A sample of an unknown polymer weighing 0.0200 g is dissolved in 100.0 mL of water at 298 K. The osmotic pressure of the resulting solution is 0.120 atm. Assuming the solution behaves ideally, calculate the molar mass of the polymer.

Step-by-step solution

1. Use the ideal solution equation: $pi=CRT$, where $pi$ is osmotic pressure, $C$ molar concentration, $R=0.082057\mathrm{Latm}{\mathrm{K}}^{-1}\mathrm{mo}{\mathrm{l}}^{-1}$, $T=298\mathrm{K}$.
2. Calculate the molar concentration: $C=\frac{\pi }{RT}=\frac{0.120\mathrm{atm}}{0.082057\times 298\mathrm{K}}=0.00491\mathrm{mol}{\mathrm{L}}^{-1}$.
3. Find the moles of polymer in the solution: $n=C\times V$, where $V=0.100\mathrm{L}$, giving $n=0.00491\times 0.100=0.000491\mathrm{mol}$.
4. Compute the molar mass: $M=\frac{\text{mass of polymer}}{n}=\frac{0.0200\mathrm{g}}{0.000491\mathrm{mol}}=40.75\mathrm{gmo}{\mathrm{l}}^{-1}$.
5. Round to three significant figures: $40.8g/mol$.

Concept tested: Osmotic pressure and molar mass

Published 10 September 2026 · Last updated 16 September 2026 · How this solution was prepared and checked