Why PV = nRT quietly stops working at high pressure — and what a gas is actually doing that the ideal gas law simply assumes away.
PV = nRT is usually the first equation anyone learns about gases, and it's taught with so little qualification that it's easy to walk away treating it as a law of nature rather than what it actually is: a deliberately simplified model. It works remarkably well across a wide range of everyday conditions. It also rests on two assumptions that no real gas actually satisfies — and the moment those assumptions stop being reasonable, the equation's predictions quietly drift away from reality, with no warning built into the math itself.