Gas mixtures

We don’t always work with a pure gas. Gases are often mixtures. For instance, the atmosphere is a mixture of nitrogen and oxygen.

Gas mixtures

The ideal gas law applies to both a total number of moles of gas, and also any subset of gases – i.e., different components in a mixture. The pressure of each component gas is referred to as “partial pressure”. This is the fraction of a pressure that is due to that particular gas.

Partial pressures are important because they are analogous to concentration. Everything involving equilibria and energy, that uses concentrations, can apply to gas phase reactions using partial pressures.

Mole fractions

A related concept is the mole fraction. This is the fraction (in terms of moles) of a gas in the mixture. In a system with two gases, 1 and 2, the mole fraction is:

$$ x_1=frac{n_1}{n_1+n_2} $$

In a mixture of 0.25 moles hydrogen and 0.5 mol of oxygen gases, the molar fraction of hydrogen is:

[frac{0.25}{0.25 + 0.5} = frac{0.25}{0.75} = 0.33]

A partial pressure is the mole fraction of the gas multiplied by the total pressure. So if the above hydrogen and oxygen mixture was at a pressure of 1.5 atm, the partial pressure of hydrogen would be:

[1.5 atm times 0.33 = 0.5 atm]

Ideal conditions

Finally, it’s worth noting ideal conditions. Ideal conditions allow us to use pressures in thermodynamic calculations. These conditions assume:

• Zero interactions between molecules
• Molecules have zero size

And this is more valid for a real gas:

• At low pressures / concentrations
• At higher temperatures