Raoult's Law

Raoult’s law is the quantitative version of “adding solute lowers vapor pressure.” It tells you exactly how much the vapor pressure drops, and the math is beautifully simple.

The Law

Since χ_solvent is always less than 1 (there is always some solute present), $P_{\text{solution}}$ is always less than P°_solvent. The vapor pressure drops.

The vapor pressure lowering (ΔP) is:

ΔP = P°_solvent - $P_{\text{solution}}$ = χ_solute × P°_solvent

This form is sometimes more convenient: the drop in vapor pressure equals the mole fraction of the solute times the pure solvent’s vapor pressure.

Worked Example

Problem: The vapor pressure of pure water at 25 C is 23.8 mmHg. What is the vapor pressure of a solution made by dissolving 0.50 mol of glucose in 2.0 mol of water?

Solution:

• χ_water = 2.0 / (2.0 + 0.50) = 2.0 / 2.5 = 0.80
• $P_{\text{solution}}$ = 0.80 × 23.8 mmHg = 19.0 mmHg
• Vapor pressure lowering: ΔP = 23.8 - 19.0 = 4.8 mmHg

Ideal vs. Non-Ideal Solutions

Raoult’s law describes ideal solutions perfectly - solutions where solute-solvent interactions are identical to solute-solute and solvent-solvent interactions. In an ideal solution, every molecule “feels” the same regardless of its neighbors.

Positive deviations from Raoult’s law: The actual vapor pressure is HIGHER than Raoult predicts. This happens when solute-solvent interactions are weaker than the original pure-component interactions. The molecules escape more easily than expected.

• Example: ethanol + hexane (breaking H-bonds in ethanol, replacing with weak LDF)
• Δ$H_{\text{mix}}$ > 0 (endothermic mixing)

Negative deviations from Raoult’s law: The actual vapor pressure is LOWER than Raoult predicts. This happens when solute-solvent interactions are stronger than the pure-component interactions. The molecules are held in more tightly.

• Example: acetone + chloroform (new H-bonding between them)
• Δ$H_{\text{mix}}$ < 0 (exothermic mixing)

Two Volatile Components

When both the solute and solvent are volatile (e.g., mixing two liquids that both evaporate), both contribute to the total vapor pressure:

$P_{\text{total}}$ = χ_A × P°_A + χ_B × P°_B

This is the extended form of Raoult’s law. The total vapor pressure is the sum of each component’s partial pressure.