ideal gas law
Squeeze a gas into half the space and its pressure roughly doubles; warm it up and it pushes harder or swells; add more gas and the effect grows. The ideal gas law is the single tidy rule that ties all of these everyday observations together into one short equation.
Written PV = nRT, it states that the pressure P times the volume V of an ideal gas equals the amount of gas n (in moles) times the gas constant R times the absolute temperature T. Fix any two of these quantities and the law tells you exactly how the others must trade off. It is the equation of state for an ideal gas.
This one line absorbs and unifies the older separate gas laws of Boyle, Charles and Avogadro, each of which is just a special case got by holding some variables fixed. It is wonderfully reliable for ordinary gases but, being built on the ideal-gas picture, slowly loses accuracy at high pressure or low temperature, where real gases need fuller equations.
To find how many moles of helium fill a balloon, you measure its volume, the room's pressure and temperature, and rearrange PV = nRT to n = PV / RT — the whole calculation hangs on this one law.
PV = nRT links pressure, volume, amount and temperature in one step.
Temperature here must be the absolute (kelvin) temperature, never Celsius — using degrees Celsius in PV = nRT is one of the most common and disastrous beginner mistakes.