Osmotic pressure of 0.02 M urea solution at 27 °C, is (given \( R = 0.0821\, atm\, L\, mol^{-1}\, K^{-1} \))
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 0.4926 atm
Osmotic pressure is a colligative property: it depends on the concentration of solute particles. For a dilute solution it is given by the van’t Hoff equation:
\( \displaystyle \pi = iCRT \)
Urea is a non-electrolyte; it does not dissociate in water, so each molecule gives one particle and i = 1. The temperature must be in kelvin:
\( \displaystyle T = 27 + 273 = 300\,\mathrm{K} \)
Substituting \( C = 0.02\,\mathrm{mol\,L^{-1}} \) and \( R = 0.0821\,\mathrm{atm\,L\,mol^{-1}\,K^{-1}} \):
\( \displaystyle \pi = 1 \times 0.02 \times 0.0821 \times 300 \)
\( \displaystyle \pi = 0.4926\,\mathrm{atm} \)
So the osmotic pressure is 0.4926 atm.
Shortcut: \( 0.02 \times 300 = 6 \), and \( 6 \times 0.0821 = 0.4926 \).