Last updated: 2026-06-16

Understanding Dalton's law

In a mixture of gases that do not react, each component pushes on the container walls as though the others were not there. Dalton's law adds those individual contributions together:

The pressure a single component contributes is its partial pressure. Because pressure is proportional to the number of moles at a fixed temperature and volume, a component's partial pressure is simply its mole fraction times the total pressure:

The mole fraction $x_i$ is the moles of one component divided by the total moles in the mixture, so every mole fraction lies between 0 and 1, and they all sum to 1.

Worked example

Dry air at sea level sits at a total pressure of about 1 atm and is roughly 21% oxygen by moles, so the mole fraction of oxygen is $x = 0.21$. Its partial pressure is:

Now run the law in reverse. A gas whose partial pressure is measured at 0.5 atm and whose mole fraction is known to be 0.25 belongs to a mixture whose total pressure is:

Reading a composition from pressures

Because $P_i = x_i P_{total}$ rearranges to $x_i = P_i / P_{total}$, the ratio of a component's partial pressure to the total pressure is exactly its mole fraction. Measuring partial pressures therefore measures composition directly, without weighing anything.

The partial pressures in the last column add back to the 1 atm total, which is Dalton's law restated.

Why the gases act independently

The law works because an ideal gas has molecules far enough apart that they ignore one another between collisions. Each species fills the whole volume and collides with the walls at a rate set only by its own count of molecules, so its pressure depends on its own mole number, not on which other gases share the space. The assumption holds well at ordinary pressures; it weakens at high pressure or low temperature, where molecules crowd close enough to interact and the simple sum begins to drift.