Raoult's Law Calculator

Compute partial pressures, total vapor pressure, and vapor composition for ideal binary liquid mixtures. Interactive pressure-composition diagram visualizes Raoult's law behavior.

Component A (More volatile)
0 1
Component B (Less volatile)
? Benzene–Toluene (25°C)
? Ethanol–Water (25°C)
? Methanol–Water (25°C)
⚗️ Acetone–Chloroform (ideal ref.)
Privacy-first: All calculations run locally in your browser. No data is sent to any server.

Understanding Raoult's Law: The Foundation of Ideal Solutions

Raoult's Law states that for an ideal solution, the partial vapor pressure of each component is directly proportional to its mole fraction in the liquid phase: pi = xi · P°i, where P°i is the vapor pressure of the pure component at the same temperature. This linear relationship is the cornerstone of distillation theory, vapor-liquid equilibrium (VLE), and chemical engineering thermodynamics.

For a binary mixture:
pA = xA·P°A,   pB = xB·P°B = (1-xA)·P°B
Ptotal = pA + pB
yA = pA / Ptotal (vapor mole fraction, Dalton's law)

Historical Context & Scientific Significance

French chemist François-Marie Raoult (1830–1901) experimentally established the relationship between vapor pressure lowering and solute concentration. His work (1880s) enabled the understanding of colligative properties and laid the groundwork for ideal solution theory. Raoult's law is exact only for ideal mixtures where intermolecular forces between unlike molecules are identical to those between like molecules. Real solutions show positive or negative deviations, but the law remains a powerful reference.

How to Use This Interactive Calculator

  • Enter component properties: Provide names, pure vapor pressures (kPa) at the desired temperature, and liquid mole fraction xA (0–1).
  • Real-time phase diagram: The pressure-composition graph updates automatically, showing pA, pB, and total pressure vs xA.
  • Vapor composition: Obtain yA and relative volatility α, critical for distillation column design.
  • Preset examples: Explore benzene-toluene (ideal), ethanol-water (slightly non-ideal reference), methanol-water.
  • Safety note: Vapor pressure data are temperature dependent. For process design, always use data at the relevant operating temperature and pressure.

Step-by-Step Calculation Derivation

Given P°A = 12.7 kPa, P°B = 3.79 kPa, xA = 0.5:

1. pA = 0.5 × 12.7 = 6.35 kPa
2. xB = 1 – 0.5 = 0.5, pB = 0.5 × 3.79 = 1.895 kPa
3. Ptotal = 6.35 + 1.895 = 8.245 kPa
4. yA = 6.35 / 8.245 ≈ 0.770, yB = 0.230
5. Relative volatility α = (yA/xA) / (yB/xB) = (0.77/0.5)/(0.23/0.5) = 3.35.

This calculator automates the process and draws the complete P-x-y diagram using 200 points for high accuracy.

Real-World Applications & Case Study

Case Study: Distillation of Benzene–Toluene

In a petrochemical plant, a benzene-toluene mixture is separated via distillation. Using Raoult's law, engineers calculate the vapor-liquid equilibrium (VLE) curve. For a feed with xbenzene = 0.4 at 85°C (P°benzene ≈ 116.9 kPa, P°toluene ≈ 46.0 kPa), the total pressure is 74.4 kPa, and vapor phase ybenzene ≈ 0.628, enabling the design of tray columns. This interactive tool replicates such analysis instantly, helping students and professionals validate process simulations.

Limitations & Non-Ideal Systems

⚠️ Important Note on Assumptions: Raoult's Law is an ideal model. Real solution behavior may differ significantly from these calculations. For engineering design, always consult experimental VLE data or use models incorporating activity coefficients (γi).

Raoult's law holds strictly for ideal solutions where ΔHmix = 0, ΔVmix = 0, and intermolecular forces between unlike molecules are identical to those between like molecules. Many real mixtures exhibit:

  • Positive deviations (e.g., ethanol–hexane, higher total pressure): When A-B attractions are weaker than A-A and B-B attractions.
  • Negative deviations (e.g., acetone–chloroform, lower total pressure): When A-B attractions are stronger, possibly due to hydrogen bonding or complex formation.

For non-ideal systems, activity coefficients (γi) are introduced: pi = γi xi P°i. Activity coefficients are temperature and composition dependent, requiring experimental measurement or advanced thermodynamic models (e.g., Wilson, NRTL, UNIQUAC). This calculator provides exact results for ideal behavior, which serves as a valuable reference point for analyzing real systems.

Theoretical Background: Derivation from Thermodynamics

At equilibrium, the chemical potential of component i in the liquid equals that in the vapor. For an ideal gas and ideal liquid solution, μiliq = μi°(T) + RT ln xi, and μivap = μi°(T) + RT ln (pi/P°). Equating leads to pi = xi P°i. This elegant derivation is a staple in physical chemistry courses.

