# Van der Waals Equation

The Van der Waals equation is commonly written as either:

 (P + a 1 Vm2 ) (Vm - b) = RT
 (P + a 1 Vm2 ) (Vm - b) = RT

 (P + a n2 V2 ) (V - nb) = nRT
 (P + a n2 V2 ) (V - nb) = nRT

In thermodynamics and chemistry, the Van der Waals equation of state generalizes the ideal gas law based on the fact that real gases do not act ideally. This law considers gas molecules as point particles which can only interact with their containers, which means that they cannot change their kinetic energy nor take up space during collisions, making them perfectly elastic.

The ideal gas law states that volume (V) occupied by n moles of any gas has a pressure (P) at temperature (T) in kelvins given by the following relationship, where R is the gas constant:

PV = nRT

PV = nRT

To account for the volume that a real gas molecule takes up, the Van der Waals equation replaces V in the ideal gas law with (Vm - b), where Vm is the molar volume of the gas and b is the volume that is occupied by one mole of the molecules. This leads to:

P (Vm - b) = RT

P (Vm - b) = RT

 Van der Waals Coefficients Gas a (Pa m6) b (m3/mol) Helium 3.46 x 10-3 23.71 x 10-6 Neon 2.12 x 10-2 17.10 x 10-6 Hydrogen 2.45 x 10-2 26.61 x 10-6 Carbon dioxide 3.96 x 10-1 42.69 x 10-6 Water vapor 5.47 x 10-1 30.52 x 10-6