Engineering · Chemical Engineering · Separation Processes
Raoult's Law Calculator
Calculates the partial vapor pressure of a component in an ideal liquid mixture using Raoult's Law.
Calculator
Formula
p_i is the partial vapor pressure of component i (Pa or kPa); x_i is the mole fraction of component i in the liquid phase (dimensionless, 0 to 1); p_i^* is the pure-component vapor pressure of component i at the system temperature (Pa or kPa). The total pressure of the mixture is P_{\text{total}} = \sum_i p_i = \sum_i x_i \cdot p_i^*. The vapor-phase mole fraction is given by y_i = p_i / P_{\text{total}}.
Source: F. M. Raoult, Comptes Rendus de l'Académie des Sciences, 1887; Smith, Van Ness & Abbott, Introduction to Chemical Engineering Thermodynamics, 8th ed., McGraw-Hill.
How it works
Raoult's Law, formulated by French chemist François-Marie Raoult in 1887, states that the partial vapor pressure of each component in an ideal liquid mixture is equal to the product of its mole fraction in the liquid phase and its pure-component vapor pressure at the same temperature. This relationship arises because, in an ideal mixture, all intermolecular interactions between unlike molecules are the same as those between like molecules — meaning there is no enthalpy of mixing and the mixture obeys thermodynamic ideality.
The core formula is p_i = x_i × p_i*, where p_i is the partial vapor pressure, x_i is the liquid-phase mole fraction of component i, and p_i* is the saturation (pure) vapor pressure of component i at the system temperature. For a binary mixture, the total pressure is P_total = x₁·p₁* + x₂·p₂*, where x₁ + x₂ = 1. The vapor-phase mole fraction of each component, y_i, is then computed using Dalton's Law: y_i = p_i / P_total. Pure vapor pressures are typically obtained from the Antoine equation or standard property tables (e.g., NIST, Perry's Chemical Engineers' Handbook).
Raoult's Law is the starting point for constructing vapor-liquid equilibrium (VLE) diagrams — P-x-y and T-x-y plots — used extensively in distillation design. It also underpins the calculation of relative volatility (α₁₂ = p₁*/p₂*), which quantifies the ease of separating two components by distillation. When mixtures deviate from ideality (due to unlike molecular interactions), modified models such as the Wilson, NRTL, or UNIQUAC activity coefficient models are applied to correct the liquid-phase fugacity.
Worked example
Consider a binary mixture of benzene (component 1) and toluene (component 2) at 80°C. At this temperature, the pure vapor pressure of benzene is approximately 101.3 kPa and that of toluene is approximately 40.0 kPa. Suppose the liquid-phase mole fraction of benzene is x₁ = 0.40.
Step 1 — Liquid mole fractions: Since the mixture is binary, x₂ = 1 − 0.40 = 0.60.
Step 2 — Partial pressures:
p₁ = x₁ × p₁* = 0.40 × 101.3 = 40.52 kPa
p₂ = x₂ × p₂* = 0.60 × 40.0 = 24.00 kPa
Step 3 — Total pressure:
P_total = 40.52 + 24.00 = 64.52 kPa
Step 4 — Vapor mole fractions:
y₁ = 40.52 / 64.52 = 0.6281
y₂ = 24.00 / 64.52 = 0.3719
This result shows that the vapor phase is enriched in benzene (y₁ = 0.628) relative to the liquid phase (x₁ = 0.40), which is expected since benzene has a higher vapor pressure and is more volatile than toluene. This enrichment is the principle that drives distillation separation.
Limitations & notes
Raoult's Law applies strictly to ideal mixtures, where unlike intermolecular forces are equal to like-like forces — a condition best met by structurally similar components such as benzene-toluene or hexane-heptane pairs. Real mixtures often exhibit positive deviations (e.g., ethanol-water, where unlike interactions are weaker) or negative deviations (e.g., acetone-chloroform, where unlike interactions are stronger), leading to azeotrope formation that Raoult's Law cannot predict. The law is also only valid at low to moderate pressures where the vapor phase behaves as an ideal gas; at high pressures, fugacity corrections via an equation of state are required. Pure vapor pressures (p*) must be determined at the exact system temperature, typically via the Antoine equation, and errors in these values propagate directly into all computed outputs. For multicomponent systems, the approach extends naturally (P_total = Σ x_i · p_i*), but the computational complexity increases. Finally, the law does not account for chemical reactions between mixture components or electrolyte dissociation effects.
Frequently asked questions
What is Raoult's Law and when does it apply?
Raoult's Law states that the partial vapor pressure of a component in a liquid mixture equals its mole fraction multiplied by its pure-component vapor pressure. It applies to ideal mixtures — typically those consisting of chemically similar molecules — at low to moderate pressures and temperatures below the critical point of either component.
How do I find the pure vapor pressure (p*) for a given temperature?
Pure component vapor pressures are most commonly calculated using the Antoine equation, log₁₀(p*) = A − B/(C + T), with constants tabulated in sources like NIST WebBook, Perry's Chemical Engineers' Handbook, or the DIPPR database. Experimental steam tables and databooks also list saturation pressures for common substances at standard temperatures.
What is the difference between Raoult's Law and Henry's Law?
Raoult's Law applies to the major (solvent) component of a mixture and uses the pure-component vapor pressure as the reference state. Henry's Law applies to dilute (solute) components and uses an empirically determined Henry's constant instead of p*, which accounts for the different molecular environment a solute experiences when highly diluted in a solvent.
What causes positive and negative deviations from Raoult's Law?
Positive deviations occur when unlike-molecule interactions are weaker than like-molecule interactions, causing the mixture to have a higher total pressure than Raoult's Law predicts (e.g., ethanol-water). Negative deviations arise when unlike interactions are stronger, reducing total pressure below the ideal prediction (e.g., acetone-chloroform). Large deviations can create maximum-boiling or minimum-boiling azeotropes.
How is relative volatility related to Raoult's Law?
Relative volatility (α₁₂) is the ratio of the vapor pressures of the two pure components: α₁₂ = p₁*/p₂*. A value significantly different from 1.0 indicates that distillation separation is feasible; when α₁₂ approaches 1.0, the components are nearly impossible to separate by simple distillation. Raoult's Law provides the theoretical basis for this metric in ideal systems.
Last updated: 2025-01-15 · Formula verified against primary sources.