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Raoult's Law Calculator

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How it Works

01Component Vapor P

Pure-component vapor pressures (mmHg or kPa).

02Mole Fractions

x_A + x_B must equal 1.

03Calculate

Returns P_total + vapor-phase composition.

04Read Composition

y_A and y_B give vapor-phase mole fractions for distillation design.

What is Raoult's Law and How Does the Calculator Work?

Raoult’s Law describes the vapor pressure of an ideal solution: each component contributes vapor pressure proportionally to its mole fraction times its pure-component vapor pressure. The total vapor pressure above a binary mixture is P_total = x_A × P°_A + x_B × P°_B, where x_i is the liquid-phase mole fraction and P°_i is the vapor pressure of the pure component at that temperature. Discovered by François-Marie Raoult in 1882, this is the foundational equation of vapor-liquid equilibrium and the starting point for distillation theory.


The vapor phase above the solution is enriched in whichever component has the higher pure vapor pressure (the more volatile one). Dalton’s Law gives the vapor mole fraction: y_A = (x_A × P°_A) / P_total. This enrichment is what makes distillation possible — vapor that condenses has a different composition than the liquid it came from, and repeating the process (multiple stages, packed column, fractional distillation) successively enriches the more volatile component until it reaches usable purity.


The calculator handles the simplest case: a binary mixture at known mole fractions and known pure-component vapor pressures. Inputs: P°_A, x_A, P°_B (with x_B implied as 1 − x_A). Outputs: total vapor pressure, partial pressures of each component, and vapor-phase mole fractions. The standard unit is mmHg (or torr), but the math works identically in kPa, atm, or any pressure unit as long as both P° values use the same unit.


Raoult’s Law strictly holds only for ideal solutions — mixtures where the molecular interactions between unlike components (A-B) are essentially identical to the average of like-component interactions (A-A and B-B). Benzene/toluene is the textbook ideal example because both molecules are similar size, similar shape, similar polarity. Most real mixtures show deviations: positive deviations (when A-B interactions are weaker than expected, leading to higher vapor pressure than Raoult predicts, often forming minimum-boiling azeotropes like ethanol/water) or negative deviations (stronger A-B interactions, lower pressure, maximum-boiling azeotropes like nitric acid/water).


For non-ideal mixtures, you replace Raoult with P_i = γ_i × x_i × P°_i, where γ_i is the activity coefficient. Activity-coefficient models (Wilson, NRTL, UNIQUAC, UNIFAC) are how real chemical engineering simulators handle distillation column design. Raoult is the starting point and the limiting case — necessary background for any of those more sophisticated treatments.


Used by physical chemistry students working through textbook VLE problems, distillation engineers designing separation columns, petroleum engineers modeling crude oil fractionation, perfumers and essential-oil producers understanding steam distillation, and brewers/distillers calculating ethanol vapor concentrations, Raoult’s Law is the universal first-pass calculation for any vapor-liquid equilibrium problem. Use it to set expectations; use activity coefficients when the answer needs to be quantitatively right for non-ideal systems.

How to Use the Calculator

Identify the Components: Two pure liquids that will mix together. Common pairs: benzene/toluene, methanol/water, ethanol/water (non-ideal), hexane/octane.
Find Pure-Component Vapor Pressures (P°): Look up at the temperature of interest from CRC Handbook, NIST WebBook, or estimate from Antoine equation parameters.
Determine Mole Fractions in the Liquid: x_A + x_B = 1.0. Convert mass fractions to mole fractions if needed using molecular weights.
Calculate Total Pressure: P_total = x_A × P°_A + x_B × P°_B.
Calculate Vapor Composition: y_A = (x_A × P°_A) / P_total. The vapor is enriched in the more volatile component.
Compare to Experiment: If predicted P_total significantly differs from measured, the mixture is non-ideal — use activity coefficients.

