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Chapter 12 - Van der Waals Activity Models
Chapter 12 - Van der Waals Activity Models
12.01 - The van der Waals Perspective for Mixtures
12.01 - The van der Waals Perspective for Mixtures
Mixing Rules (7:23)
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.
Configurational Energy:Molecular Basis of Quadratic Mixing Rules
Configurational Energy and Quadratic Mixing Rules (uakron, 15min) van der Waals mixing rules can also be derived by counting the molecular energies, like we did in Section 1.2 and referring to the configurational energy departure function from Chapter 7. This approach lays the foundation for non-quadratic mixtures too, as discussed in Section 13.7. In this way, the concepts of Chapter 1 are connected to the model equations applied throughout the text.
12.02 - The van Laar Model
12.02 - The van Laar Model
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The van Laar Equation (5:54)
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
12.03 - Scatchard-Hildebrand Theory
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Scatchard-Hildebrand Theory (6:53)
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
_____ ______ ______ ______
Scatchard-Hildebrand in Excel
This video walks you through the process of transforming the M1/MAB model into the Scatchard-Hildebrand model using Excel (6min, uakron.edu) It steps systematically through the modifications to the spreadsheet to obtain each new model. You should implement the M1/MAB model before implementing this procedure.
Comprehension Questions:
1. Modify the M1/MAB spreadsheet to obtain Pxy diagrams with the Scatchard-Hildebrand, M2, and van Laar models.
2. Add Txy capability to each of the models.
3. Search for experimental data on the system ethanol+toluene. Modify your spreadsheets to plot the experimental data (points) on the same plot with the predictions. Which model (MAB or ScHil) provides the most accurate predictions when compared to data?
12.04 - The Flory-Huggins Model
12.04 - The Flory-Huggins Model
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The Flory and Flory-Huggins Models (7:05)
The Flory and Flory-Huggins Models (7:05) (msu.edu)
Flory recognized the importance of molecular size on entropy, and the Flory equation is an important building block for many equations in Chapter 13. Flory introduced the importance of free volume. The Flory-Huggins model combines the Flory equation with the Scatchard-Hildebrand model using the degree of polymerization and the parameter χ. The Flory-Huggins model is used widely in the polymer industry.
Comprehension Questions:
Assume δP=δS for polystyrene, where δS is the solubility parameter for styrene. Also, polystyrene typically has a molecular weight of about 15,000. Room temperature is 25°C.
1. Estimate the infinite dilution activity coefficient of styrene in polystyrene.
2. Estimate the infinite dilution activity coefficient of toluene in polystyrene.
3. Estimate the infinite dilution activity coefficient of acetone in polystyrene.
4. Which of the above would be the "best" solvent for polystyrene? Explain quantitatively.
12.05 - MOSCED and SSCED Theory
12.05 - MOSCED and SSCED Theory
Transforming Pxy of M1 Model to SSCED
This video walks you through the process of transforming the Scatchard-Hildebrand model into the SSCED model using Excel (6min, uakron.edu) It steps systematically through the modifications to the spreadsheet to obtain the new model. You should implement the Scatchard-Hildebrand model before implementing this procedure.
Comprehension Questions:
1. Add Txy capability to this model.
2. Predict the Txy diagram for methanol+benzene by the SSCED model at 2222mmHg. Estimate the phase compositions and phase amounts for the following operating temperatures and feed compositions. (a) 370K and zm = 0.30 (b) 350K and zm = 0.20 (c) 370K and zm = 0.70.
3. Compare your predicted Txy diagram to the predictions by the MAB and Scatchard-Hildebrand models. Describe the differences briefly for each case.
4. Search for experimental data on the system ethanol+toluene. Modify your spreadsheets to plot the experimental data (points) on the same plot with the predictions. Which model provides the most accurate predictions when compared to data?
