Mixtures of Gases: Dalton’s Law of Partial Pressures and Mole Fractions

Unless individual gases chemically react with each other, the individual gases in a mixture of gases do not affect each other’s pressure. Each gas in a mixture exerts the same pressure that it would exert if it were present alone in the container. The pressure exerted by each individual gas in a mixture is called its partial pressure.

This means that in a mixture containing three different gases A, B, and C, if P_A is the partial pressure of gas A; P_B is the partial pressure of gas B; P_C is the partial pressure of gas C; then the total pressure is given by equation 1: 

This is Dalton’s law of partial pressures: The total pressure of a mixture of ideal gases is equal to the sum of the partial pressures of the component gases.

Let n_A, n_B, and n_C be the number of moles of each of the gases in the mixture. If each gas obeys the ideal-gas equation, the partial pressure can be written as:

Since all gases are at the same temperature and occupy the same volume, substituting into equation 1 gives:

The equation indicates that at constant temperature and constant volume, the total pressure of a gas sample is determined by the total number of moles of gas present.

For mixtures of gases, it is convenient to introduce a quantity called the mole fraction, χ, which is defined as the number of moles of a particular substance in a mixture divided by the total number of moles of all substances present. Mathematically, the mole fraction of a substance A in a mixture with B and C is expressed as

Similarly, the mole fraction of B and C are;

Combining the equation for the mole fraction of A and the equation for partial pressure gives:

The partial pressure of gas A is related to the total pressure of the gas mixture via its mole fraction.

In other words, the pressure of a gas in a mixture of gases is the product of its mole fraction and the total pressure of the mixture.

This text is adapted from Openstax, Chemistry 2e, Section 9.3: Stoichiometry of Gaseous Substances, Mixtures, and Reactions.