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Raoult's Law
Predicts the partial vapor pressure of a component in an ideal liquid mixture from its mole fraction and pure-component vapor pressure.
Interpretation
Raoult's law: P_i = x_i · P_i_sat for ideal mixtures. Partial pressure is proportional to liquid mole fraction. Example: x=0.5, P_sat=100 kPa → P_i=50 kPa.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| P_i | Partial pressure of component i | kPa |
| x_i | Liquid mole fraction of component i | |
| P_i_sat | Pure-component vapor pressure at system temperature | kPa |
What it means
Raoult’s law describes the vapour‑liquid equilibrium for ideal mixtures. It states that the partial pressure of component i in the vapour phase is equal to the product of its liquid mole fraction x_i and the vapour pressure of the pure component at the same temperature, P_i_sat. This law applies when the liquid solution is ideal (intermolecular forces are similar) and the vapour behaves as an ideal gas. It is the foundation of distillation calculations, as it relates composition to temperature and pressure. For non‑ideal mixtures, Raoult’s law is modified with activity coefficients. Raoult’s law is used to generate T‑x‑y diagrams, to calculate bubble and dew points, and to design distillation columns. It is also applied in environmental engineering to estimate the partitioning of volatile organic compounds between air and water. Though idealisation, it provides a good starting point for many separation processes.
Worked example
Raoult's Law – Two Examples
Real‑World| Parameter | Value |
|---|---|
| xᵢ | 0.4 |
| Pᵢ_sat | 101.3 kPa |
| Parameter | Value |
|---|---|
| xᵢ | 0.6 |
| Pᵢ_sat | 50 kPa |
Common mistakes
- Ideal solution: Raoult’s law applies only to ideal mixtures; for non‑ideal, use activity coefficients.
- Vapour pressure P_i_sat: At the system temperature, often from Antoine or other correlations.
- Mole fraction x_i: In the liquid phase, dimensionless.
- Partial pressure P_i: In the same units as P_i_sat.
- Total pressure: If the vapour is ideal, P_total = sum(P_i).
Applications
Raoult's law, P_i = x_i·P_i_sat, describes the vapour‑liquid equilibrium for ideal mixtures, where the partial pressure of each component is proportional to its liquid mole fraction and its pure‑component vapour pressure. This law is the foundation of distillation calculations, flash separations, and condensation processes. Engineers use it to estimate bubble and dew points, to determine relative volatility, and to design distillation columns. Although ideal mixtures are rare, Raoult's law provides a useful first approximation and is the basis for more advanced activity coefficient models. It is also applied in environmental engineering to estimate the fate of volatile organic compounds. By applying this law, professionals can predict phase behaviour and design separation units effectively.
- Bubble‑point and dew‑point calculations for distillation
- Design of flash separators and partial condensers
- Estimation of relative volatility for distillation column design
- Environmental assessment of volatile chemical emissions
- Base case for activity coefficient models (e.g., Wilson, NRTL)
Frequently Asked Questions
Raoult's law states that the partial vapor pressure of a component in an ideal liquid mixture is equal to the product of its mole fraction in the liquid (x_i) and its vapor pressure as a pure component (P_i^sat): P_i = x_i · P_i^sat. It applies to ideal solutions and is the basis for simple distillation calculations.
- Liquid solution is ideal (no interactions between components).
- Vapour phase behaves as an ideal gas.
- Temperature is constant.
- Applying it to strongly non‑ideal mixtures without activity coefficients.
- Using it for components with very different molecular sizes or polarities.
- Forgetting that the total pressure is the sum of partial pressures (Dalton's law).
- Using the wrong vapor pressure (e.g., at a different temperature).
For a binary mixture, the bubble point temperature is found by solving P = x_A·P_A^sat(T) + x_B·P_B^sat(T) for T. Then the vapour composition is y_A = x_A·P_A^sat(T)/P. This gives the equilibrium curve.
Raoult's law applies to the solvent (major component) and is based on mole fraction. Henry's law applies to solutes at low concentrations and uses a Henry constant: P_i = H·x_i. Both are limiting laws; Raoult's law is valid as x_i → 1, Henry's law as x_i → 0.
An ideal solution is one where the interactions between unlike molecules are the same as between like molecules. Raoult's law is the defining equation for ideal solutions. Real solutions show positive or negative deviations.
Use activity coefficients (γ_i): P_i = γ_i·x_i·P_i^sat. γ_i is obtained from excess Gibbs free energy models (e.g., Wilson, NRTL).
- Distillation column design.
- Flash calculations.
- Vapor‑liquid equilibrium (VLE) data generation.
- Environmental fate modelling.