Raoult's Law
Raoult's law P = xP0 calculates the vapor pressure of an ideal solution from mole fractions.
Learn with worked examples.
The Formula
Raoult's law states that the vapor pressure of a solvent above an ideal solution is proportional to the mole fraction of the solvent. Adding a non-volatile solute lowers the vapor pressure of the solvent.
French chemist Francois-Marie Raoult established this law in 1887. It applies to ideal solutions where the interactions between solute and solvent molecules are similar to the interactions between like molecules. Real solutions may deviate from Raoult's law, showing positive or negative deviations.
For a binary mixture of two volatile liquids, the total vapor pressure is the sum of partial pressures. P_total = x_A × P°_A + x_B × P°_B, where x_A + x_B = 1. This is the basis for understanding distillation, which separates liquids based on their different vapor pressures.
Variables
| Symbol | Meaning |
|---|---|
| Psolution | Vapor pressure of the solution (atm, mmHg, or Pa) |
| xA | Mole fraction of the solvent (dimensionless, 0 to 1) |
| P°A | Vapor pressure of the pure solvent |
Example 1
100 g of sugar (C₁₂H₂₂O₁₁, MW = 342) is dissolved in 500 g of water (MW = 18). Pure water vapor pressure at 25°C is 23.8 mmHg. What is the solution vapor pressure?
Moles of sugar: 100/342 = 0.292 mol
Moles of water: 500/18 = 27.78 mol
Mole fraction of water: x = 27.78/(27.78 + 0.292) = 0.9896
P = 0.9896 × 23.8
P = 23.55 mmHg (vapor pressure decreased by 0.25 mmHg)
Example 2
A mixture of benzene (P° = 95 mmHg) and toluene (P° = 28 mmHg) has a benzene mole fraction of 0.4. What is the total vapor pressure?
P_benzene = 0.4 × 95 = 38 mmHg
P_toluene = 0.6 × 28 = 16.8 mmHg
P_total = 38 + 16.8
P_total = 54.8 mmHg
When to Use It
Use Raoult's law to calculate vapor pressures of solutions and analyze liquid-vapor equilibria.
- Predicting boiling point elevation of solutions
- Designing distillation columns for chemical separation
- Calculating colligative properties of solutions
- Understanding how antifreeze lowers the freezing point of water