5. Suppose you set k12=0 in the SSCED model. Does that improve the comparison to experimental data? Other models? Does the combination of k12=0 and k12=k12(alpha,beta) bracket the range of values that fit reasonably?
Conceptual Basis of SSCED, MAB, and Scatchard-Hildebrand
There are so many activity models, how can you keep them straight? This video shows how MAB, SSCED, and Scatchard-Hildebrand models are all closely related.(9min,uakron.edu) By changing the assumptions, one model can be transformed into the other. So focus on remembering one model very well, then remember the small adjustments to obtain the other models.
Comprehension Questions:
1. Suppose we are trying to find the solvent most compatible with dilute ethanol. Which of the following is most compatible according to the MAB model? (a) water (b) benzene (c) n-octanol.
2. Suppose we are trying to find the solvent most compatible with dilute ethanol. Which of the following is most compatible according to the ScHil model? (a) water (b) benzene (c) n-octanol.
3. Suppose we are trying to find the solvent most compatible with dilute ethanol. Which of the following is most compatible according to the SSCED model? (a) water (b) benzene (c) n-octanol. (Hint: consider the infinite dilution activity coefficient.)
12.07 Multicomponent Extensions of van Der Waals' Models
12.07 Multicomponent Extensions of van Der Waals' Models
Multicomponent M1/MAB Flash in Excel
M1/MAB Extension of the Multicomponent Flash Spreadsheet (19min, uakron.edu) adapted from Ideal Solutions (cf Section 10.4)
Shows how to modify the spreadsheet created for Ideal Solutions (Section 10.4) to apply modified Raoult's law for 5 components using the M1/MAB model.
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:
1. Find the bubble and dew pressures of an equimolar mixture of chloroform, acetone, and ethanol at 5 bars using the MAB model. Then compute V/F x and y at the pressure that is halfway between dew and bubble. Is it what you expected?
2. Find the bubble and dew pressures of an equimolar mixture of acetone, ethanol, and methane at 5 bars using the MAB model. Then compute V/F x and y at the pressure that is halfway between dew and bubble. Is it what you expected?
3. Find the bubble and dew pressures of an equimolar mixture of chloroform, acetone, and ethanol at 5 bars using the MAB model. Then compute V/F x and y at the pressure that is halfway between dew and bubble. Is it what you expected?
4. Find the bubble and dew pressures of an equimolar mixture of acetone, ethanol, and methane at 5 bars using the MAB model. Then compute V/F x and y at the pressure that is halfway between dew and bubble. Is it what you expected?
Multicomponent M2 Spreadsheet
The extension to the multicomponent M2 flash spreadsheet (uakron.edu, 10min) adapts the multicomponent M1 spreadsheet by recognizing that summing rows of a matrix times mole fractions involves a simple matrix multiplication. (Matrix operations involve highlighting the cells of interest, typing the MMULT function, and hitting ctrl+shift+enter.) The column multiplication simply applies the sumproduct function. In this way, we just need to insert one more column relative to the multicomponent M1 spreadsheet, then change the expression for gi, and we are done.
Comprehension Questions:
1. Find the bubble and dew temperatures of an equimolar mixture of 2-propanol, water, and methanol at 2 bars using the M2 model. Then compute V/F x and y at the temperature that is halfway between dew and bubble. Is it what you expected?
2. Find the bubble and dew temperatures of an equimolar mixture of 2-propanol, water, and methanol at 3 bars using the M2 model. Then compute V/F x and y at the temperature that is halfway between dew and bubble. Is it what you expected?
3. Find the bubble and dew temperatures of an equimolar mixture of 2-propanol, water, and methanol at 4 bars using the M2 model. Then compute V/F x and y at the temperature that is halfway between dew and bubble. Is it what you expected?
4. Find the bubble and dew temperatures of an equimolar mixture of 2-propanol, water, and methanol at 5 bars using the M2 model. Then compute V/F x and y at the temperature that is halfway between dew and bubble. Is it what you expected?