Ideal gas law
PV = nRT — the single equation onto which Boyle, Charles and Avogadro collapse, valid for any gas dilute enough that its molecules barely notice one another.
Definition
The ideal gas law states that the pressure P, volume V and absolute temperature T of a gas are tied together by PV = nRT, where n is the amount of gas in moles and R is the universal gas constant. Written per molecule it reads PV = Nk_BT, with N the number of molecules and k_B the Boltzmann constant. It is the equation of state of an idealised gas whose molecules are treated as point particles with no mutual forces except instantaneous elastic collisions.
The law unifies three empirical results discovered over a century and a half: Boyle's law (PV constant at fixed T), Charles's law (V proportional to T at fixed P), and Avogadro's hypothesis (V proportional to n at fixed P and T). Their common proportionality constant R = 8.314 J/(mol·K) is the same for every gas, which is the deepest content of the law: at low density the chemical identity of the gas drops out entirely.
The ideal gas law is an excellent approximation for real gases at ordinary temperatures and pressures, and it becomes exact in the limit of vanishing density. It breaks down where intermolecular forces or molecular volume can no longer be ignored — at high pressure, near condensation, or at very low temperature — deviations captured by the compressibility factor and the van der Waals equation.