Dalton's law of partial pressures
Mix several gases in one container and they share the space without getting in each other's way. Dalton's law says the total pressure they push with is simply the sum of the pressures each one would exert if it had the container all to itself — the partial pressures just add up.
Put as a formula, the total pressure equals the partial pressure of the first gas plus that of the second plus the third, and so on. It works because, in an ideal mixture, the molecules of one gas ignore the molecules of the others; each gas drums on the walls as though the rest were not there, and the drumming simply totals up.
Dalton's law matters wherever gases are mixed or collected, which is almost everywhere — in your lungs, in industrial reactors, and in the lab. A classic use is collecting a gas over water: the measured pressure includes water vapour, so you subtract water's partial pressure to find the pressure of the gas you actually want.
When hydrogen is collected by bubbling it up through water, the jar holds hydrogen plus water vapour; to get the true hydrogen pressure you subtract the water's partial pressure, exactly as Dalton's law instructs.
Collecting gas over water: subtract the water vapour's partial pressure.
Dalton's law is an ideal-gas result. It holds well for ordinary mixtures but, like all ideal-gas laws, weakens at high pressure where the molecules of different gases start to attract and crowd one another.