The Math Behind It

Raoult’s Law (binary): P_total = x_A × P°_A + x_B × P°_B


Generalized n-component: P_total = Σ x_i × P°_i (summed over all components)


Vapor-phase mole fraction (Dalton): y_i = (x_i × P°_i) / P_total


Relative volatility: α_AB = (y_A/x_A) / (y_B/x_B) = P°_A / P°_B (for ideal mixtures)


Relative volatility α tells you how easy it is to separate two components by distillation. α = 1 → impossible (azeotrope or identical components). α > 1 → A is more volatile; higher α = easier separation. Most refinery distillations work in the 1.5–4.0 range; difficult separations (extractive distillation, crystallization) handle α < 1.2.


For non-ideal mixtures: P_i = γ_i × x_i × P°_i, where γ_i is the activity coefficient (γ = 1 for ideal). Positive deviation: γ > 1, possible minimum-boiling azeotrope. Negative deviation: γ < 1, possible maximum-boiling azeotrope. Activity coefficients depend on composition and temperature; models like Wilson, NRTL, UNIQUAC fit them from experimental VLE data.

Real-World Example

Worked Example

Benzene/toluene mixture at 60°C — the textbook ideal example. Pure vapor pressures at 60°C: benzene P° = 760 mmHg, toluene P° = 420 mmHg. Liquid composition: x_benzene = 0.40, x_toluene = 0.60.

  • Partial pressure of benzene = 0.40 × 760 = 304 mmHg
  • Partial pressure of toluene = 0.60 × 420 = 252 mmHg
  • Total vapor pressure = 304 + 252 = 556 mmHg
  • Vapor mole fraction benzene y = 304 / 556 = 0.547
  • Vapor mole fraction toluene = 0.453

Notice: the liquid is 40% benzene, but the vapor is 54.7% benzene — vapor is enriched in the more volatile component. Condense that vapor and you have a 54.7% benzene liquid; vaporize that liquid and the new vapor is enriched again, and so on. Ten stages of this gets you near-pure benzene at the top of a fractional distillation column.

Relative volatility = (0.547/0.40) / (0.453/0.60) = 1.367 / 0.755 = 1.81. That’s exactly P°_benzene / P°_toluene = 760/420 = 1.81 (matches because the system is ideal). Distillation engineers use α = 1.81 to estimate the number of theoretical plates needed for any benzene-toluene separation: about 10 plates for 99.5% purity from a 50/50 feed, using the Fenske-Underwood-Gilliland method.

Who Uses It

1
Distillation Column Designers: Initial sizing and feed-tray placement decisions.
2
Petrochemical Engineers: Crude oil fractionation modeling.
3
Essential Oil Producers: Steam distillation theory and recovery yield estimates.
4
Distillers and Brewers: Ethanol-water separation (note: highly non-ideal, but Raoult sets the upper bound).
5
Physical Chemistry Students: Solve textbook VLE and Raoult homework problems.
6
Solvent Extraction Designers: Predict partition behavior between phases.
7
Process Simulator Users: Sanity-check ASPEN, ChemCAD, or HYSYS results against Raoult predictions.

Technical Reference

Pure-Component Vapor Pressures at 25°C (mmHg):

  • Acetone: 230
  • Benzene: 95
  • Methanol: 127
  • Ethanol: 59
  • n-Propanol: 21
  • Water: 24
  • Toluene: 28
  • n-Hexane: 152
  • n-Heptane: 46
  • Chloroform: 197
  • Dichloromethane: 436
  • Diethyl ether: 537

Antoine Equation gives P° as a function of temperature: log₁₀(P°) = A − B / (T + C), where A, B, C are species-specific constants (NIST WebBook tabulates them).

