No matter what your misty-eyed grandparents tell you, there were never halcyon Days of
Old when all the gases were ideal. To be perfectly frank, not a single gas is really, truly ideal.
Some gases just approach the ideal more closely than others. At very high pressures, even
gases that normally behave close to the ideal cease to follow the ideal gas laws that we talk
about in Chapter 11.
When gases deviate from the ideal, we call them real gases. Real gases have properties that
are significantly shaped by the volumes of the gas particles and/or by interparticle forces. To
account for these nonideal factors, chemists use the van der Waals equation. Compared to
the ideal gas equation, , the following van der Waals equation includes two extra
variables, a and b. The variable a corrects for effects due to particle volume. The variable b
corrects for interparticle forces. The van der Waals equation is appropriate for gases at very
high pressure, in low-temperature conditions, and when gas particles have strong mutual
attraction or repulsion.