The osmotic pressure of a solution is 0.0821 atm at 300 K. What is the concentration of the solution in mol L−1? (R = 0.0821 L atm K−1 mol−1)
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 3.3 × 10−3
For a dilute solution the osmotic pressure is proportional to the molar concentration C, so C is found by dividing Π by RT:
\( \displaystyle \Pi=CRT \qquad C=\frac{\Pi}{RT} \)
\( \displaystyle C=\frac{0.0821\,\mathrm{atm}}{0.0821\,\mathrm{L\,atm\,K^{-1}\,mol^{-1}}\times 300\,\mathrm{K}}=\frac{1}{300}\,\mathrm{mol\,L^{-1}} \)
\( \displaystyle C=3.3\times 10^{-3}\,\mathrm{mol\,L^{-1}} \)
The concentration of the solution is 3.3 × 10−3 mol L−1.
NCERT (2026-27 edition):
1.6.4 Osmosis and Osmotic Pressure – “… For dilute solutions, it has been found experimentally that osmotic pressure is proportional to the molarity, C of the solution at a given temperature T. Thus:
\( \displaystyle \Pi=C\,R\,T \qquad (1.39) \)”