Raoult's Law Partial Pressure Calculator

Introduction to Raoult's Law Partial Pressure Estimates

Raoult's law is the standard starting point for estimating how a binary liquid mixture shares its vapor pressure between two components. For an ideal or nearly ideal solution, each component's contribution to the vapor is its liquid mole fraction multiplied by its pure-component vapor pressure at the same temperature. When those two partial pressures are added together, you get the total pressure above the liquid.

This calculator keeps the problem focused on a two-component system, so it reports the partial pressure of A, the partial pressure of B, the total vapor pressure, and the implied vapor-phase composition from Dalton's law. If you enter activity coefficients, the same structure becomes the modified Raoult's-law form, which is useful when you already have non-ideal data and want to see its effect on the vapor estimate.

The result is especially helpful for quick checks before distillation work, solvent blending, or classroom VLE problems, where the key question is often not whether a liquid evaporates, but which component dominates the vapor at the temperature of interest.

How to use this Raoult's law calculator

Start with the liquid mole fraction of component A. The calculator automatically assigns component B as the remainder so the mixture stays binary. Next, enter the pure-component vapor pressures for A and B in kPa at the same temperature that the liquid mixture is being considered.

Leave both activity coefficients at 1 when you want the ideal Raoult's-law estimate. If you have measured coefficients, or a separate thermodynamic model that supplies them, you can enter those values to see how non-ideality shifts the partial pressures and vapor composition.

The numbers must be internally consistent. Raoult's law only makes sense when the vapor pressures refer to the same temperature, and the calculator cannot repair a mismatch between data taken from different sources. If you are checking a mixture with strong molecular attractions, a known azeotrope, or very uneven component volatility, use the output as a screening estimate rather than a final design value.

Formula and method for Raoult's law partial pressure

For an ideal binary liquid solution, the calculator applies Raoult's law to each component separately:

In words, component i's partial pressure equals its liquid mole fraction times its pure-component vapor pressure at the same temperature. Once the two partial pressures are known, the total pressure is their sum, and the vapor mole fractions follow from yi = Pi / Ptotal. That is why a component with a modest liquid fraction can still dominate the vapor if its pure vapor pressure is much higher than the other's.

If activity coefficients are entered, the calculator uses the modified expression Pi = xi gammai Pi*. That keeps the same structure but scales each component by the correction you supplied. It does not estimate gamma on its own, and it does not solve a full vapor-liquid equilibrium problem across temperature.

Worked example: an ideal binary Raoult's-law estimate

Suppose component A makes up 0.400 of the liquid and component B makes up 0.600. If the pure-component vapor pressures at the same temperature are 30.0 kPa for A and 7.9 kPa for B, and both activity coefficients are 1, the calculator treats the mixture as ideal and computes each partial pressure directly from those inputs.

That means A contributes 12.00 kPa and B contributes 4.74 kPa, for a total vapor pressure of 16.74 kPa. Even though A is only 40% of the liquid, it is the more volatile component here, so it occupies about 71.7% of the vapor phase. That kind of enrichment is exactly why Raoult's law is useful when you want a quick sense of separation behavior before you move on to a more detailed model.

The worked example is not a special case hidden behind the scenes; it simply shows how the inputs combine. If you change the composition, the most volatile component tends to pull the vapor composition toward itself, while the less volatile component contributes more modestly unless its liquid fraction becomes very large.

How to interpret the Raoult's-law result

The partial pressures show how the liquid mixture divides its vapor pressure between the two components. The larger the partial pressure, the more strongly that component appears in the vapor above the liquid. When the vapor composition is more concentrated in one component than the liquid composition, that component is the more volatile species under the chosen conditions.

The total pressure is a quick measure of volatility at the selected temperature. If you are comparing this number to an external pressure, remember that boiling occurs when the sum of the component partial pressures matches that outside pressure, which usually means the pure vapor pressures must be evaluated again at a different temperature.

For headspace calculations, solvent screening, or first-pass distillation checks, the output is often most useful as a direction-of-change tool: increasing xA pushes A's partial pressure upward, increasing P*A raises A's contribution directly, and changing gammaA or gammaB nudges the total away from the ideal case.

Limitations and assumptions for Raoult's law

• Binary mixture. The calculator only accepts A and B, so it is meant for a two-component liquid rather than a multicomponent blend.
• Same temperature required. Both pure vapor pressures must represent the same temperature as the liquid mixture; otherwise the sum is not a physically consistent Raoult's-law estimate.
• Ideal solution by default. Gamma values of 1 assume the two liquids behave similarly enough that their interactions do not distort the vapor pressure too strongly.
• Non-ideal systems need data. Strongly associating, ionic, or azeotropic systems can deviate enough that measured VLE data or a proper activity-coefficient model is needed.
• No temperature solver. This page does not calculate the temperature at which boiling occurs; you would need a vapor-pressure correlation or measured curve for that.
• Educational estimate. Use the result as a learning or screening aid, not as the sole basis for safety-critical distillation, emissions, flammability, or process decisions.

FAQ about Raoult's law partial pressure

What does this Raoult's law calculator calculate?

It estimates the partial vapor pressure of each liquid component from its mole fraction and pure-component vapor pressure, then adds those contributions to give total pressure and vapor composition. In the modified form, the activity coefficients you enter scale the partial pressures before the total is summed.

When is Raoult's law a good approximation?

It is most reliable for ideal or near-ideal liquid mixtures whose components have similar size, polarity, and intermolecular forces. It is a screening model for ordinary solvent blends and classroom problems, but mixtures with strong association, electrolytes, or azeotropes often need measured vapor-liquid equilibrium data or a more detailed activity-coefficient model.

Why must the vapor pressures be at the same temperature?

Raoult's law compares each component at one shared temperature because vapor pressure changes quickly with temperature. Mixing a 25 °C value for one component with a 40 °C value for the other would distort the partial pressures and make the total pressure meaningless. If your source data are on different temperatures, convert them to the same basis before using the calculator.