A solution of nonvolatile solute is obtained by dissolving 0.8 g in $0.3 \mathrm{dm}^3$ water has osmotic…

A solution of nonvolatile solute is obtained by dissolving 0.8 g in $0.3 \mathrm{dm}^3$ water has osmotic pressure 0.2 atm at 300 K . Calculate the molar mass of solute. $\left[\mathrm{R}=0.082 \mathrm{~atm} \mathrm{dm}^3 \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\right]$
  1. $\quad 300 \mathrm{~g} \mathrm{~mol}^{-1}$
  2. $340 \mathrm{~g} \mathrm{~mol}^{-1}$
  3. $328 \mathrm{~g} \mathrm{~mol}^{-1}$
  4. $352 \mathrm{~g} \mathrm{~mol}^{-1}$

Solution

$\begin{aligned} \mathrm{M}_2 & =\frac{\mathrm{W}_2 \mathrm{RT}}{\pi \mathrm{V}} \\ & =\frac{0.8 \mathrm{~g} \times 0.082 \mathrm{dm}^3 \mathrm{~atm} \mathrm{~K}^{-1} \mathrm{~mol}^{-1} \times 300 \mathrm{~K}}{0.2 \mathrm{~atm} \times 0.3 \mathrm{dm}^3} \\ & =328 \mathrm{~g} \mathrm{~mol}^{-1}\end{aligned}$

Asked in: MHT CET 2024 (15 May Shift 1)

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