Partial pressure calculator

What is Dalton’s law?

In a mixture of gases, each gas’s partial pressure is its mole fraction times the total pressure: P_A = X_A × P_total, where X_A = moles of A ÷ total moles. The partial pressures add up to the total (OpenStax Chemistry 2e).

Example

OpenStax: an anesthetic mixture of 2.83 mol O₂ and 8.41 mol N₂O at 192 kPa. The mole fractions are 0.252 and 0.748, so the partial pressures are 48.4 kPa and 144 kPa.

How do I enter the gases?

List the moles of each gas, separated by commas. Gas 1 is shown first; the table lists every gas.

Which pressure units can I use?

Any — atm, kPa, mm Hg, psi or bar. The partial pressures come out in the same unit.

Does it work with percentages?

Yes — for gases, mole percent works the same as moles. Enter 21, 78 and 1 for a simplified air mixture.

How do I correct for a gas collected over water?

A gas bubbled through water is saturated with water vapor, so the total pressure is the sum of the gas and the vapor. Subtract the vapor pressure of water at that temperature to get the dry gas. OpenStax Example 9.16 collects argon at 26 °C and 750 torr total; water’s vapor pressure at 26 °C is 25.2 torr, so the argon is at 724.8 torr, the book’s 725 torr.

Does it work when the gases react with each other?

No. Dalton’s law treats each gas as if it were alone in the container, which holds only while the gases do not react (OpenStax Chemistry 2e, section 9.3). Work out the mixture after the reaction first, then apply the law to what is left.

The two equations

Dalton’s law says the total pressure of an ideal gas mixture is the sum of the partial pressures of its components: P_total = P_A + P_B + P_C, and each partial pressure equals the mole fraction times the total, P_A = X_A × P_total, where X_A = n_A ÷ n_total (OpenStax Chemistry 2e, section 9.3). The mole fractions of all the gases add up to 1, so the partial pressures always add back to the total you entered. The calculator needs only the relative amounts, which is why mole percent or volume percent work as well as moles: at the same temperature and pressure, equal volumes of ideal gases hold equal numbers of moles.

Worked example

Suppose you know the amounts, the volume and the temperature but not the total pressure. OpenStax Example 9.14 puts 2.50 × 10⁻³ mol H₂, 1.00 × 10⁻³ mol He and 3.00 × 10⁻⁴ mol Ne in a 10.0 L flask at 35 °C. Each gas follows the ideal gas law on its own, P = nRT ÷ V, giving 0.00632 atm for H₂, 0.00253 atm for He and 7.59 × 10⁻⁴ atm for Ne (the book, using a rounded R, prints 7.58 × 10⁻⁴ for neon). The total is 0.00961 atm. Type “2.5, 1, 0.3” (millimoles work as well as moles) with that total and the table returns the same three pressures, with mole fractions 0.658, 0.263 and 0.079. The anesthetic mixture of Example 9.15 is the first example above.

Common mistakes

People often enter masses, or mass percent, where the calculator wants moles; convert grams to moles first, because a heavy gas carries fewer molecules per gram. Second, forgetting the water vapor when a gas was collected over water makes the dry gas look more abundant than it is. Third, applying the law to gases that react. Fourth, mixing up total and partial pressure: the “total pressure” field is the pressure of the whole mixture, not of any one gas, and all outputs share its unit. Finally, remember that Dalton’s law is an ideal-gas statement and is most accurate at low pressure.

Sources: OpenStax Chemistry 2e, section 9.3 “Stoichiometry of Gaseous Substances, Mixtures, and Reactions” (Dalton’s law, mole fraction, gas collected over water, Table 9.2, Examples 9.14 to 9.16). Related: ideal gas law calculator, combined gas law calculator, Graham’s law calculator and grams to moles calculator.