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|06.1 The Fundamental Property Relation||Click here.||70||2||
From the physical world to the realm of mathematics (uakron.edu, 15min) In Unit I, students develop the skills to infer simplified energy and entropy balances for various physical situations. In order to facilitate that approach for applications involving chemicals other than steam and ideal gases, we need to transform that approach into a realm of pure mathematics. In this context it suffices to apply the energy and entropy balance of a very simple system (piston/cylinder) then focus on the state functions that are involved (U,H,S,...). The mathematical realm is relatively abstract, but it is ideally suited for the generalizations required to extend our principles from steam and ideal gases to any chemical.
1. In example 4.16, we noted that the estimated work to compress steam was less when treated with the steam tables than when treated as an ideal gas. Explain why while referring to the molecular perspective.
2. In Chapter 5, we noted that the temperature drops when dropping the pressure across a valve when treating steam or a refrigerant with thermodynamic tables, but the energy balance suggests that the temperature drop for an ideal gas should be zero. Explain how these two apparently contradictory observations can both be true while referring to the molecular perspective.
3. What is the relation of the state variable dU to the state variables S and V according to the fundamental property relation?
4. What is the relation of the state variable dH to the state variables S and P according to the fundamental property relation?
5. What is the significance of writing changes of state variables in terms of changes in other state variables?
6. Why is the compressibility factor (Z=PV/RT) less than one sometimes?
7. Is it possible for Z to be greater than one? Explain.
8. What is the significance of having a relation for P = P(V,T)? How will that help us to solve problems involving chemicals other than steam and ideal gases?
|12.01 - The van der Waals Perspective for Mixtures||Click here.||70||4||
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.
|11.13 - Osmotic Pressure||Click here.||70||2||
MW of protein by osmotic pressure - (8:23) (learncheme.com)
An application of osmotic pressure measurement to determine MW of a protein.
|12.02 - The van Laar Model||Click here.||70||6||
The van Laar Equation (5:54) (msu.edu)
The van Laar equation uses the random mixing rules discussed in Section 12.1 with the internal energy to approximate the excess Gibbs Energy. What we learn is that it is possible to develop models using fundamental principles. Though this model is not used widely in process simulators, it provides a stepping stone to more advanced models.
|12.03 - Scatchard-Hildebrand Theory||Click here.||68.8889||9||
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,
_____ ______ ______ ______
|13.01 - Local Composition Theory||Click here.||68||10||
Local Composition Concepts (6:51) (msu.edu)
The local composition models of chapter 13 share common features covered in this screencasts. An understanding of these principles will make all the algebra in the models less daunting.
1. In the picture of molecules given in the presentation on slide 2, what is the numerical value of the local composition x11?
|13.02 - Wilson's Equation||Click here.||66.6667||6||
Wilson's model concepts (2:44) (msu.edu)
The background on the assumptions and development of Wilson's activity coefficient model.
1. What value is assumed by Wilson's model for the coordination number (z)?
|11.02 - Calculations with Activity Coefficients||Click here.||65||4||
This example shows how to incorporate activity calculations into Excel for solutions that follow the Margules 1-parameter (M1) model.(9min, uakron.edu)
You should be able to adapt this procedure along with the procedure for the multicomponent ideal solutions to create a multicomponent M1 model. If you are having trouble, the video for the multicomponent SSCED model illustrates a very similar procedure. You can check your answers by putting in the same component twice. For example, instead of an equimolar binary mixture, input a quaternary mixture with 0.25 moles of methanol, 0.25 methanol (ie. type it as if it was another component), 0.25 of benzene and 0.25 of benzene. If you don't get the same results as for the binary equimolar system, check your calculations.Note: This is a companion file in a series. You may wish to choose your own order for viewing them. For example, you should implement the first three videos before implementing this one. Also, you might like to see how to quickly visualize the Txy analog of the Pxy phase diagram. If you see a phase diagram like the ones in section 11.8, you might want to learn about LLE phase diagrams. The links on the software tutorial present a summary of the techniques to be implemented throughout Unit3 in a quick access format that is more compact than what is presented elsewhere. Some students may find it helpful to refer to this compact list when they find themselves "not being able to find the forest because of all the trees."
Comprehension Questions: Assume the SCVP model (Eq. 2.47).
|04.02 The Microscopic View of Entropy||Click here.||65||4||
Principles of Probability I, General Concepts, Correlated and Conditional Events. (msu.edu, 17min) (Flash)
|04.02 The Microscopic View of Entropy||Click here.||65||4||
Principles of Probability II, Counting Events, Permutations and Combinations. This part discusses the binomial and multinomial coefficients for putting particles in boxes. The binomial and multinomial coefficient are used in section 4.2 to quantify configurational entropy. (msu.edu, 16min) (Flash) You might like to check out the sample calculations below before attempting the comprehension questions.