Lecture #23

Chapter 5

  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.

Lecture Outline

Intermolecular Interactions

Ideal gases

Real gases (Van der Waals)

  • Excluded volume effect
  • Intermolecular attractions
Behavior of collections of molecules depends on intermolecular interactions, which we now begin to explore.
The "ideal gas" is defined. It has no intermolecular interactions.
The "ideal gas equation" relating measurable properties of an ideal gas.
The ease with which a gas can be compressed is measured through its "compressibility", defined here.
Continued discussion about the ease with which a gas can be compressed to smaller and smaller volumes.
Sample calculations of compressibilities. If H2 and NH3 were ideal, their compressibilities would have been unity (1.0000).
A brief table of compressibilities.
The Van der Waals interaction between two molecules. At large distances, there is no interaction (E=0). At close distances, the interaction is repulsive: the molecules cannot get too close without having to add energy to the system. At intermediate distance there is a range of separations where the interaction is attractive.
Van der Waals recognizes that a volume, equivalent to that occupied by the gas molecules themselves, is excluded from the space over which molecules can move.
The excluded volume for a molecule is calculated from the molecule's geometric characteristics -- here just the radius.
The compressibility of a gas whose molecules have size varies linearly with pressure, P.
A graph of the compressibility (PV/RT) of a gas which interacts through a repulsive force (has size).
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. Even the text has this as an unnumbered equation (p. 210).
Behavior of some common real gases as a function of pressure.
Behavior of nitrogen as a function of pressure at three different temperatures.
Typical parameters of the van der Waals real gas equation. Their relationship to structure will be discussed.