Raoult's Law Fundamentals
Raoult's law is the starting point for all vapor-liquid equilibrium calculations. Proposed by Francois-Marie Raoult in 1887, it states that each component in an ideal liquid mixture contributes a partial vapor pressure equal to its mole fraction times its pure-component vapor pressure: p_i = x_i·P_i^sat. The total pressure above the liquid is the sum of all partial pressures. This beautifully simple relationship arises when molecules of different species are so similar that swapping one for another in the liquid structure has no energetic or volumetric effect.
P-x-y Diagram
The P-x-y diagram at constant temperature shows total pressure and vapor composition as functions of liquid composition. For an ideal system, the total pressure P = x_A·P_A^sat + (1-x_A)·P_B^sat is a straight line between the two pure-component vapor pressures — a defining characteristic of Raoult's law. The vapor curve y_A = x_A·P_A^sat/P always lies above the liquid line, reflecting the enrichment of the more volatile component in the vapor phase. The simulation draws both curves and the operating point as you adjust composition.
Deviations from Ideality
Real mixtures deviate from Raoult's law whenever unlike molecular interactions differ from like interactions. Positive deviations (γ > 1) occur in mixtures like ethanol-water, where hydrogen bonding between ethanol molecules is disrupted by water, increasing the tendency to vaporize. Negative deviations (γ < 1) appear in systems like chloroform-acetone, where cross-species hydrogen bonds stabilize the liquid. The activity coefficient γ quantifies this deviation: modified Raoult's law p_i = γ_i·x_i·P_i^sat handles both ideal and non-ideal systems.
Engineering Significance
Raoult's law provides the foundation for distillation design. The ratio P_A^sat/P_B^sat determines the ideal-system relative volatility α, which directly controls the number of distillation stages required. When pure-component vapor pressures are close, α ≈ 1 and separation is difficult regardless of column design. Activity coefficient deviations can either help (increasing effective α) or hinder (decreasing α or forming azeotropes) the separation. Understanding Raoult's law and its limitations is therefore the first step in designing any distillation process.