Solve P = X·P° to find the vapor pressure of an ideal solution from the solvent's mole fraction and its pure vapor pressure — a colligative property. Compute the solution's vapor pressure directly, find how much a solute lowers it, or combine two volatile components.
Inputs
Fraction of moles in the solution that are solvent, between 0 and 1.
Vapor pressure of the pure solvent, in mmHg (water at 25°C ≈ 23.8 mmHg).
Result
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Enter the solvent's mole fraction and pure vapor pressure to compute the solution's vapor pressure.
Inputs
The solute's mole fraction is calculated as 1 − Xsolvent.
Vapor pressure of the pure solvent, in mmHg.
Result
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Enter the solvent's mole fraction and pure vapor pressure to compute the vapor-pressure lowering.
Solution vapor pressure—
Two volatile components
Mole fraction of component A. XA + XB must equal 1.
Vapor pressure of pure component A, in mmHg.
Mole fraction of component B.
Vapor pressure of pure component B, in mmHg.
Result
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Enter both mole fractions (summing to 1) and pure vapor pressures to compute the total vapor pressure.
Enter the solvent's mole fraction and pure vapor pressure
On the Solution VP tab, enter the mole fraction of the solvent in the solution (a number between 0 and 1) and the vapor pressure of the pure solvent at your working temperature. Water at 25°C, for example, has a pure vapor pressure of about 23.8 mmHg.
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Read the solution's vapor pressure
The result card shows P, the vapor pressure of the solution, along with how much lower it is than the pure solvent's vapor pressure. Switch to the VP Lowering tab to see that drop, ΔP, computed directly from the solute's mole fraction.
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Combine two volatile liquids
If both components of the mixture are volatile (each contributes its own vapor pressure), use the Two Components tab. Enter each component's mole fraction and pure vapor pressure — the mole fractions must sum to 1 — to get the total vapor pressure over the mixture.
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Reference
Formula & Methodology
3 formulas▸
Solution vapor pressure (Raoult's law)
P = X_solvent · P°
P is the vapor pressure of the solution. X_solvent is the mole fraction of the solvent (moles of solvent divided by total moles in solution). P° is the vapor pressure of the pure solvent at the same temperature. This holds exactly only for an ideal solution — one where solvent-solvent, solute-solute, and solvent-solute interactions are all essentially the same.
Vapor-pressure lowering
ΔP = X_solute · P° = P° − P
ΔP is how much the solution's vapor pressure falls below the pure solvent's. Because mole fractions in a solution sum to 1, X_solute = 1 − X_solvent, so the lowering and the solution vapor pressure are two views of the same relationship.
Two volatile components
P_total = X_A·P°_A + X_B·P°_B
When both components of a mixture are volatile, each contributes its own mole-fraction-weighted share of vapor pressure. The total vapor pressure over the mixture is the sum of both partial contributions — this is the basis for reading vapor-liquid equilibrium diagrams.
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Glossary
Key Terms Explained
7 terms▸
Raoult's law ↗The principle that a component's partial vapor pressure over a solution equals its mole fraction in the liquid times its vapor pressure as a pure substance. It holds exactly for ideal solutions and approximately for dilute real solutions.
Vapor pressure ↗The pressure exerted by a substance's vapor when it is in equilibrium with its liquid (or solid) phase at a given temperature, commonly measured in mmHg, kPa, or atm. Higher vapor pressure means the substance evaporates more readily.
Mole fraction ↗The ratio of moles of one component to the total moles of all components in a mixture, always between 0 and 1. The mole fractions of every component in a mixture sum to exactly 1.
Vapor-pressure lowering ↗The amount by which a solution's vapor pressure falls below the pure solvent's vapor pressure due to a dissolved solute, denoted ΔP. It is one of the four classic colligative properties, alongside boiling point elevation, freezing point depression, and osmotic pressure.
Colligative property ↗A property of a solution that depends only on the concentration (mole fraction or molality) of dissolved particles, not on their chemical identity. Vapor-pressure lowering, boiling point elevation, freezing point depression, and osmotic pressure are the four classic examples.
Ideal solution ↗A hypothetical solution in which the intermolecular forces between different components are the same as those between like components, so Raoult's law holds exactly across the entire composition range. Real solutions of chemically similar liquids (like benzene and toluene) approximate this closely.
Volatile ↗Describes a substance with a measurable vapor pressure that evaporates readily at a given temperature. A non-volatile solute (like table salt or sugar) is assumed to contribute essentially zero vapor pressure of its own, which is why the basic Raoult's law formula only tracks the solvent.
