Intro to the vdW EOS. (LearnCheme.com, 5min) Provides a brief overview of the van der Waals (vdW) 1873 equation of state (EOS), which served as a prototype for EOS development for over 100 years. Note: the vdW EOS is just one conjecture of how equations of state for real fluids may be formulated. In reality, each fluid has its own unique EOS. The vdW model conjectures that the pressure is altered relative to the ideal gas by the presence of attractive forces and repulsive forces.

Comprehension Questions:

1. Of the two parameters a and b, which is related to attractive forces and which is related to attractive forces?
2. How are the parameters a and b typically characterized/computed? ie. To what experimental constants are they related in order to compute them?
3. Is the vdW EOS an example of a 2-parameter EOS or 3-parameter EOS?
4. When writing the term (V-b) we subtract b because the molecules occupy volume and when V=b, all the "free volume" is gone. Can you explain the term (P+a/V²) in a similar manner?
5. In the presented example of CO2 at 0.2L and 269K, how does the pressure compare when computed by the ideal gas law vs. the vdW model? (Give both values.)
6. In the presented example of CO2 at 0.0L and 269K, how does the pressure compare when computed by the ideal gas law vs. the vdW model? (Give both values.)

Molecular Nature of Energy and Temperature (msu.edu) (3:34)
This introduction shows the connection with temperature and kinetic energy.  When applying Eqn. 1.1, you must be careful to keep your units straight, as illustrated in this sample calculation of the molecular temperature for xenon (Mw=131). (uakron, 5min).

Comprehension Questions:

1. A 1m3 vessel contains 0.5m3 of saturated liquid in equilibrium with 0.5 m3 of saturated vapor. Which molecules are moving slower? (a) the vapor (b) the liquid (c) they are all the same.

2. A glass of ice water is sitting in your freezer, set to 0C and fully equilibrated. Which molecules are moving slower? (a) the gas (b) the liquid (c) the solid (d) they are all the same.

3. You walk into the kitchen in the morning to get some breakfast. The ceiling fan is on. You forgot your slippers. Which one is "hotter?" (a) the floor (b) the ceiling (c) the granite counter top (d) the air in the room (e) they are all the same.

Scatchard-Hildebrand Theory (6:53) (msu.edu)

Have you ever heard 'Like dissolves like'? Here we see that numerically. The Scatchard-Hildebrand model builds on the van Laar equation by using pure component information. Scatchard and Hildebrand replaced the energy departure with the experimental energy of vaporization. Because this is related to the 'a' parameter in the van Laar theory, they developed a parameter called the 'solubility parameter', but based it on the energy of vaporization. Interestingly, the model reduces to the one parameter Margules equation when the molar volumes are the same.

Comprehension Questions:

1. Based on the Scatchard-Hildebrand  model, arrange the following mixtures from  most compatible to least compatible.  (a) Pentane+hexane,   (b) decane+decalin,  (c) 1-hexene+dodecanol,   (d) pyridine+methanol,
Most compatible                                                                     Least compatible

 _____                          ______                             ______                          ______

Vocabulary in Sections 2.1-2.3: Forms of "Work." (uakron.edu, 11 min) Making cookies is hard work. In discussing work, we develop several shorthand terms to refer to specific common situations: expansion-contraction work, shaft work, flow work, stirring work, "lost" work. These terms comprise the headings of sections 2.1-2.3, but it is convenient to discuss them all at once. The important thing to remember is that work is really just force times distance, pure and simple. The shorthand terms are not intended to complicate the discussion, but to expedite the analysis of the energy balance. Developing some familiarity with the terms related to common daily experiences may help you to assimilate this new vocabulary. Sample calculations (13min) illustrate a remarkable difference when one is faced with gas compression vs. liquid pump work. 

Comprehension Questions:
1. How is "expansion-contraction" work related to force times distance?
2. What is the expression for "flow" work? Explain how it relates to force times distance for fluid flowing in a pipe.
3. What expression can we use for calculating "shaft" work, as in a pump or turbine? What is the technique of calculus to which it is related?