In an ideal-gas mixture whose components do not chemically react with one another, each gas contributes to the total pressure independently.

The pressure that component $i$ would exert if it alone occupied the mixture's volume at the same temperature is its partial pressure, $p_i$.

Dalton's law states

$$\boxed{p_{\mathrm{tot}}=\sum_i p_i}.$$

For each ideal-gas component,

$$p_iV=n_iR_uT,$$

while the whole mixture obeys

$$p_{\mathrm{tot}}V=n_{\mathrm{tot}}R_uT.$$

Dividing gives

$$\boxed{p_i=x_i p_{\mathrm{tot}}},$$

where

$$x_i=\frac{n_i}{n_{\mathrm{tot}}}$$

is the component's mole fraction.

Example

A gas mixture contains $2.0,\mathrm{mol}$ of nitrogen and $1.0,\mathrm{mol}$ of oxygen at a total pressure of $120,\mathrm{kPa}$.

The mole fractions are

$$x_{N_2}=\frac23,\qquad x_{O_2}=\frac13.$$

Therefore

$$p_{N_2}=\frac23(120)=80,\mathrm{kPa},$$

$$p_{O_2}=\frac13(120)=40,\mathrm{kPa},$$

and

$$80+40=120,\mathrm{kPa}.$$

Partial pressure is therefore both a mechanical contribution to total pressure and a convenient measure of gas-mixture composition.

A common laboratory application is gas collected over water. The measured total pressure includes water vapor:

$$p_{\mathrm{tot}}=p_{\mathrm{gas}}+p_{\mathrm{H_2O}}.$$

So the dry-gas pressure is found by subtracting the water-vapor partial pressure at the collection temperature.

Dalton's law is exact for an ideal-gas mixture and a useful approximation for many dilute real-gas mixtures. Strong nonideal interactions can make the simple independent-component picture less accurate.