solute in $50 \mathrm{~g}$ solvent has elevation in boiling…

A solution of $5.6 \mathrm{~g}$ nonvolatile solute in $50 \mathrm{~g}$ solvent has elevation in boiling point $1.75 \mathrm{~K}$. What is the molar mass of solute $\left(\mathrm{K}_{\mathrm{b}}=3 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\right)$ ?
  1. $192 \mathrm{~g} \mathrm{~mol}^{-1}$
  2. $200 \mathrm{~g} \mathrm{~mol}^{-1}$
  3. $184 \mathrm{~g} \mathrm{~mol}^{-1}$
  4. $176 \mathrm{~g} \mathrm{~mol}^{-1}$

Solution

$\begin{aligned} \mathrm{M}_2 & =\frac{1000 \mathrm{~K}_{\mathrm{b}} \mathrm{W}_2}{\Delta \mathrm{T}_{\mathrm{b}} \mathrm{W}_1} \\ & =\frac{1000 \times 3 \times 5.6}{1.75 \times 50}=192 \mathrm{~g} \mathrm{~mol}^{-1}\end{aligned}$

Asked in: MHT CET 2023 (13 May Shift 1)

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