Raoult's Law Calculator
ChemistryCalculate vapor pressure of a binary ideal solution using Raoult's law: P = xA×P°A + xB×P°B. Find total vapor pressure and composition of vapor phase.
400
150
Total Vapor Pressure (mmHg)
250
Partial Pressure of A (mmHg)
160
Partial Pressure of B (mmHg)
90
Vapor Mole Fraction of A (yA)
0.64
What is a Raoult's Law?
The Raoult's Law Calculator computes the total vapour pressure of an ideal binary solution and the vapour phase composition using Raoult's law: P_A = x_A × P°_A and P_B = x_B × P°_B, where x_A and x_B are mole fractions in the liquid and P°_A and P°_B are the pure component vapour pressures at the same temperature. Enter the liquid mole fraction of component A, the vapour pressure of pure A, and the vapour pressure of pure B to get total vapour pressure and vapour mole fraction y_A.
Raoult's law is the foundation of vapour-liquid equilibrium thermodynamics — the bedrock on which distillation design, solvent selection, and colligative property analysis are built. For an ideal binary solution, it predicts how the total vapour pressure varies between P°_B (pure B) and P°_A (pure A) as composition changes, and how the vapour is enriched in the more volatile component relative to the liquid.
The vapour mole fraction y_A is the critical output for distillation: y_A − x_A represents the enrichment achieved per theoretical plate. Where y_A > x_A (the more volatile component is enriched in the vapour), successive distillation stages progressively increase purity. The Partial Pressure Calculator handles gas-phase mixtures; this calculator handles the liquid-vapour interface using the vapour pressures from the Vapor Pressure Calculator.
How to use this Raoult's Law calculator
- Enter the Mole Fraction of A (xA) in the liquid phase, between 0 and 1. The mole fraction of B is automatically 1 − xA.
- Enter Pure Vapor Pressure of A (P°A) in mmHg at the temperature of interest. Use the Vapor Pressure Calculator to find P°A at any temperature.
- Enter Pure Vapor Pressure of B (P°B) in mmHg at the same temperature.
- Read Total Vapor Pressure (mmHg) — for an ideal solution this lies between P°_B and P°_A.
- Note Vapor Mole Fraction of A (y_A) — compare to x_A to assess distillation enrichment. If y_A ≈ x_A (small separation), many distillation stages are needed; if y_A >> x_A, separation is easy.
Formula & Methodology
Raoult's law for ideal binary solution:P_A = x_A × P°_A P_B = x_B × P°_B = (1 − x_A) × P°_B P_total = P_A + P_B y_A = P_A / P_totalWorked example — benzene-toluene system at 25°C: P°(benzene) = 95.2 mmHg, P°(toluene) = 28.4 mmHg. Liquid composition x_benzene = 0.4.P_benzene = 0.4 × 95.2 = 38.08 mmHg P_toluene = 0.6 × 28.4 = 17.04 mmHg P_total = 38.08 + 17.04 = 55.12 mmHg y_benzene = 38.08 / 55.12 = 0.691The vapour phase is enriched from x = 0.40 to y = 0.691 in benzene (the more volatile component). One theoretical stage of distillation increases the benzene mole fraction from 0.40 to 0.69 — a significant enrichment that makes benzene-toluene one of the easier binary separations in industrial distillation.
Frequently Asked Questions
Raoult's law states that the partial vapour pressure of a component in an ideal solution is proportional to its mole fraction in the liquid phase: P_A = x_A × P°_A, where P°_A is the vapour pressure of the pure liquid A at the same temperature. For a binary ideal solution, the total vapour pressure is P_total = x_A × P°_A + x_B × P°_B = x_A × P°_A + (1 − x_A) × P°_B. Raoult's law was established by François-Marie Raoult in 1882.
An ideal solution follows Raoult's law exactly at all concentrations. This requires that the intermolecular forces between like molecules (A-A and B-B) are the same as between unlike molecules (A-B). In practice, ideal behaviour is approached when A and B are structurally similar: benzene-toluene, hexane-heptane, and ethanol-methanol are nearly ideal. Raoult's law also holds exactly for the solvent in dilute solutions (Henry's law applies to the solute in dilute solutions), even for non-ideal systems.
