Preview, November 9, 2001
  CURMUDGEON GENERAL'S WARNING. These "slides" represent highlights from lecture and are neither complete nor meant to replace lecture. It is advised not to use these as a reliable means to replace missed lecture material. Do so at risk to healthy academic performance in 09-105.
Besides repulsive interactions at short ranges associated with the excluded volume "b", we have attractive interactions at distances somewhat greater than the contact distance between molecules.
For real gas molecules, the attractions due to neighboring molecules retards the velocity of the collisions at the walls, reducing the pressure expected for ideal gases (where there are no such interactions).
The ideal pressure would be equal to the measured pressure plus a correction factor to account for the reduction by attractive molecule-molecule forces.
The gas compressibility, PV/RT, when the size effect ("b") is ignored, can be approximated by a linear relationship, varying with P with a negative slope.
A graph of the compressibility of a gas in which there are attractive, intermolecular forces (and in which the excluded volume effect is ignored).
The combined intermolecular forces produce a compressibility dependence on pressure that looks like this.
The "van der Waals" equation for real gas behavior has treated the excluded volume repulsion and intermolecular attraction separately and introduces the correction from each separately into the "V" and "P" terms of the ideal gas equation. You do not need to know the van der Waals equation.