The Raoult's law calculator above computes the vapour pressure above a liquid mixture. Each component contributes its own pure vapour pressure scaled down by how much of the liquid it makes up, and the total is the sum. The tool reports both partial pressures, the total, the composition of the vapour that results, and how far the total sits below the vapour pressure of pure component A. Switch to non-volatile mode and it becomes the classic colligative calculation: how much a dissolved solid lowers the vapour pressure of its solvent.
Arb Digital publishes free calculators that show the part of the answer people usually miss. With Raoult's law, that part is the vapour composition. Almost every worked example stops at the total pressure, yet the interesting number is the mole fraction of each component in the vapour, because that is what separates in a distillation and what a still actually collects. Both come out of the same two multiplications.
What This Raoult's Law Calculator Does
Raoult's law states that the partial vapour pressure of a component above an ideal solution equals its mole fraction in the liquid multiplied by the vapour pressure it would have as a pure liquid at the same temperature. The calculator takes the amounts of both components, converts them to mole fractions, multiplies each by the pure vapour pressure you supply, and adds them.
It then applies Dalton's law in the vapour phase to get the composition of that vapour. Since each component's share of the total pressure is its mole fraction in the gas, the mole fraction of A in the vapour is simply its partial pressure divided by the total. The two bars compare the liquid composition to the vapour composition side by side.
Two boundaries are worth stating. Our vapour pressure calculator handles a single pure liquid and answers a different question: how its vapour pressure changes with temperature. Use it to get the pure-component values you feed into this page. And our partial pressure calculator splits a measured total pressure among gases that are already in a mixture; this page predicts what that total will be from a liquid's composition in the first place.
How to Use It
- Pick the mode. Two volatile components for something like benzene and toluene, non-volatile for a dissolved solid such as sugar or salt.
- Enter the amounts in moles. Only the ratio matters, so 0.5 and 0.5 gives the same result as 2 and 2. If you have masses, convert them first with the molar mass calculator.
- Enter both pure vapour pressures at the same temperature, in whatever unit you like, as long as it is the same unit for both.
- Read the vapour composition tile to see how much the vapour is enriched in the more volatile component compared with the liquid.
- Use the lowering tile when you are working a colligative problem. In non-volatile mode it is the vapour pressure lowering exactly as the textbook defines it.
The Formula and How It Is Calculated
For component A, pA = xA × P°A, and likewise for B. The total is P = xAP°A + xBP°B. The mole fractions come from the amounts: xA = nA / (nA + nB). In the vapour, yA = pA / P.
Take the default. An equimolar mixture of benzene and toluene at 25 °C, where pure benzene is 95.1 mmHg and pure toluene 28.4 mmHg, gives xA = xB = 0.500. So pbenzene = 0.500 × 95.1 = 47.55 mmHg, ptoluene = 0.500 × 28.4 = 14.20 mmHg, and the total is 61.75 mmHg. The vapour composition is ybenzene = 47.55 / 61.75 = 0.770. Half the liquid is benzene and 77 percent of the vapour is — the enrichment that makes fractional distillation possible.
For a non-volatile solute the second term vanishes and the total collapses to P = xsolventP°solvent. The lowering is then ΔP = P° − P = xsoluteP°, which is the form most textbooks quote and the reason vapour pressure lowering is called a colligative property: it depends on how many solute particles there are, not what they are. Pure-component vapour pressures for thousands of substances are tabulated in the NIST Chemistry WebBook, and the water values used in the examples here come from its phase-change data for water.
The Vapour Is Never the Same Mixture as the Liquid
This is the result the calculator exists to surface. Unless the two pure vapour pressures happen to be identical, the vapour is always richer in the more volatile component than the liquid it came from. The size of the enrichment is set by the ratio of the two pure vapour pressures, called the relative volatility.
Condense that vapour and you have a new liquid of the enriched composition. Boil it again and the new vapour is richer still. Repeat the cycle enough times and you separate the components. Each repetition is a theoretical plate, and a fractionating column is a device for stacking hundreds of them into a single vertical tube. The benzene-toluene pair above has a relative volatility near 3.3, which is comfortable; pairs with a ratio near 1 need enormous columns because each stage buys so little.
The limiting case is worth knowing about because it defeats distillation entirely. Some mixtures reach a composition at which the vapour and the liquid have the same composition — an azeotrope — and boiling stops separating anything. Ethanol and water form one at about 95.6 percent ethanol by mass, which is why ordinary distillation cannot produce anhydrous ethanol no matter how tall the column. Azeotropes only occur in non-ideal mixtures, so Raoult's law in this simple form never predicts one.
When a Mixture Actually Behaves Ideally
Raoult's law assumes that a molecule of A is held in the liquid by its neighbours with the same strength whether those neighbours are A or B. That is close to true when the two components are chemically similar and comparably sized — benzene with toluene, hexane with heptane, and other members of the same homologous series. For those, the law is accurate across the whole composition range.
