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.
| Gas | Equation |
|---|---|
| Gas 1 | (p_1=frac{n_1RT}{V}) |
| Gas 2 | (p_2=frac{n_2RT}{V}) |
| Both | (p_{tot}=p_1+p_2=frac{left(n_1+n_2right)RT}{V}) |
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
