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Partial pressures and gas mixtures: Dalton's law in practice

A gas mixture has one total pressure but each component contributes its own share, called its partial pressure. Dalton's law makes the relationship quantitative: the partial pressures add up to the total, and each gas's share is its mole fraction.

This guide works through the three common descriptions of a mixture — component moles with a total pressure, the partial pressures themselves, and mole fractions — using a nitrogen-oxygen example. It also covers the unit and assumption details that decide whether a partial pressure calculation is valid.

By FormatFlow EditorialUpdated October 21, 2026More Chemistry Tools →

Mole fraction is the composition measure

The mole fraction of a component is its moles divided by the total moles of everything in the mixture: x_i = n_i / n_total. It is dimensionless, each fraction lies between 0 and 1, and the fractions of all components add up to 1. For an ideal gas, the mole fraction is also the volume fraction, which is why gas compositions are often quoted as percentages by volume.

Mole fraction is the link between composition and pressure. Once the fractions are known, the partial pressures follow from the total pressure alone, and conversely the measured partial pressures give the fractions. That two-way conversion is what makes Dalton's law useful in the lab.

From moles to partial pressures: worked example

Take a mixture of 0.20 mol of nitrogen and 0.30 mol of oxygen held at a total pressure of 100 kPa. The total moles are 0.20 + 0.30 = 0.50 mol, so nitrogen's mole fraction is 0.20 / 0.50 = 0.40 and oxygen's is 0.30 / 0.50 = 0.60. The fractions add up to 1, as they must.

Apply Dalton's law to each gas: P(N2) = 0.40 × 100 kPa = 40 kPa and P(O2) = 0.60 × 100 kPa = 60 kPa. The partial pressures add back to 100 kPa, which is the total pressure. That sum check is a quick way to catch a mole fraction that was computed with the wrong total.

From partial pressures to mole fractions

Sometimes a gas analyzer reports the pressure contributed by each component, and the total is not stated. Adding the partial pressures gives the total: in the same mixture, 40 kPa + 60 kPa = 100 kPa. Dividing each component's pressure by the total recovers the fractions 0.40 and 0.60.

This direction is useful when the mixture composition is what you want to know. It assumes the components do not react and that each reading is at the same temperature and volume; a reaction that consumes a gas would change the pressures and break the simple sum.

Partial pressures are also what many gas sensors and analyzers report for individual components, so going from measured partial pressures to mole fractions is a common analysis step. The same arithmetic works in reverse: a composition from a gas chromatograph can be turned into partial pressures once the total pressure is known.

From mole fractions to partial pressures

When the composition is given as fractions or percentages, the partial pressure of each gas is its fraction times the total pressure. Fractions of 0.40 and 0.60 at 100 kPa give 40 kPa and 60 kPa, exactly the numbers from the mole route, because the mole fraction already contains the composition information.

Rounded data often gives fractions that add to 0.99 or 1.01. Normalizing the fractions to sum to 1 before applying Dalton's law keeps the partial pressures consistent with the total; the calculator reports when it has normalized so the adjustment is visible rather than hidden.

Assumptions, units and limits

Dalton's law is exact for an ideal gas mixture with no reaction between components, all at the same temperature and sharing the same volume. Pressure and mole fraction calculations are unit-independent as long as the partial and total pressures use the same unit; this calculator converts through pascals so kPa, atm, bar and mmHg can be mixed in separate entries.

Real gases deviate at high pressure and near condensation, where the ideal partial pressure is replaced by fugacity in rigorous treatments. For mixtures at ordinary pressures and temperatures well above the boiling points, the ideal treatment is a good approximation and the one used by most lab calculations.

A unit check is worth doing explicitly. Mole fractions of 0.40 and 0.60 with a total pressure of 1.0 atm give partial pressures of 0.40 atm and 0.60 atm, which convert to about 40.5 kPa and 60.8 kPa because 1 atm is 101.325 kPa. The fractions stay the same across units; only the pressures convert.

Frequently asked questions

What is Dalton's law of partial pressures?

Dalton's law states that the total pressure of a non-reacting ideal gas mixture equals the sum of the partial pressures of its components. Each partial pressure is the pressure the gas would exert if it alone occupied the whole volume at the same temperature.

How do I calculate partial pressure from moles?

Divide each gas's moles by the total moles to get its mole fraction, then multiply by the total pressure: P_i = (n_i / n_total) × P_total. With 0.20 mol of N2 and 0.30 mol of O2 at 100 kPa total, the fractions are 0.40 and 0.60, so the partial pressures are 40 kPa and 60 kPa.

What is the difference between partial pressure and total pressure?

Total pressure is the pressure the whole mixture exerts, while a partial pressure is the contribution of one component. For an ideal non-reacting mixture the partial pressures add up to the total pressure, and each partial pressure equals its component's mole fraction times the total.

Do the partial pressures have to add up to the total pressure?

Yes for an ideal non-reacting mixture: by Dalton's law the sum of the partial pressures is the total pressure. If your numbers do not add up, check that every component is included and that the fractions or pressures were computed with the same total and the same pressure unit.

Does Dalton's law work for real gases?

It is an ideal-gas approximation. Real gases deviate at high pressure and low temperature, and rigorous treatments replace partial pressure with fugacity. At moderate pressure and well above condensation, the ideal calculation is usually accurate enough for lab work.

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