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Dalton's Law Calculator

Calculate partial pressures of each gas in a mixture using Dalton's law: P_i = chi_i x P_total. Enter the total pressure and mole fractions for each gas (must sum to 1.0).

Gas Components

Dalton’s law of partial pressures

In a mixture of ideal gases, each component contributes to the total pressure in proportion to how much of it is there:

Pᵢ = χᵢ × P_total

where χᵢ is the mole fraction of component i. Equivalently, the total pressure is the sum of the partial pressures: P_total = P₁ + P₂ + P₃ + …

This calculator takes a total pressure and a list of components with their mole fractions, validates that the fractions sum to 1.0, and returns the partial pressure of each gas. Add or remove components to handle binary mixtures or full atmospheric breakdowns.

The reason Dalton’s law works for ideal gases is that ideal-gas molecules don’t interact — each one bounces off the walls without caring what other molecules are present. So the pressure each component exerts depends only on its own number density and temperature. Mole fraction packages “how many of this molecule” into a single dimensionless number, and multiplying by total pressure recovers the absolute partial pressure in whatever pressure unit you started with.

The law shows up anywhere gas mixtures matter: respiration (alveolar P_O₂ controls oxygen uptake into blood), diving (the partial pressure of N₂ at depth, not the percentage, is what causes narcosis), and gas-phase kinetics (reaction rates depend on each reactant’s partial pressure, not the total pressure of the system).

For gases collected over water, remember the trapped gas is humid — the total pressure includes water vapor. Subtract the vapor pressure of water at your temperature to get the dry-gas pressure before applying any further calculations.

Worked examples

Atmospheric air at 1.000 atm: χ(N₂) = 0.7808, χ(O₂) = 0.2095, χ(Ar) = 0.0093, χ(CO₂) = 0.0004. P(N₂) = 0.7808 atm, P(O₂) = 0.2095 atm, P(Ar) = 0.0093 atm, P(CO₂) = 0.0004 atm.

H₂ collected over water at 25 °C, total 760 mmHg: P(water vapor) = 23.8 mmHg at 25 °C. P(H₂) = 760 − 23.8 = 736.2 mmHg. Mole fraction of H₂ in the trapped mixture = 0.969.

Nitrox 36 at 2.0 atm depth: χ(O₂) = 0.36, χ(N₂) = 0.64. P(O₂) = 0.72 atm, P(N₂) = 1.28 atm.

Frequently Asked Questions

What is Dalton's law of partial pressures?
Dalton's law says the total pressure of a gas mixture is the sum of the partial pressures each gas would exert alone in the same container at the same temperature. For ideal gases, each component contributes pressure independently of what else is in the box. The compact form is Pᵢ = χᵢ × P_total, where χᵢ is the mole fraction. Sum the partial pressures and you recover the total.
What is a partial pressure?
A partial pressure is the pressure that one component of a gas mixture would exert if it were alone in the container at the same temperature. It's also that gas's contribution to the total pressure of the mixture. The two definitions are equivalent for ideal gases — each molecule of N₂ in the atmosphere pushes against the walls the same way whether oxygen is present or not.
What is a mole fraction?
Mole fraction (χ) is the moles of one component divided by total moles of all components in the mixture. It's dimensionless and runs from 0 to 1. All mole fractions in a mixture sum to exactly 1.0 by definition. Dry air is roughly χ(N₂) = 0.78, χ(O₂) = 0.21, χ(Ar) = 0.0093, χ(CO₂) = 0.0004, with the rest being trace gases.
How is Dalton's law used in gases collected over water?
When you collect a gas by water displacement, the gas inside the inverted container is mixed with water vapor that evaporated off the surface. The pressure gauge reads total pressure, but you usually want the pressure of the dry gas. Look up the vapor pressure of water at the experiment's temperature and subtract: P_gas = P_total − P_water. At 25 °C, P_water is about 23.8 mmHg.
Does Dalton's law apply to real gases?
It's exact for ideal gases and a solid approximation for real gases at moderate temperatures and pressures. Deviations grow when intermolecular interactions matter — high pressures, low temperatures, polar molecules, or near a condensation point. In those regimes, gases interact with each other and the simple additive picture starts to fail.