Raoult's Law
Raoult's Law states that the partial vapour pressure of each volatile component in an ideal solution is equal to the vapour pressure of the pure component multiplied by its mole fraction in the solution. This law quantifies vapour pressure lowering as a colligative property and is the foundation for understanding distillation and solution thermodynamics. Solutions that obey Raoult's Law perfectly (ideal solutions) have similar intermolecular forces between all components; deviations occur in real solutions due to unlike-molecule interactions.
Key Formula
PA = xA × PA°
LaTeX: P_A = x_A \cdot P_A^\circ
| Symbol | Meaning | Unit |
|---|---|---|
| PA | Partial vapour pressure of component A above the solution | Pa or atm |
| xA | Mole fraction of component A in the solution | dimensionless |
| PA° | Vapour pressure of pure component A at the same temperature | Pa or atm |
Worked Example
Problem
A solution contains 2 mol of benzene (P° = 95.2 mmHg) and 3 mol of toluene (P° = 29.1 mmHg) at 25 °C. Calculate the total vapour pressure of the solution.
Solution
Step 1 – Total moles = 2 + 3 = 5 mol. Step 2 – Mole fraction of benzene: xB = 2/5 = 0.400. Step 3 – Mole fraction of toluene: xT = 3/5 = 0.600. Step 4 – Partial pressure of benzene: PB = 0.400 × 95.2 = 38.08 mmHg. Step 5 – Partial pressure of toluene: PT = 0.600 × 29.1 = 17.46 mmHg. Step 6 – Total pressure = 38.08 + 17.46 = 55.54 mmHg.
Answer
Total vapour pressure = 55.54 mmHg
Positive vs Negative Deviations from Raoult's Law
| Type | Observed P | Interaction | Example System | Thermodynamic Sign |
|---|---|---|---|---|
| Ideal | Predicted by law | A–B ≈ A–A ≈ B–B | Benzene–toluene | ΔHmix = 0 |
| Positive deviation | Higher than predicted | A–B weaker than A–A or B–B | Ethanol–hexane | ΔHmix > 0 |
| Negative deviation | Lower than predicted | A–B stronger than A–A or B–B | Acetone–chloroform | ΔHmix < 0 |
| Maximum azeotrope | Boils at minimum T | Positive deviation extreme | Ethanol–water (95.6%) | Cannot separate by distillation |
| Minimum azeotrope | Boils at maximum T | Negative deviation extreme | HCl–water (20.2%) | Cannot separate by distillation |
Interactive Tools
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Related Terms
Colligative Properties
Colligative properties are physical properties of solutions that depend only on the number of solute particles dissolved, not on the chemical identity of those particles. These properties include boiling point elevation, freezing point depression, vapour pressure lowering, and osmotic pressure. They are widely used in industries such as food preservation, antifreeze formulation, and clinical medicine to control solution behaviour.
Boiling Point Elevation
Boiling point elevation is the phenomenon by which the boiling point of a solution is higher than that of the pure solvent, due to the presence of dissolved solute particles lowering the vapour pressure of the solvent. The increase in boiling point is directly proportional to the molal concentration of solute particles. This principle is exploited in automotive antifreeze formulations and in certain cooking techniques to raise the boiling temperature of water.
Chemical Equilibrium
Chemical equilibrium is the state in a reversible reaction where the rates of the forward and reverse reactions are equal, resulting in no net change in the concentrations of reactants and products over time. The system appears static but is actually dynamic — molecules continuously react in both directions at matching rates. The equilibrium state is quantified by an equilibrium constant (K), whose value depends only on temperature for a given reaction.
Named after French chemist François-Marie Raoult (1830–1901) who formulated the law from systematic vapour pressure measurements in the 1880s. The name honours his extensive experimental work on solution thermodynamics.