Calculate the molar mass of solute in a solution prepared by dissolving 1 gram in $0.3 \mathrm{dm}^3$…

Calculate the molar mass of solute in a solution prepared by dissolving 1 gram in $0.3 \mathrm{dm}^3$ solvent having osmotic pressure 0.2 atm at 300 K. $\left[\mathrm{R}=0.082 \mathrm{dm}^3 \mathrm{~atm} \mathrm{~K} \mathrm{~mol}^{-1}\right]$
  1. $\quad 442 \mathrm{~g} \mathrm{~mol}^{-1}$
  2. $372 \mathrm{~g} \mathrm{~mol}^{-1}$
  3. $390 \mathrm{~g} \mathrm{~mol}^{-1}$
  4. $\quad 410 \mathrm{~g} \mathrm{~mol}^{-1}$

Solution

$\begin{aligned} \mathrm{M}_2 & =\frac{\mathrm{W}_2 \mathrm{RT}}{\pi \mathrm{V}} \\ & =\frac{1 \mathrm{~g} \times 0.0821 \mathrm{dm}^3 \mathrm{atmK}^{-1} \mathrm{~mol}^{-1} \times 300 \mathrm{~K}}{0.2 \mathrm{~atm} \times 0.3 \mathrm{dm}^3} \\ & =410 \mathrm{~g} \mathrm{~mol}^{-1}\end{aligned}$

Asked in: MHT CET 2024 (09 May Shift 2)

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