The van der Waals Equation
The ideal gas equation (PV=nRT) provides a valuable model of the relations between volume, pressure, temperature and number of particles in a gas. It also illustrates the importance of an absolute temperature scale. It is also of great interest in that it can be derived from the kinetic theory of gases. As an ideal model it serves as a reference for the behavior of real gases. The ideal gas equation makes some simplifying assumptions which are obviously not quite true. Real molecules do have volume and do attract each other. Some gases depart from ideal behavior to such an extent that some refinements became necessary.
In 1873 J. D. van der Waals proposed his equation, known as the van der Waals equation. As there are attractive forces between molecules the pressure is lower than the ideal value. To account for this the pressure term is augmented by an attractive force term a/V2. Likewise real molecules have a volume. The volume of the molecules is represented by the term b. The term b is a function of a spherical diameter d known as the van der Waals diameter. The van der Waals equation for one mole is
.
For n moles the equation is written
Tables of values for a and b are found in reference books. Below are some values for a and b. The units for a are liters2 atm. mole-2 and the units of b are liters mole-1.
| Molecule | a | b |
| H2 | 0.2444 | 0.02661 |
| O2 | 1.360 | 0.03183 |
| N2 | 1.390 | 0.03913 |
| CO2 | 3.592 | 0.04267 |
| Cl2 | 6.493 | 0.05622 |
| A | 1.345 | 0.03219 |
| Ne | 0.2107 | 0.01709 |
| He | 0.03412 | 0.02370 |