The equation PV = nRT

Unite the three partial laws, add the dependence on the number of molecules, and you obtain a single equation that governs any sufficiently dilute gas: the ideal gas law.

   P · V = n · R · T

   P : pressure (Pa)          n : amount of substance (mol)
   V : volume (m³)            R : ideal gas constant
   T : temperature (K)        R = 8.314 J/(mol·K)

This equation contains the three previous laws as special cases: freeze T, and P·V = constant remains (Boyle); freeze P, and V/T = constant remains (Charles); freeze V, and P/T = constant remains (Gay-Lussac). A single relation sums them all up.

The constant R is universal: it equals 8.314 J/(mol·K) for all gases. That is the miracle of the model: at low pressure, helium, air, carbon dioxide all obey the same equation, whatever their chemical nature.

It is in constant use. Knowing three of the quantities, you compute the fourth:

   n = P·V / (R·T)      how many moles in a balloon?
   V = n·R·T / P        what volume does one mole occupy?
   P = n·R·T / V        what pressure in a heated tyre?

For example, one mole of gas at 0 °C (273 K) and atmospheric pressure occupies about 22.4 litres — a very handy benchmark. The ideal gas law is one of the most used tools in all of physics and chemistry.