Raoult's Law Partial Pressure Calculator

Introduction

Raoult's law is a first-pass vapor-liquid equilibrium model for ideal liquid solutions. It says that each volatile component contributes a partial vapor pressure equal to its liquid mole fraction multiplied by the vapor pressure of that pure component at the same temperature. Summing the component partial pressures gives the mixture's total vapor pressure.

This calculator handles a binary mixture. It computes component A and component B partial pressures, total vapor pressure, and the vapor-phase composition implied by Dalton's law. Optional activity coefficient fields let you show the modified Raoult's-law form, while the default value of 1 keeps the calculation ideal.

How to use this calculator

Enter the liquid mole fraction of component A. Component B is automatically set to 1 minus that value. Then enter the pure-component vapor pressures for A and B in kilopascals at the same temperature. Leave both activity coefficients at 1 for an ideal solution, or enter measured or model-derived coefficients if you are intentionally using a non-ideal correction.

Use consistent temperature and units. If the pure-component vapor pressures come from different temperatures, the result is not physically meaningful. If a mixture is known to form an azeotrope or has strong hydrogen bonding, electrolyte behavior, or large molecular-size differences, treat this as a teaching estimate rather than design data.

Formula and method

For an ideal binary liquid solution, Raoult's law is

where Pi is the vapor partial pressure of component i, xi is its liquid mole fraction, and Pi* is the pure-component vapor pressure at the same temperature. The total vapor pressure is Ptotal = PA + PB. The vapor mole fraction is then yi = Pi / Ptotal.

If activity coefficients are supplied, this calculator uses the common modified form Pi = xi gammai Pi*. That does not make the page a complete non-ideal VLE model; it only applies coefficients you already trust from experiments, a data table, or a separate thermodynamic model.

Example calculation

For a liquid mixture with xA = 0.400, xB = 0.600, P*A = 30.0 kPa, P*B = 7.9 kPa, and both activity coefficients equal to 1, the partial pressure of A is 0.400 x 30.0 = 12.00 kPa. The partial pressure of B is 0.600 x 7.9 = 4.74 kPa.

The total vapor pressure is 16.74 kPa. Component A is more volatile in this example, so it is enriched in the vapor phase: yA = 12.00 / 16.74 = 71.7%, while yB is 28.3%.

How to interpret the result

The larger partial pressure shows which component contributes more to the vapor above the liquid. A component can dominate the vapor phase even when it is not the majority of the liquid if its pure vapor pressure is much higher. The vapor mole fractions are useful for first-pass distillation, solvent recovery, headspace, and classroom vapor-liquid equilibrium exercises.

Total pressure also provides a rough volatility signal at the selected temperature. However, boiling behavior at a specified external pressure requires solving for the temperature at which the sum of partial pressures reaches that external pressure, with pure-component vapor pressures updated as temperature changes.

Limitations and assumptions

• Binary mixture. The form generalizes to more components, but this tool accepts only A and B for clarity.
• Same temperature required. Both pure vapor pressures must be measured or calculated at the mixture temperature.
• Ideal solution by default. The default gamma values are 1, which assumes similar intermolecular interactions and no strong heat of mixing.
• Non-ideal systems need data. Azeotropes, electrolytes, associating mixtures, strong hydrogen bonding, and large polarity differences can deviate substantially.
• No temperature solver. Antoine, Clausius-Clapeyron, or measured vapor-pressure curves are needed to predict pressure across temperature.
• Educational estimate. Do not use this page alone for safety-critical distillation, emissions, flammability, or process design decisions.

FAQ

What does Raoult's law calculate?

Raoult's law estimates each component's vapor partial pressure by multiplying its liquid mole fraction by its pure-component vapor pressure at the same temperature. The partial pressures add to the total vapor pressure.

When is Raoult's law accurate?

It works best for ideal or nearly ideal liquid mixtures whose molecules have similar sizes and intermolecular forces. Strongly non-ideal mixtures need activity coefficients or measured vapor-liquid equilibrium data.

Why must pure-component vapor pressures use the same temperature?

Vapor pressure changes strongly with temperature. Mixing values from different temperatures breaks the physical basis of the calculation and can give misleading total pressures.