QuestionSolutions / colligative relations
Which one of the following equations represents the correct relation between relative lowering in vapour pressure and osmotic pressure (π) for a dilute aqueous solution?
- (a) \(\frac{\Delta P}{P^0} = \frac{\pi \bar{V}}{RT}\)
- (b) \(\frac{\Delta P}{P^0} = \frac{\pi RT}{\bar{V}}\)
- (c) \(\frac{\Delta P}{P^0} = \frac{\pi R}{T\bar{V}}\)
- (d) \(\frac{\Delta P}{P^0} = \pi RT\)
Answer: (a) \(\frac{\Delta P}{P^0} = \frac{\pi \bar{V}}{RT}\)
Dilute solution: ΔP/P° = x₂ ≈ n₂/n₁. Osmotic pressure π = n₂RT/V with V ≈ n₁V̄ (V̄ = molar volume of solvent) → n₂/n₁ = πV̄/RT. So ΔP/P° = πV̄/RT → (a).