Positive deviations occur when A-B interactions are weaker than A-A and B-B: the mixture has higher vapour pressure than predicted by Raoult's law. Ethanol-water and acetone-chloroform show positive deviations. In extreme cases, positive-deviation systems form maximum-boiling azeotropes where vapour pressure peaks at a specific composition. Negative deviations occur when A-B interactions are stronger than pure-component interactions, lowering vapour pressure below Raoult's law prediction. These form minimum-boiling azeotropes or show reduced volatility.
The vapour phase composition (mole fraction y_A) differs from the liquid phase mole fraction x_A in ideal solutions: y_A = P_A / P_total = (x_A × P°_A) / (x_A × P°_A + x_B × P°_B). The more volatile component (higher P°) is enriched in the vapour — this is the basis of distillation. If P°_A > P°_B, then y_A > x_A — the vapour is richer in A than the liquid. This enrichment continues with each successive vapour-liquid equilibrium stage in a distillation column.
Enter the mole fraction of component A (x_A) in the liquid phase (the mole fraction of B is automatically 1 − x_A). Enter the vapour pressure of pure liquid A (P°_A) and pure liquid B (P°_B) in mmHg at the same temperature. The calculator returns: partial pressure of A, partial pressure of B, total vapour pressure of the solution, and the mole fraction of A in the vapour phase (y_A).
At 25°C: Water: 23.8 mmHg; Ethanol: 59.0 mmHg; Methanol: 127 mmHg; Acetone: 231 mmHg; Benzene: 95.2 mmHg; Toluene: 28.4 mmHg; Hexane: 151 mmHg; Diethyl ether: 537 mmHg. Use the [Vapor Pressure of Water Calculator](/vapor-pressure-of-water-calculator/) to get the pure vapour pressure of water at any temperature, and the [Vapor Pressure Calculator](/vapor-pressure-calculator/) for any other liquid using the Clausius-Clapeyron equation.
Henry's law describes the solubility of a sparingly soluble gas in a liquid: p = K_H × x, where K_H is the Henry's law constant and x is the mole fraction of dissolved gas. Henry's law applies to the solute in dilute solutions (x → 0); Raoult's law applies to the solvent in dilute solutions and to all components in ideal solutions. Both are limiting laws: Raoult's law applies at x → 1 (pure solvent); Henry's law applies at x → 0 (trace solute). Together they describe the full vapour-liquid equilibrium behaviour of dilute binary solutions.
Vapour pressure lowering is the decrease in vapour pressure of a solvent when a non-volatile solute is dissolved. Since the solute has P°_B ≈ 0, the total vapour pressure P = x_A × P°_A + x_B × 0 = x_A × P°_A < P°_A. The vapour pressure is lowered by the factor x_A = 1 − x_B, where x_B is the mole fraction of the non-volatile solute. This is a colligative property — it depends only on x_B, not on what B is. Vapour pressure lowering is the root cause of both boiling point elevation and freezing point depression.
Extensively — Raoult's law is the foundation for designing distillation columns in India's large petrochemical and pharmaceutical sectors. Reliance Industries' Jamnagar refinery and ONGC refineries use Raoult's law (and its deviations) to design distillation trains separating crude oil fractions. In pharmaceutical manufacturing, solvent selection and azeotrope avoidance in recrystallisation and solvent recovery systems require Raoult's law analysis. Indian chemical engineering curricula require mastery of vapour-liquid equilibrium based on Raoult's law.
An azeotrope is a mixture of two or more liquids that has a fixed boiling point and vapour composition identical to its liquid composition — it cannot be further separated by simple distillation. Ideal solutions following Raoult's law cannot form azeotropes (y_A always differs from x_A unless x_A = 0 or 1). Azeotropes arise from positive or negative deviations from Raoult's law. The ethanol-water azeotrope (95.6% ethanol by mass, boiling at 78.1°C) prevents production of absolute ethanol by ordinary distillation — azeotropic distillation or molecular sieve drying must be used.