What is the molar mass of solute if a solution is prepared by dissolving 4.5 gram solute in $3…

What is the molar mass of solute if a solution is prepared by dissolving 4.5 gram solute in $3 \mathrm{dm}^3$ water having osmotic pressure $0.25 \mathrm{~atm}$ at $300 \mathrm{~K}$ ? $\left(\mathrm{R}=0.0821 \mathrm{dm}^3 \mathrm{~atm} \mathrm{~K} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\right)$
  1. $148 \mathrm{~g} \mathrm{~mol}^{-1}$
  2. $160 \mathrm{~g} \mathrm{~mol}^{-1}$
  3. $172 \mathrm{~g} \mathrm{~mol}^{-1}$
  4. $136 \mathrm{~g} \mathrm{~mol}^{-1}$

Solution

$\pi=\mathrm{CRT}$ $0.25=\frac{4.5}{\mathrm{M}_{\mathrm{B}}} \times \frac{1000}{3000} \times 0.0821 \times 300$ $\mathrm{M}_{\mathrm{B}}=147.78 \mathrm{~g} / \mathrm{mol}$

Asked in: MHT CET 2022 (08 Aug Shift 2)

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