A 0.0200 g sample of an unknown solute is dissolved in 50.0 mL of water. The osmotic pressure of the solution measured at 298 K is 0.120 atm. Assuming the solute behaves ideally, calculate its molar mass.

hard 4 marks Class 12 · Chemistry · Solutions

Answer

81.5 g mol⁻¹

The correct answer is 81.5 g mol⁻¹ — Calculate molar mass: $M = \frac{m}{n} = \frac{0.0200 g}{2.45 \times 1 0 ^{- 4} mol} = 81.5 g mol^{- 1}$ .

Step-by-step solution

Write the ideal osmotic pressure equation: $P = \frac{n R T}{V}$ .
Rearrange to find the number of moles: $n = \frac{P V}{R T} = \frac{0.120 atm \times 0.0500 L}{0.0821 L atm mol ^{- 1} K ^{- 1} \times 298 K} = 2.45 \times 1 0^{- 4} mol$ .
Calculate molar mass: $M = \frac{m}{n} = \frac{0.0200 g}{2.45 \times 1 0 ^{- 4} mol} = 81.5 g mol^{- 1}$ .

Common mistake: Using volume of solvent instead of volume of solution in the equation

Concept tested: Osmotic pressure and molar mass

Published 5 September 2026 · Last updated 16 September 2026 · How this solution was prepared and checked