Vapor Pressure Calculator (Raoult's Law)

Raoult’s Law describes the vapor pressure of ideal solutions, meaning mixtures whose components pull on each other about as hard as they pull on themselves.

Partial pressure of component A:

P_A = x_A × P°_A

Total vapor pressure:

P_total = x_A × P°_A + x_B × P°_B

Where:

• x_A, x_B = mole fractions in the liquid phase (x_A + x_B = 1)
• P°_A, P°_B = vapor pressures of pure components

Vapor composition (mole fraction in vapor):

y_A = P_A / P_total = x_A × P°_A / P_total

Positive and negative deviations from Raoult’s Law:

• Ideal (Raoult’s Law): A-B interactions ≈ A-A and B-B interactions (e.g., benzene-toluene)
• Positive deviation: A-B interactions weaker than pure components (e.g., ethanol-water, acetone-hexane) → P_total > Raoult’s Law
• Negative deviation: A-B interactions stronger (e.g., acetone-chloroform, HCl-water) → P_total < Raoult’s Law

Benzene-toluene system at 80°C (approximately ideal):

• P°_benzene ≈ 760 mmHg, which is why benzene boils at 80.1°C
• P°_toluene ≈ 290 mmHg

Those two are worth trusting because they are not rounded guesses. Run 80°C through the Antoine equation and it returns 757.7 mmHg for benzene and 291.2 for toluene, which is where the round numbers above come from. Benzene and toluene are the textbook ideal pair because they are chemically so similar that a benzene molecule barely notices whether its neighbor is benzene or toluene.

Relative volatility, the number distillation actually uses

Divide one pure vapor pressure by the other and you get α, the relative volatility:

α = P°_A / P°_B

For benzene over toluene at 80°C that is 760/290, about 2.6. The bigger α is, the easier the separation: an α of 2.6 separates in a handful of theoretical plates, an α of 1.1 needs dozens, and at α = 1 no amount of distillation will separate the pair at all. That last case is what an azeotrope looks like from the outside, and it is why ethanol and water stall at 95.6%.

Applications:

• Fractional distillation (separating components by boiling point)
• Understanding azeotropes (constant-boiling mixtures that cannot be separated by simple distillation)
• Colligative properties (related: vapor pressure lowering by non-volatile solutes)

Colligative properties connection: When a non-volatile solute dissolves, x_solvent decreases → vapor pressure decreases. ΔP = x_solute × P°_solvent, which is Raoult’s Law applied to a solute that contributes no vapor of its own. The vapor pressure lowering calculator handles that case directly.