Dalton's law of partial pressures states that if a container contains a mixture of ideal gases the total pressure exerted by the gas is the sum of the pressures exerted by each individual gas if they alone occupied the entire volume of the container. Ideally the ratio of partial pressures is the same as the ratio of molecules. That is, the mole fraction of an individual gas component in an ideal gas mixture can be expressed in terms of the component's partial pressure or the moles of the component:
hence the partial pressure of an individual gas component gas can be obtained from rearranging to give
where: | |
| = mole fraction of any individual gas component in a gas mixture |
|---|---|
| = partial pressure of any individual gas component in a gas mixture |
| = moles of any individual gas component in a gas mixture |
| = total moles of the gas mixture |
| = total pressure of the gas mixture |
The mole fraction of a gas component in a gas mixture is equal to the volumetric fraction of that component in a gas mixture.
The law can be obtained naturally from the ideal gas equation
Applying this for each gas (note that V is the same for each gas – it is the volume of the container) in turn gives
Adding these equations gives
then the total pressure is
and the total number of mols is