P = 0.9 × 23.8 = 21.42 mmHg. Dissolving enough non-volatile solute to make the solvent 90% of the moles present lowers the vapor pressure from 23.8 to 21.42 mmHg — a drop of 2.38 mmHg.
The solute's mole fraction is 1 − 0.9 = 0.1, so ΔP = 0.1 × 23.8 = 2.38 mmHg. This matches the difference between the pure solvent's 23.8 mmHg and the solution's 21.42 mmHg from the Solution VP tab — the two tabs describe the same physical change from opposite directions.
P_total = 0.4×100 + 0.6×40 = 64 mmHg. Because benzene is more volatile (higher pure vapor pressure) than toluene, even a minority mole fraction of benzene contributes a large share of the total vapor pressure — this is the starting point for distillation calculations.
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Reference
Cite This Calculator
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Use either format to cite this calculator in a paper, report, or resource list.
Raoult's law is the simplest quantitative link between a solution's composition and how readily it evaporates: the vapor pressure of a component above a solution is just its mole fraction times its vapor pressure as a pure substance. It explains why dissolving something in a liquid always suppresses evaporation, and it's the foundation for distillation, humidity calculations, and every other colligative property.
How the formula works
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In a pure liquid, molecules at the surface constantly escape into the vapor phase and re-condense, reaching an equilibrium vapor pressure P°. Add a solute, and some of the surface is now occupied by solute particles instead of solvent — fewer solvent molecules are available to escape at any instant, so the vapor pressure drops in direct proportion to how much of the solution is still solvent. That proportion is exactly the solvent's mole fraction, which is why P = X_solvent·P° holds so cleanly for ideal solutions.
The same logic extends to mixtures where both components are volatile: each component's presence at the surface is proportional to its own mole fraction, so each contributes its own mole-fraction-weighted vapor pressure, and the total is just the sum of both contributions.
Inputs and what they mean
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Mole fraction must be a value between 0 and 1, and for a two-component solution the solvent and solute mole fractions always add up to exactly 1 — that's what lets the calculator derive one from the other automatically on the VP Lowering tab. Pure vapor pressure (P°) is temperature-dependent, so make sure the value you enter matches the temperature you care about; water's vapor pressure is about 23.8 mmHg at 25°C but roughly 760 mmHg at its 100°C boiling point. For the Two Components tab, both mole fractions must sum to 1 since they describe the same mixture.
Limits and edge cases
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Raoult's law is exact only for an ideal solution, where the forces between different molecules are essentially identical to the forces between like molecules — chemically similar liquids like benzene and toluene come very close. Real solutions with strong specific interactions (hydrogen bonding, ion-dipole forces) show positive or negative deviations from the ideal prediction, especially at higher concentrations. The basic single-component formula also assumes the solute itself is non-volatile; if the solute evaporates too, you need the two-component form instead, since it also contributes its own vapor pressure to the total.
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Questions
Frequently Asked Questions
6 questions▸
What is the formula for Raoult's law?+
P = X_solvent · P°, where P is the solution's vapor pressure, X_solvent is the solvent's mole fraction, and P° is the vapor pressure of the pure solvent at the same temperature.
How do I find the vapor-pressure lowering?+
ΔP = X_solute · P°, where X_solute is the solute's mole fraction (1 minus the solvent's mole fraction). This equals the difference between the pure solvent's vapor pressure and the solution's vapor pressure.
What happens with a non-volatile solute?+
A non-volatile solute (like table salt or sugar) contributes essentially no vapor pressure of its own. Its only effect is to dilute the solvent's mole fraction, which lowers the solution's overall vapor pressure below the pure solvent's.
What if both components are volatile?+
When both liquids in a mixture have their own vapor pressure, sum the mole-fraction-weighted contribution of each: P_total = X_A·P°_A + X_B·P°_B. This is the basis for reading vapor-liquid equilibrium behavior in distillation.
Does Raoult's law always hold exactly?+
It's exact only for an ideal solution, where interactions between different molecules match interactions between like molecules. Chemically similar liquids approximate this well; solutions with strong specific interactions (like hydrogen bonding) deviate from the ideal prediction, more so at higher concentrations.
What units does the calculator use?+
Mole fractions are unitless, between 0 and 1. Vapor pressure can be entered in any consistent pressure unit (mmHg, kPa, atm) — the output is reported in the same unit you entered, since the formula is a pure ratio calculation.
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