Calculate molar mass of a solute at 300 K if 400 mg of it is dissolved in 300 mL of water exerts osmotic…

Calculate molar mass of a solute at 300 K if 400 mg of it is dissolved in 300 mL of water exerts osmotic pressure of 0.2 atm . $\left(\mathrm{R}=0.0821 \mathrm{~L} \mathrm{~atm} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\right)$
  1. $90 \mathrm{~g} \mathrm{~mol}^{-1}$
  2. $120 \mathrm{~g} \mathrm{~mol}^{-1}$
  3. $164 \mathrm{~g} \mathrm{~mol}^{-1}$
  4. $180 \mathrm{~g} \mathrm{~mol}^{-1}$

Solution

$\begin{aligned} \mathrm{M}_2 & =\frac{\mathrm{W}_2 \mathrm{RT}}{\pi \mathrm{V}} \\ & =\frac{0.4 \mathrm{~g} \times 0.0821 \mathrm{dm}^3 \mathrm{atmK}^{-1} \mathrm{~mol}^{-1} \times 300 \mathrm{~K}}{0.2 \mathrm{~atm} \times 0.3 \mathrm{dm}^3} \\ & =164.2 \mathrm{~g} \mathrm{~mol}^{-1} \approx 164 \mathrm{~g} \mathrm{~mol}^{-1}\end{aligned}$

Asked in: MHT CET 2024 (15 May Shift 2)

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