The ideal gas law is a very clean, efficient way to deal with gases. Unfortunately, the two basic assumptions of the ideal gas law, that molecules are point masses and that they do not attract, are ideals. In reality, every molecule has a volume and attracts other molecules, to some extent. At low pressure and high temperature, this effect is negligible. As the pressure rises and temperature drops, however, the behavior of real gases strays from the ideal. At extremes of pressur e and temperature, the attractive forces and proximity may even force the gas into a liquid.

The van der Waals equation corrects the ideal gas law for real behavior:

(P + )(V - nb) = nRT    

This SparkNote examines how the van der Waals equation predicts real gas behavior.