Hong Life CalculatorsUnderstanding the ideal vapour–liquid equilibrium calculator — concept and principle
For an ideal binary liquid mixture, Raoult's law links the liquid composition to the vapour in equilibrium with it. Given the liquid mole fraction of the lighter (more volatile) component and the pure-component vapour pressures at the chosen temperature, the calculator gives the vapour mole fraction y, the bubble-point pressure and the relative volatility α. These are the building blocks of distillation and flash calculations.
How it is calculated
- Partial pressures: p₁ = x P₁*, p₂ = (1 − x) P₂*.
- Bubble pressure P = x P₁* + (1 − x) P₂*.
- Vapour fraction y = x P₁* ÷ P (Dalton's law: y = p₁/P).
- Relative volatility α = P₁* ÷ P₂*.
P₁* and P₂* are the vapour pressures of the pure light and heavy components at the same temperature, in kPa.
The principle
In an ideal solution the molecules of both components interact about as strongly with each other as with their own kind. Each component then escapes into the vapour in proportion to its share of the liquid surface, so its partial pressure is simply its pure vapour pressure scaled by its mole fraction. Because the lighter component has the higher vapour pressure, the vapour is richer in it than the liquid; that enrichment is what distillation exploits. The ratio of the two K-values (y/x) reduces to P₁*/P₂*, so α does not depend on composition in an ideal system.
Worked example
- Inputs: x = 0.4, P₁* = 101.3 kPa, P₂* = 38.9 kPa (roughly benzene and toluene at 80 °C).
- p₁ = 0.4 × 101.3 = 40.52 kPa; p₂ = 0.6 × 38.9 = 23.34 kPa.
- Bubble pressure P = 40.52 + 23.34 = 63.86 kPa.
- y = 40.52 ÷ 63.86 = 0.6345.
- α = 101.3 ÷ 38.9 = 2.604.
| Liquid mole fraction of light component | Vapour mole fraction y |
|---|---|
| 0.1 | 0.2244129375 |
| 0.2 | 0.3943168548 |
| 0.3 | 0.5274210344 |
| 0.4 | 0.6345129972 |
| 0.5 | 0.7225392297 |
| 0.6 | 0.7961750065 |
| 0.8 | 0.9124071155 |
How to read the result
A liquid with 40% benzene produces a vapour with about 63% benzene, so one equilibrium stage raises the light component by more than 20 percentage points. α well above 1 means easy separation; α close to 1 means many stages or another method. The bubble pressure is the pressure at which this liquid starts to boil at the given temperature: at 63.86 kPa it boils at 80 °C, while at atmospheric pressure it needs a higher temperature.
Common mistakes
- Using vapour pressures taken at different temperatures.
- Swapping the components so that y comes out smaller than x.
- Applying Raoult's law to strongly non-ideal mixtures such as ethanol–water, which form azeotropes and need activity coefficients.
Frequently asked questions
How do I get the vapour pressures?
Use an Antoine equation or tabulated data for each pure component at your temperature, for example from the NIST Chemistry WebBook.
How do I find the boiling temperature at 1 atm instead?
Adjust the temperature until x P₁*(T) + (1 − x) P₂*(T) equals 101.325 kPa; that temperature is the bubble point.
What is a K-value?
K = y/x for each component. Here K₁ = 0.6345/0.4 ≈ 1.59, and α is K₁/K₂.
Sources: J. M. Smith, H. C. Van Ness and M. M. Abbott, Introduction to Chemical Engineering Thermodynamics, McGraw-Hill · NIST Chemistry WebBook, NIST Standard Reference Database 69