# Top-rated ScreenCasts

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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.

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.

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.

Comprehension Questions:

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?

MW of protein by osmotic pressure - (8:23) (learncheme.com)

An application of osmotic pressure measurement to determine MW of a protein.

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

_____                          ______                             ______                          ______

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.

Comprehension Questions:

1. In the picture of molecules given in the presentation on slide 2, what is the numerical value of the local composition x11?
2. In the same picture, what is overall composition x1?
3. What value of Ω21 can you infer from 1 and 2 above and the equations on slide 3?

Wilson's model concepts (2:44) (msu.edu)

The background on the assumptions and development of Wilson's activity coefficient model.

Comprehension Questions:

1. What value is assumed by Wilson's model for the coordination number (z)?
2. What are the values of Λ21 and Λ12 at infinite temperature, according to Wilson's equation?
3. Solve for x1+x2Λ12 in terms of volume fraction (Φ1) and mole fraction (x1) at infinite temperature.
4. What type of phase behavior is impossible to represent by Wilson's equation?

Principles of Probability I, General Concepts, Correlated and Conditional Events. (msu.edu, 17min) (Flash)
Comprehension Questions:
1. Estimate the probability of pulling an king from a randomly shuffled deck of 52 cards.
2. A coin is flipped 5 times. Estimate the probability that heads is observed three of the 5 times.
3. A die (singular of dice) is a cube with the numbers 1-6 inscribed on its 6 faces. If you roll the die 7 times, what is the probability that 5 will be observed on all 7 rolls?

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.
Comprehension Questions:
1. Write the formulas for the binomial coefficient, the multinomial coefficient, and the multinomial with repetition.
2. Ten particles are distributed between two boxes. Compute the number of possible ways of achieving 7 particles in Box A and 3 particles in Box B.
3. Note that the binomial distribution is a special case of the multinomial distribution where the number of categories is 2. Also note that the total number of events for a multinomial distribution is given by M^N where M is the number of categories (aka. outcomes, e.g. boxes) and N is the number of objects (aka. trials, e.g. particles). The probability of a particular observation is given by the number of combinations divided by the total number of events. Compute the probability of observing 7 particles in Box A and 3 Particles in Box B.
4. Ten particles are distributed between three boxes. Compute the probability of observing 7 particles in Box A, 3 particles in Box B, and zero particles in Box C.
5. Ten particles are distributed between three boxes. Compute the probability of observing 3 particles in Box A, 3 particles in Box B, and 4 particles in Box C.