The Ideal Gas Law

A gas is just a swarm of particles bouncing around, hitting the walls of their container and each other. Pressure comes from how hard and how often those collisions happen, volume is the space the particles are confined to, moles counts how many particles there are, and temperature measures their average kinetic energy. The ideal gas law, PV = nRT, ties all four together with R, the gas constant, as the conversion factor that makes the units work. Squeeze the volume down and collisions get more frequent, so pressure rises. Heat the gas and the particles move faster, hitting the walls harder, so pressure or volume rises too. That is why a sealed bag of chips puffs up at high altitude: outside pressure drops as you climb, but the gas trapped inside still pushes out just as hard, so the bag expands until the lower outside pressure is matched.

The law assumes particles have no volume themselves and do not attract or repel each other, which is close enough to true for most gases at normal pressures and temperatures. This idea sits right next to the individual gas laws, Boyle's, Charles's, and Avogadro's: each of those is just PV = nRT with two variables held constant. It also connects forward to partial pressures and to using gas data to find molar mass, since rearranging the law lets you solve for whichever quantity you do not know, as long as you have the other three.