# Top-rated ScreenCasts

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In a contest for "the most hated word in Chemical Engineering," fugacity won by a landslide. This video (15min, uakron.edu) reviews how the term was developed and why it's not really as bad as all that. In fact, it's a nice word that sets the stage for all of phase and reaction equilibrium with a straightforward extension of the same conceptual basis to mixtures. On second thought, perhaps the power of that conceptual basis and all that it implies is what really intimidates new students. Many perspectives have been offered to help overcome the frustration that students feel toward fugacity. If you like a comic book perspective, even that is available.

Comprehension Questions:

1.What is the fugacity of a vapor phase component in a mixture according to Raoult's law?
2.What is the fugacity of a liquid phase component in a mixture according to Raoult's law?
3. What word is modern usage is closely related to the latin root "fuga-"?
4. Water is in VLE at 0.7 bars in a fixed volume vessel. Five cm3 of air are injected into the vessel and the temperature is allowed to return to its original value. Does the water in the vapor phase increase, decrease, or remain the same? (Learncheme.com, 2min) (Hint: you may assume that air does not dissolve in the liquid water and the pressure is sufficiently low that the vapor can be assumed to behave as an ideal gas.)

15.04 - VLE calculations by an equation of state Click here. 80 1

PRMix.xlsx - Tutorial on use for bubble pressure (msu.edu) (10:06)

An overview of the organization of PRMix.xlsx, and a tutorial on the strategy to solve bubble pressure problems. Example 15.6 is worked in the screencast. After watching this screencast, you should be able to also solve dew or flash problems if you think about the strategy used to solve the problem. You may also be interested in a similar presentation from U.Colorado (learncheme, 6min).

01.2 Molecular Nature of Temperature, Pressure, and Energy Click here. 79.2 25

Molecular Nature of Internal Energy: Thermal Energy
This introduction to "thermal energy" elaborates on the ideal gas definition of temperature, which derives from the way that PV is related to kinetic energy. This PV relation can be easily understood in terms of an ultrasimplified model of ideal gas pressure. (uakron, 6min). Noting empirically from the ideal gas law that PV=nRT, we are led to the derivation of Eqn. 1.1 (uakron, 5min, same as above). This result suggests counter-intuitive implications about the the ways that solid, liquid, and gas molecular velocities must be related. When applying Eqn. 1.1, you must be careful to keep your units straight, as illustrated in this sample calculation of molecular temperature for Xenon (Mw=131g/mol) (uakron, 5min). On a closely related note, we could perform a sample calculation of molecular pressure for Xenon using Eqn. 1.21.

Comprehension Questions:
1. If two phases are in equilibrium (e.g. a vapor with a solid), then their temperatures are equal and the rate at which molecules leave the solid equals the rate at which molecules enter the solid. Which molecules are moving faster, solid or vapor? For simplicity, assume that the vapor is xenon and the solid is xenon. Hint: think about the exchange of momentum when the vapor molecules collide with the solid.
2. Compute the average (root mean square) velocity (m/s) of molecules at room temperature and pressure and compare to their speeds of sound. You can search the internet to find the speed of sound.
a. Argon
b. Xenon
3. Three xenon atoms are moving with (x,y,z) velocities in m/s of (300,-450,100), (-100,300,-50), (-200,-150,-50). Estimate the temperature (K) of this fluid.
4. Estimate the pressure of the xenon atoms in Q3 above in a vessel that is 4nm3 in size.

01.2 Molecular Nature of Temperature, Pressure, and Energy Click here. 78.0282 71

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.

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?

Departure Function Overview (11:22) (msu.edu)
The philosophy and overall approach for using departure functions.

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.

Comprehension Questions:

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.

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.

Comprehension Questions:

1. What is the value of T(∂P/∂T)V - P for an ideal gas?
2. What is the value of (∂U/∂V)T for an ideal gas and how can you explain this result at the molecular scale?
3. The Redlich-Kwong (RK) EOS is: P=RT/(V-b) -a/(V2RT1.5). Use Eqn. 8.13 to solve for (U-Uig)/RT of the RK EOS.
4. The RK EOS can be written as: Z = 1/(1-) - /(RT1.5). Use Eqn. 8.14 to solve for (U-Uig)/RT of the RK EOS.

Raoult's Law Calculation Procedures (11:45) (msu.edu)
Details on how to implement bubble, dew, and flash calculations for Raoult's Law. This screencast shows sample calculations for the bubble pressure and dew pressure of methanol+ethanol.

Comprehension Questions: Assume the ideal solution SCVP model (Eqns. 2.47 and 10.8).

1. Estimate the bubble pressure (bars) of 30% acetone + 70% benzene at 333K.
2. Estimate the dew temperature (K) of 30% acetone + 70% benzene at 1 bar.
3. Estimate the fraction vapor and phase compositions ethylamine+ethanol at 298K, 400mmHg and a feed of 60%amine.

Virial and Cubic EOS (11:18) (msu.edu)
Discusses the strategy of the virial EOS and the cubic EOS and the strategy used to solve as a cubic in Z. Gives formulas for calculating the a and b parameters of both the vdW and Peng-Robinson EOS's, as well as the virial EOS. You might want to watch the video on "Visualizing the vdW EOS" if you want to understand where the equations for a and b come from or how to make quantitative plots of isotherms.

Comprehension Questions:

1. To what region of pressure is the virial EOS limited at a given temperature? Why?
2. Is the Pitzer EOS limited to the same conditions as the virial EOS?
3. Is the virial EOS a 2-parameter or 3-parameter EOS?
4. Is the Peng-Robinson (PR) EOS a 2-parameter or 3-parameter EOS?
5. What is the primary shortcoming of the vdW EOS, as described on slide 4 of this presentation?
6. Is the PR EOS limited to the same conditions as the virial EOS? Explain.
7. How does the "fugacity" help you to identify the stable root of a cubic EOS?
8. When there are 3 real roots to a cubic EOS, what do we do with the center root? Why?