Mixture (25°C) P°A (kPa) P°B (kPa) xA Ptotal (kPa) yA Notes
Benzene (A) – Toluene (B) 12.7 3.79 0.5 8.245 0.770 Classic ideal system
Methanol (A) – Water (B) 16.9 3.17 0.4 8.66 0.781 Exhibits moderate positive deviation*
Ethanol (A) – Water (B) 7.87 3.17 0.3 4.58 0.515 Exhibits positive deviation, forms azeotrope*

*Non‑ideal systems shown for reference; actual Ptotal and yA will differ from Raoult's law prediction due to activity coefficients ≠ 1.

Frequently Asked Questions

Raoult's law applies to the solvent in an ideal solution, stating its partial pressure is proportional to its mole fraction with the proportionality constant being the pure component vapor pressure. Henry's law describes the solute (typically a gas) at low concentrations, with partial pressure proportional to concentration but with a different constant (Henry's constant, KH). Both are limiting laws: Raoult's law applies as xi → 1, Henry's law as xi → 0.

This version supports binary (two-component) mixtures. For multicomponent ideal solutions, Raoult's law extends directly: pi = xiP°i and Ptotal = Σpi. The vapor composition is yi = pi/Ptotal. However, visualization becomes challenging beyond two components. For ternary mixtures, triangular diagrams are used. An extended multicomponent version may be released in the future.

Pressure is entered and computed in kilopascals (kPa). Since Raoult's law is unit-consistent, you may use any pressure unit (atm, mmHg, bar) provided both pure vapor pressures use the same unit. The calculator will return results in that same unit. For temperature-dependent P° values, use the Antoine Equation Calculator first to obtain P° at your desired temperature.

For an ideal binary mixture, total pressure Ptotal = xA(P°A – P°B) + P°B is linear with respect to xA. This linearity is a direct mathematical consequence of Raoult's law. Graphically, the total pressure line connects the two pure-component vapor pressures (P°B at xA=0 and P°A at xA=1). This straight line is a hallmark of ideal binary VLE.

Relative volatility αAB = (yA/xA) / (yB/xB) quantifies the ease of separation. For ideal solutions, α = P°A/P°B (constant, independent of composition). Values far from 1 indicate easier separation by distillation. α > 1 means A is more volatile (enriched in vapor). α = 1 means no separation (azeotrope). This calculator shows α, a key parameter in the McCabe-Thiele method for distillation column design.

The calculation is valid at the temperature for which the input pure vapor pressures (P°A, P°B) are defined. Temperature dramatically affects P° via the Clausius–Clapeyron relation. For example, benzene's vapor pressure is 12.7 kPa at 25°C but ~101.3 kPa at 80°C. To analyze a different temperature, first obtain the corresponding P° values (e.g., using Antoine equation: log10P° = A - B/(T+C)). The provided examples are at 25°C unless noted.

Positive deviations (e.g., ethanol–water, acetone–carbon disulfide) occur when unlike‑molecule interactions are weaker, leading to higher total pressure than Raoult's law predicts. Negative deviations (e.g., chloroform–acetone, nitric acid–water) occur when specific interactions (e.g., hydrogen bonding) strengthen the mixture, giving lower total pressure. In such cases, the simple linear P‑x curve becomes curved, and constant relative volatility no longer holds. For real mixtures, use experimental VLE data or thermodynamic models (Wilson, NRTL, UNIQUAC) that incorporate activity coefficients (γ).

Trusted thermodynamic reference
This calculator implements Raoult's law as defined in the IUPAC Gold Book and standard physical chemistry textbooks (Atkins' Physical Chemistry, Smith & Van Ness "Introduction to Chemical Engineering Thermodynamics"). The algorithm and educational content have been verified by getzenquery tech team. Numerical results for benzene–toluene match NIST Chemistry WebBook data within rounding error. The interactive graph uses Canvas API for pixel‑precise rendering. Last updated: April 2026.

Academic References & Further Reading:
  1. IUPAC. (2019). "Raoult's law". In Compendium of Chemical Terminology (the "Gold Book"). https://goldbook.iupac.org/terms/view/R05141.
  2. Atkins, P., de Paula, J., & Keeler, J. (2018). Physical Chemistry (11th ed.). Oxford University Press. pp. 137–139.
  3. Smith, J. M., Van Ness, H. C., & Abbott, M. M. (2018). Introduction to Chemical Engineering Thermodynamics (8th ed.). McGraw-Hill. Chapter 10: Vapor/Liquid Equilibrium.