Dalton's Law of Partial Pressures

In a gas mixture, each gas exerts a partial pressure proportional to its mole fraction, and the total is their sum.

P_{\text{total}} = P_1 + P_2 + \cdots \quad ; \quad P_i = X_i \, P_{\text{total}}

P_total = P1 + P2 + ... ; Pi = Xi × P_total

What it means

Dalton's law treats a gas mixture democratically: every molecule contributes to the wall collisions independently of its identity, so the total pressure is simply the sum of each gas's partial pressure. Since pressure from each gas is proportional to its particle count, a gas's partial pressure equals its mole fraction times the total pressure — a mixture that is one-third nitrogen by moles is one-third nitrogen by pressure. When to use it: for any gas mixture problem — air composition, gas collected over water (where water vapor is one of the components), or finding a single gas's contribution to total pressure.

Variables

Symbol	Name	Unit	Meaning
$P_total$	Total pressure	atm (or Pa, kPa)	The sum of all partial pressures in the mixture.
$Pi$	Partial pressure of gas i	atm (or Pa, kPa)	The pressure one gas would exert if it alone occupied the container at the same temperature.
$Xi$	Mole fraction	unitless	The fraction of all gas molecules that are of type i (n_i / n_total).

Assumptions

The gases do not react with each other.
All gases share the same temperature and occupy the same volume.
Each gas behaves ideally, so particles collide without attracting or repelling.

Worked example

Problem

A container holds 1.00 mol N2 and 2.00 mol O2 at a total pressure of 3.00 atm. Find each gas's partial pressure.

Given:

1.00 mol N2 and 2.00 mol O2 in a container
P_total = 3.00 atm

Find total moles: n_total = 1.00 + 2.00 = 3.00 mol.
Mole fraction of N2: X_N2 = 1.00 / 3.00 = 0.333.
Mole fraction of O2: X_O2 = 2.00 / 3.00 = 0.667.
Partial pressure of N2: P_N2 = 0.333 × 3.00 atm = 1.00 atm.
Partial pressure of O2: P_O2 = 0.667 × 3.00 atm = 2.00 atm.
Check: 1.00 + 2.00 = 3.00 atm, matching the total.

P(N2) = 1.00 atm, P(O2) = 2.00 atm (sum = 3.00 atm)

Oxygen, being twice as abundant, contributes twice the pressure — each gas's share of the total pressure matches its share of the molecules.