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|08.02 - The Internal Energy Departure Function||Click here.||80||4||
The Internal Energy Departure Function (11min, uakron.edu) Deriving departure functions for a variety of equations of state is simplified by transforming to dimensionless units and using density instead of volume. This also leads to an extra simplification for the internal energy departure function.
1. What is the value of T(∂P/∂T)V - P for an ideal gas?
|10.10 - Mixture Properties for Ideal Solutions||Click here.||80||1||
10.9 - 10.12 Mixture Properties Overview (6:53) (msu.edu)
This section of the text is thick with lots of equations. It may help to filter out the most important equations and results so that you have the perspective of the overall objectives of this section. There are a lot of equations in this section to show that the component fugacity in an ideal solution is simply the mole fraction multiplied by the pure component fugacity. In a liquid mixture, this is approximated as the mole fraction times the vapor pressure! This screencast goes on to preview the most important results of the next section to help you see the overall story.
|07.05 Cubic Equations of State||Click here.||80||1||
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.
1. Of the two parameters a and b, which is related to attractive forces and which is related to attractive forces?
|08.05 - Summary of Density Dependent Formulas||Click here.||80||1||
Enthalpy Departure Function for the vdW Fluid (5min) (LearnChemE.com) This short video shows the application of Eqn. 8.24 and the van der Waals equation of state. This is a simple equation of state and the derivation is easy, so it is a good place to start in order to understand the process.
|01.2 Molecular Nature of Temperature, Pressure, and Energy||Click here.||76.962||79||
Molecular Nature of Energy and Temperature (msu.edu) (3:34)
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.
|12.01 - The van der Waals Perspective for Mixtures||Click here.||76.6667||6||
Mixing Rules (7:23) (msu.edu)
How should energy depend on composition? Should it be linear or non-linear? What does the van der Waals approach tell us about composition dependence? This screencasts shows that the mixing rule for 'a' in a random mixture should be quadratic. A linear mixing rule is usually used for the van der Waals size parameter.
|12.03 - Scatchard-Hildebrand Theory||Click here.||74.5455||11||
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.
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,
_____ ______ ______ ______
|13.05 - UNIFAC||Click here.||73.3333||6||
UNIFAC concepts (8:17) (msu.edu)
UNIFAC is an extension of the UNIQUAC method where the residual contribution is predicted based on group contributions using energy parameters regressed from a large data set of mixtures. This screecast introduces the concepts used in model development. You may want to review group contribution methods before watching this presentation.
1. What is the difference between the upper case Θ of UNIFAC and the lower cast θ of UNIQUAC?
2. Suppose you had a mixture that was exactly the same proportions as the lower right "bubble" in slide 2. Compute ΘOH for that mixture.
3. Compare your value computed in 2 to the value given by unifac.xls.
|02.01 Expansion/Contraction Work||Click here.||73.3333||3||
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.
|08.01 - The Departure Function Pathway||Click here.||73.3333||6||
Departure Function Overview (11:22) (msu.edu)