The ideal gas law is an equation of state of a hypothetical ideal gas. It is an approximation to the behaviour of many gases under many conditions. The ideal gas law however has many limitations. Emile Clapeyron was the first the state the equation in 1834 as a combination of Boyle’s law and Charles’ law. The ideal gas law is
PV = nRT
Where P is pressure, V is volume, n is the number of moles, T is the temperature, and R is the universal gas constant.
In Statistical mechanics, the ideal gas law is
PV = NkT
Where P is the absolute pressure, V is the volume, N is the number of particles in the gas, k is the Boltzmann constant and T is the temperature.
These equations only apply to ideal gas. There are many other forms of equations of states. The ideal gas law neglects both molecular size and intermolecular attractions. It is most accurate for monatomic gases at high temperatures and low pressures. The neglect of molecular size becomes less important for lower densities.