Common Azeotropes:

  • Ethanol/Water: 95.6% EtOH at 78.2°C (minimum-boiling, positive deviation)
  • HNO₃/Water: 68.5% HNO₃ at 121°C (maximum-boiling, negative deviation)
  • Acetone/Chloroform: 80% chloroform (negative deviation, hydrogen bonding)
  • Benzene/Methanol: 39.5% MeOH at 58°C (positive deviation)

Key Takeaways

Raoult’s Law works best for chemically similar components (size, shape, polarity). For polar/nonpolar, hydrogen-bonding, or otherwise dissimilar mixtures, use activity coefficient models. Vapor enrichment in the more volatile component is the basis for distillation; relative volatility α determines how easily the separation can be done. For ideal mixtures, α = P°_A / P°_B. For real mixtures, α is composition-dependent and can drop to 1.0 (azeotrope) or even invert.


The history matters: Raoult’s Law was the first quantitative description of solution thermodynamics and established the concept of mole fraction as the natural composition variable for thermodynamic equations. It led directly to the Gibbs phase rule, colligative property theory, and modern chemical engineering practice.

Frequently Asked Questions

When does Raoult’s Law fail?
For chemically dissimilar mixtures. Polar/nonpolar combinations, hydrogen-bonding systems, and significant size differences all break the ideality assumption. Ethanol/water shows positive deviation forming the famous 95.6% azeotrope; nitric acid/water shows negative deviation. For real systems, multiply each Raoult term by the activity coefficient γ_i.
What’s the relationship to Henry’s Law?
Henry’s Law applies to dilute solutes (where Raoult fails); Raoult applies to solvents (and to ideal mixtures across all compositions). They’re actually two limiting cases of the same underlying physics: Raoult is the high-concentration limit; Henry is the dilute limit.
How does this connect to distillation?
The vapor enrichment in the more volatile component is what allows separation. Each "theoretical plate" in a distillation column carries out one Raoult step. The number of plates needed for a given purity comes from the Fenske equation, which uses relative volatility α directly.
How do I extend to multicomponent mixtures?
Generalize: P_total = Σ x_i × P°_i over all components. Vapor composition: y_i = (x_i × P°_i) / P_total. The math scales straightforwardly; the bookkeeping is just longer.
Temperature dependence?
P°_i depends very strongly on temperature (Clausius-Clapeyron or Antoine equations). Raoult’s Law itself is temperature-agnostic in form, but the P° values must be at the system temperature. Boiling-point calculations (where P_total = ambient pressure) iterate on T until the equation is satisfied.
What about azeotropes?
Compositions where vapor and liquid have identical composition — distillation cannot separate further past the azeotrope point. Indicate strongly non-ideal behavior. Raoult does NOT predict azeotropes. To break azeotropes industrially: extractive distillation (add a third component), pressure-swing distillation, or membrane separation (pervaporation).
Activity coefficients — how do I find them?
Either fit from experimental VLE data using a model (Wilson, NRTL, UNIQUAC) or estimate from group-contribution methods (UNIFAC) when no data is available. Modern process simulators (ASPEN, ChemCAD) include extensive activity-coefficient databases.
Does pressure matter?
For typical conditions (1 atm or below), no. The pure-component vapor pressures and mole fractions don’t change with system pressure for liquid-vapor systems. For very high pressures (above 5–10 atm), liquid-phase non-ideality (Poynting correction) starts to matter.
Can I use this for solid-liquid systems?
No — Raoult is liquid-vapor specifically. For solid-liquid, you need solubility theory (Schroeder-van Laar equation) which has analogous structure but different physics.
What’s the simplest way to remember the formula?
P_total = sum of (mole fraction × pure vapor pressure). Each component contributes "its share" weighted by how much of it is there. And the vapor enriches in whichever component has the higher pure vapor pressure — which is intuitive once you see it.

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The ToolsACE Team

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Disclaimer

Raoult’s Law assumes ideal solution behavior. Real mixtures with hydrogen bonding, polar/nonpolar interactions, or significant size mismatch deviate measurably (often by 20–50% in vapor pressure or more). For precise design work, use activity-coefficient models or experimental VLE data. Azeotropes cannot be predicted by Raoult alone.