Mixture of gases - Dalton's law of partial pressures

When several non-reacting gases are mixed together, each component behaves independently of the others -- so it is natural to ask how the pressure of each individual gas contributes to the total pressure of the mixture.

John Dalton stated the answer: the total pressure of a mixture of non-reacting gases equals the sum of the partial pressures of the individual gases present, where the partial pressure of one component is the pressure that gas alone would exert if it occupied the same volume, at the same temperature, by itself. For a mixture of three gases 1, 2, 3 with partial pressures $p_1,p_2,p_3$ in a container of volume V,

Assuming each gas behaves ideally, $p_1=\dfrac{n_1RT}{V}$, $p_2=\dfrac{n_2RT}{V}$, $p_3=\dfrac{n_3RT}{V}$, so

Dividing the partial-pressure expression for gas $i$ by this total-pressure expression, the common factor $RT/V$ cancels, leaving the partial pressure written in terms of mole fraction $x_i=n_i/n_{Total}$:

Application: gas collected over water. When a gas is collected in the laboratory by downward displacement of water, the collected gas is never pure -- it is always mixed with water vapour, since some of the water evaporates into the collection space. Dalton's law lets this be corrected for directly:

where $P_{water\ vapour}$ (often called the aqueous tension) is looked up from standard tables of water's vapour pressure at the relevant temperature. …