Raoult's Law Calculator
Get partial pressures, total pressure, and vapor composition for a two-part mixture.
What it does
Raoult's law connects the vapor pressure of a mixture to the vapor pressures of its pure components. For an ideal solution, each component contributes a partial pressure equal to its liquid mole fraction times its pure vapor pressure.
The total pressure is the sum of those partial pressures. The vapor phase is usually richer in the more volatile component, which is the one with the higher pure vapor pressure. That is the basis for distillation.
The defaults are 1 mol of A and 2 mol of B, with pure vapor pressures of 744 mmHg and 290 mmHg. A is more volatile, so it makes up only one third of the liquid but 56.2% of the vapor. The partial pressures are 248.0 mmHg and 193.3 mmHg, and the total is 441.3 mmHg.
The result assumes an ideal solution. Molecules of A and B are treated as if they interact in the same way as molecules of each pure liquid. Real mixtures can deviate, especially when one component is polar, when hydrogen bonding occurs, or when the components associate. For those cases, activity coefficients are needed.
How to use
- Enter the moles of component A and component B.
- Enter the pure vapor pressure of each component at the same temperature.
- Pick the pressure unit. Both pure pressures and all outputs use that unit.
- Read the total pressure and the two partial pressures.
- Read the vapor mole fraction of A. It tells you the vapor's composition on a mole basis.
- Check that the total pressure is below the sum of the pure pressures, as Raoult's law predicts for an ideal mixture.
Formula
- n_A
- Moles of component A in the liquid.
- n_B
- Moles of component B in the liquid.
- x_A
- Liquid mole fraction of A.
- x_B
- Liquid mole fraction of B.
- P_A
- Pure vapor pressure of A at the mixture temperature.
- P_B
- Pure vapor pressure of B at the mixture temperature.
- p_A
- Partial pressure of A above the solution.
- p_B
- Partial pressure of B above the solution.
- y_A
- Mole fraction of A in the vapor.
The pure vapor pressures must be for the same temperature. If one component is nonvolatile, set its pure vapor pressure to 0. The model assumes the vapor behaves as an ideal gas and that the liquid is an ideal solution. For a real mixture, replace the mole fraction with activity, a_i = gamma_i x_i, where gamma is the activity coefficient.
Worked example
Example: 1 mol A and 2 mol B
Defaults: 1 mol A, 2 mol B, pure vapor pressures 744 mmHg and 290 mmHg.
- Total moles: 1 + 2 = 3 mol.
- Liquid mole fractions: x_A = 1/3 = 0.3333 and x_B = 2/3 = 0.6667.
- Partial pressure of A: 0.3333 x 744 = 248.0 mmHg.
- Partial pressure of B: 0.6667 x 290 = 193.3 mmHg.
- Total pressure: 248.0 + 193.3 = 441.3 mmHg.
- Vapor mole fraction of A: 248.0 / 441.3 = 0.562. The tool shows 441.3 mmHg, 248.0 mmHg, 193.3 mmHg, and 0.562.
Reference table
| Mole ratio A:B | Pure pressures A/B | Total pressure | Vapor fraction A |
|---|---|---|---|
| 1:1 | 75 / 22 mmHg | 48.50 mmHg | 0.773 |
| 1:2 | 75 / 22 mmHg | 39.67 mmHg | 0.630 |
| 2:1 | 75 / 22 mmHg | 57.33 mmHg | 0.872 |
| 1:3 | 100 / 30 mmHg | 47.50 mmHg | 0.526 |
| 3:1 | 100 / 30 mmHg | 82.50 mmHg | 0.909 |
Limits
- Two components only. Mixtures with three or more volatile components need an extra term for each one.
- Assumes an ideal solution. Real mixtures with strong interactions can deviate in either direction.
- Assumes the vapor is an ideal gas and that the pure vapor pressures are measured at the same temperature.
- Does not model a nonvolatile solute's effect on the solvent beyond setting its pure pressure to zero.
Common mistakes
- Using mass fractions instead of mole fractions.
- Using pure vapor pressures measured at different temperatures.
- Forgetting that the vapor mole fraction is not the same as the liquid mole fraction.
- Setting the total pressure equal to the larger pure vapor pressure. The total is a weighted sum.
- Applying Raoult's law to a mixture that strongly deviates from ideal behavior without activity coefficients.
Try it yourself
Quick checks. Answers sit tucked under each question.
Equal moles of A and B have pure vapor pressures of 75 and 22 mmHg. What is the total pressure?
x_A = x_B = 0.5. Partial pressures are 37.5 and 11.0 mmHg. Total is 48.5 mmHg. The vapor mole fraction of A is 0.773.
Two moles of A and one mole of B have pure vapor pressures of 75 and 22 mmHg. What is the total pressure?
x_A = 0.667 and x_B = 0.333. Partial pressures are 50.0 and 7.33 mmHg. Total is 57.33 mmHg. The vapor mole fraction of A is 0.872.
One mole of A and three moles of B have pure vapor pressures of 100 and 30 mmHg. What is the total pressure?
x_A = 0.25 and x_B = 0.75. Partial pressures are 25.0 and 22.5 mmHg. Total is 47.5 mmHg. The vapor mole fraction of A is 0.526.
Questions
What is Raoult's law?
It says the partial vapor pressure of a component in an ideal solution equals its liquid mole fraction times its pure vapor pressure.
Why is the vapor richer in the more volatile component?
The more volatile component has a higher pure vapor pressure, so it contributes more vapor per mole in the liquid. That raises its share in the vapor.
Can I use Raoult's law for a nonvolatile solute?
Yes. Set the solute's pure vapor pressure to 0. The solvent's partial pressure is then its mole fraction times its pure vapor pressure.
What is the difference between Raoult's law and Dalton's law?
Raoult's law gives the partial pressure above the liquid. Dalton's law says the total pressure is the sum of the partial pressures. The two are used together here.
Does temperature matter?
Yes. Pure vapor pressures change strongly with temperature. Use values for the temperature of the mixture.
When does Raoult's law fail?
It fails when the mixture is nonideal, such as ethanol and water or acetone and chloroform. Activity coefficients are needed for those cases.
Sources
- LibreTexts: Ideal solutions obey Raoult's law
- University of Toronto Scarborough: Reflux and Raoult's law