How can the ideal gas law be used for a mixture of gases?

The ideal gas law, expressed as $PV=nRT$, can be applied to a mixture of gases by defining $n$ as the total number of moles of all species present in the volume $V$. In this context, $n$ is the sum of the moles of each individual component ($n=n_1+n_2+\dots$).1

Alternatively, the law can be applied to each component individually to determine its partial pressure. The partial pressure of a specific gas ($p_1$) is the pressure it would exert if it alone occupied the total volume of the mixture at the same temperature, calculated as $p_1=n_{1}RT/V$. According to Dalton’s law, the total pressure of the mixture is simply the sum of these individual partial pressures ($p=p_1+p_2+\dots$).21

This approach assumes that the gases do not chemically interact and behave as ideal gases, which is a valid approximation for real gases at sufficiently low pressures and high temperatures.23