Mixtures that are not similar deviate, and the direction of the deviation tells you what is going on. If A and B attract each other more strongly than they attract themselves, fewer molecules escape and the real vapour pressure is lower than Raoult predicts — a negative deviation, as with chloroform and acetone, which form a weak hydrogen bond. If they attract each other less, more escape and the pressure is higher — a positive deviation, as with ethanol and water, where mixing breaks the alcohol's own hydrogen-bonded network. Positive deviations frequently produce a minimum-boiling azeotrope, negative ones a maximum-boiling azeotrope.
Real work handles this with an activity coefficient γ, writing pA = γAxAP°A. The coefficient is one for an ideal mixture and departs from one as the mixture misbehaves; it is measured, or fitted from a model, rather than predicted from first principles. Nothing on this page estimates it, so treat the output as the ideal reference case that a real measurement should be compared against.
One Law Behind Four Colligative Properties
Vapour pressure lowering is the parent of the other colligative properties, and seeing the connection makes them easier to keep straight. Lowering the vapour pressure of a solvent means the solution must be heated further before its vapour pressure reaches atmospheric — that is boiling point elevation. The same lowering shifts the temperature at which the liquid and solid have equal vapour pressure downwards, which is freezing point depression. Osmotic pressure comes from the same reduced escaping tendency across a membrane.
All four scale with the number of dissolved particles rather than their identity, which means an ionic solute counts more than once. One mole of glucose gives one mole of particles; one mole of sodium chloride gives close to two moles of ions, and one mole of calcium chloride close to three. The van't Hoff factor accounts for this, and it is why entering the moles of formula units rather than moles of particles will understate the effect for any salt. Our molality calculator shows the freezing-point side of this, and the osmotic pressure calculator the membrane side.
The boiling-point link is the most directly useful. A solution's boiling point is where its total vapour pressure reaches the surrounding pressure, so the total this page reports tells you which way the boiling point has moved. Our boiling point calculator solves that condition for the temperature itself.
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Browse All Free Tools Suggest a ToolCommon Mistakes to Avoid
- Using the solute's mole fraction where the solvent's belongs — the total vapour pressure uses the solvent fraction; the solute fraction gives the lowering. Swapping them inverts the answer.
- Mixing masses with moles — mole fractions need amounts. Convert every mass through its molar mass before entering it.
- Ignoring dissociation of an ionic solute — a mole of sodium chloride supplies about two moles of particles, so it lowers vapour pressure roughly twice as much as a mole of sugar.
- Reading the pure vapour pressures at different temperatures — both values must come from the same temperature or the total is meaningless.
- Expecting ideal behaviour from dissimilar liquids — ethanol and water deviate strongly and form an azeotrope, which Raoult's law in this form cannot predict.
Related Free Tools From Arb Digital
Get the pure-component numbers this page needs with the vapour pressure calculator, then split a measured mixture pressure with the partial pressure calculator. Work out composition ratios using the mole fraction calculator, convert masses to amounts with the molar mass calculator, and follow the colligative chain into the boiling point calculator, the molality calculator and the osmotic pressure calculator. The full free online tools hub lists everything else.
Frequently Asked Questions
Raoult's law says the partial vapour pressure of a component above an ideal solution equals its mole fraction in the liquid multiplied by the vapour pressure of that component when pure, at the same temperature. The total vapour pressure is the sum over all components.
Multiply each component's liquid mole fraction by its pure vapour pressure and add the results. An equimolar benzene and toluene mixture at 25 degrees Celsius gives 0.5 times 95.1 plus 0.5 times 28.4, which is 61.75 mmHg.
Because each component contributes in proportion to its own pure vapour pressure, the more volatile one takes a larger share of the gas than it holds in the liquid. In the benzene and toluene example the liquid is 50 percent benzene while the vapour is 77 percent benzene.
It is the amount by which a non-volatile solute reduces the vapour pressure of its solvent, equal to the solute's mole fraction times the pure solvent's vapour pressure. It is a colligative property, so it depends on how many particles dissolve rather than what they are.
Chemically similar liquids of comparable size, such as benzene with toluene or hexane with heptane. Dissimilar pairs deviate: chloroform and acetone show negative deviation because they attract each other more strongly, while ethanol and water show positive deviation.
No. Sodium chloride separates into two ions, so a mole of it lowers vapour pressure roughly twice as much as a mole of a molecular solute. Enter the moles of particles rather than moles of formula units to model that correctly.
The pair forms an azeotrope at about 95.6 percent ethanol by mass, a composition at which the vapour and the liquid are identical. Once a column reaches that point further boiling changes nothing, and azeotropes are a non-ideal effect that this simple form of Raoult's law cannot predict.
It is a correction factor that turns Raoult's law into a statement about real mixtures, written as partial pressure equals gamma times mole fraction times pure vapour pressure. It equals one for an ideal solution and is measured or fitted rather than predicted from the formula.
This calculator is provided for education and general reference. It describes how vapour pressures above ideal solutions are computed and is not laboratory, distillation or safety guidance; follow the procedures and risk assessments issued by your own institution.
