Detailed Step-by-Step Solution
We are given vapour pressures of pure liquids A and B at 350 K. We must calculate:
- (a) Composition of liquid mixture
- (b) Composition of vapour phase
P°B = 700 mm Hg
Total vapour pressure = 600 mm Hg
Temperature = 350 K
Step 1: Apply Raoult’s Law
For an ideal solution:250XA = 100
XA = 100 / 250
XA = 0.4
XB = 0.6
Step 2: Find Partial Pressures
PB = 0.6 × 700 = 420 mm Hg
Step 3: Composition of Vapour Phase
Vapour phase mole fraction:YA = 180 / 600
YA = 0.30
YB = 0.70
XA = 0.40
XB = 0.60
Vapour phase composition:
YA = 0.30
YB = 0.70
Theory: Raoult’s Law for Binary Solutions
Raoult’s law states that the partial vapour pressure of each component in an ideal solution is directly proportional to its mole fraction in the liquid phase.
PB = XB P°B
The component with higher vapour pressure is more volatile and is enriched in vapour phase.
Frequently Asked Questions
Why is liquid B more abundant in the vapour phase?
Liquid B has a higher vapour pressure (700 mm Hg) compared to liquid A (450 mm Hg). A higher vapour pressure means that B molecules escape more easily from the liquid phase into the vapour phase. Therefore, even if the liquid contains 60% B, the vapour becomes even richer in B (70%). This is because vapour phase always contains a larger proportion of the more volatile component.
Why is vapour composition different from liquid composition?
In an ideal solution, each component contributes to vapour pressure according to its volatility. The more volatile component (higher P°) contributes more to total vapour pressure. Since vapour phase composition depends on partial pressures, the vapour becomes enriched in the more volatile component. This is the basic principle behind fractional distillation.
What does it mean for a solution to be ideal?
An ideal solution is one that obeys Raoult’s law over the entire composition range. This means intermolecular forces between A–A, B–B, and A–B molecules are nearly equal. There is no heat change on mixing (ΔHmix = 0) and no volume change (ΔVmix = 0). Such solutions show linear variation of vapour pressure with composition.
Why do we use mole fraction instead of mass fraction?
Raoult’s law is based on number of particles, not mass. Since vapour pressure depends on escaping tendency of molecules, we use mole fraction because it represents relative number of molecules present. Mass fraction does not correctly represent particle ratio.
What would happen if the solution showed deviation from Raoult’s law?
If intermolecular attractions between unlike molecules differ significantly, the solution may show positive or negative deviation. In positive deviation, vapour pressure is higher than expected. In negative deviation, vapour pressure is lower. Such systems may form azeotropes.
What is the physical meaning of partial pressure?
Partial pressure is the pressure exerted by one component of a gas mixture. In vapour phase above solution, each component contributes independently to total vapour pressure. Total pressure is simply the sum of all partial pressures.
Why does vapour phase become richer in the more volatile component?
Because molecules with weaker intermolecular forces escape more easily. Higher vapour pressure indicates weaker intermolecular forces, so those molecules dominate in vapour phase.
Is this concept important for competitive exams?
Yes. Questions involving Raoult’s law, vapour phase composition, ideal vs non-ideal solutions, and azeotropes are very common in CBSE, ISC, NEET, and JEE exams.
How is this concept used in real life?
This principle is used in distillation processes in chemical industries, petroleum refining, and separation of liquid mixtures. It is also important in understanding boiling point diagrams.
What graphical representation is associated with this topic?
A pressure-composition (P–X) diagram. For an ideal solution, total vapour pressure varies linearly with mole fraction. The vapour composition curve lies above the liquid composition curve.