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09.10 - Saturation Conditions from an Equation of State Click here. 60 1

We can combine the definition of fugacity in terms of the Gibbs Energy Departure Function with the procedure of visualizing an equation of state to visualize the fugacity as characterized by the PR EOS. (21min, uakron.edu) This amounts to plotting Z vs. density, similar to visualizing the vdW EOS. Then we simply type in the departure function formula. Since the PR EOS describes both vapors and liquids, we can calculate fugacity for both gases and liquids. Taking the reciprocal of the dimensionless density ( V/b=1/(bρ) ) gives a dimensionless volume. When the dimensionless pressure (bP/RT) is plotted vs. the dimensionless volume, the equal area rule indicates the pressure where equilibrium occurs and this can be checked by comparing the ln(f/P) values for the liquid and vapor roots. When the pressure is not exactly saturated, we may still be in the 3-root region. Then you need to check the fugacity to determine which phase is stable.

Concept Questions:

1. What equation can we use to estimate the fugacity of a compressed liquid relative to its saturation value?
2. How accurate is that equation relative to the change in pressure when we are close to saturation?
3. The video shows a graph of ln(f/P) vs. P. Which phase gives the lower value of fugacity when you are to the right of the intersection point? (ie. vapor or liquid?)
03.1 - Heat Engines and Heat Pumps: The Carnot Cycle Click here. 60 2

Heat Engine Introduction (LearnChemE.com, 6min) introduction to Carnot heat engine and Rankine cycle. The Carnot cycle is an idealized conceptual process in the sense that it provides the maximum possible fractional conversion of heat into work (aka. thermal efficiency, ηθ). But it is impractical for several reasons as discussed in the video. When operating on steam as the working fluid, as is common in nuclear power plants, coal fired power plants, and concentrated solar power plants, the Rankine cycle is much more practical, as explained here. This LearnChemE video is short and sweet, but it applies the property of entropy, which is not introduced until Chapter 4. All you need to know about entropy at this stage is that the change in entropy is zero for an adiabatic and reversible process and the change in entropy is greater than zero when you add heat or cause irreversibility. Since entropy is a state function, we can use the steam tables to facilitate accounting for inefficiencies. Entropy becomes essential when using steam as the working fluid because working out ∫PdV of steam is much more difficult than for an ideal gas. We reiterate this video in Chapter 5, where we discuss calculations for several practical cyclic processes.

Comprehension Questions:
1. Why is the Carnot cycle impractical when it comes to running steam through a turbine? How does the Rankine cycle solve this problem?
2. Why is the Carnot cycle impractical when it comes to running steam through a pump? How does the Rankine cycle solve this problem?
3. It is obvious which temperatures are the "high" and "low" temperatures in the Carnot cycle, but not so much in the Rankine cycle. The "boiler" in a Rankine cycle actually consists of "simple boiling" where the saturated liquid is converted to saturated vapor, and superheating where the saturated vapor is raised to the temperature entering the turbine. When comparing the thermal efficiency of a Rankine cycle to the Carnot efficiency, should we substitute the temperature during "simple" boiling, or the temperature entering the turbine into the formula for the Carnot efficiency? Explain.
07.06 Solving The Cubic EOS for Z Click here. 60 4

5. Peng Robinson Using Solver for PVT and Vapor Pressure - Excel (4:42) (msu.edu)

Describes use of the Goal Seek and Solver tools for Peng-Robinson PVT properties and vapor pressure.

Comprehension Questions:

1. Which of the following represents the vapor pressure for argon at 100K?
(a) 3.000 bars (b) 4.000 bars (c) 3.26903 bars.
11.02 - Calculations with Activity Coefficients Click here. 60 2

This example shows how to predict activity coefficients in Excel using the Margules Acid-Base (MAB) model.(8min, uakron.edu) Sometimes you just need a quick estimate of whether to suspect an azeotrope or LLE or some other anomalous behavior. If the MAB model indicates a possible problem, it's time to go to the library or the lab and validate your model with experimental data.

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. Order the following binary systems from most compatible to least compatible according to the MAB model:
(Note: negative deviations from Raoult's law indicate greater "compatibility," although they may generate azeotropes.)
(a) ethanol+water (b) ethanol+benzene (c) ethanol+diethylamine (d) n-pentane+n-pentanol (e) n-hexane+benzene
2. Pick a couple of binary systems from the Korean Database (Hint: use Internet Explorer for KDB) and compare the experimental data to the MAB predictions. Refine your predicted M1 parameter by calling the solver to minimize the sum of squared deviations between the predicted and experimental pressures. If there was an azeotrope in one of your systems, did the MAB model miss it or was it qualitatively correct?
07.06 Solving The Cubic EOS for Z Click here. 60 4

2. Solving the PR EOS for Z . (learncheme.com, 5min) Shows how to copy/paste from "Crit.Props" and "IG Cps" to "Props". Then compute some properties. Note: this video incorrectly uses a simple copy/paste instead of "paste special." Therefore, the color of the values on the "Props" tab changes from blue to black. Blue values should indicate values that you can change and black values should indicate cells that you should not alter. If you are having trouble finding a particular compound in the database, try searching for a piece of the name. e.g. if the compound is "nitrous oxide," search for "nitro."

Comprehension Questions:

1. What is the value for Zc of nitrous oxide? What is its "abbreviated name?"

2. What is the value of Tc for R1234yf?

3. Estimate the entropy of vaporization of toluene at 383.4K according to the Peng-Robinson EOS.

4. Estimate the entropy of vaporization of ethanol at 0.1MPa according to the Peng-Robinson EOS. Compare to the value you infer from Appendix E.
01.5 Real Fluids and Tabulated Properties Click here. 60 2

Steam Tables (LearnChemE.com) (5:59) calculate enthalpy of steam by interpolation
01.2 Molecular Nature of Temperature, Pressure, and Energy Click here. 60 9

Molecular Nature of Internal Energy: Configurational Energy. (uakron.edu, 19min) Making the connection between "u" and "U" requires the concept configuring the molecules such that their potentials overlap. Then it is a simple matter (conceptually) to count the number of overlaps that occur and multiply by the energy of the overlap to get the "configurational energy." Adding the configurational energy to the translational (and vibrational) energy (Uig, discussed above), gives the total "U."

Comprehension Questions:

For 1-4, assume 100 molecules are held in a cylinder with solid walls. A piston in the cylinder can move to adjust the density.
1. Suppose the range of the potential (λ) was increased. Would the configurational energy increase, decrease, or stay the same?
2. Suppose the density was decreased. Would the configurational energy increase, decrease, or stay the same?
3. Suppose the temperature was increased at constant density. Would the configurational energy increase, decrease, or stay the same?
4. Suppose the temperature was increased at constant density. Would the configurational energy characterized by (U-Uig)/RT  increase, decrease, or stay the same?
5. Molecules A and B can be represented by the square-well potential. For molecule A, σ = 0.2 nm and ε = 30e-22 J. For molecule B, σ = 0.35 nm and ε = 20e-22 J.  Sketch the potential models for the two molecules on the same pair of axes clearly indicating σ's and ε's of each species. Start your x-axis at zero and scale your drawing properly.  Make molecule A a solid line and B a dashed line. Which molecule would you expect to have the higher boiling temperature? (Hint: check out Figure 1.2.)
6. Sketch the potential and the force between two molecules vs. dimensionless distance, r/σ, according to the Lennard-Jones potential. Considering the value of r/σ when the force is equal to zero, is it greater, equal, or less than unity?
10.03 - Binary VLE using Raoult's Law Click here. 60 2

Raoult's Law (5:39) (msu.edu)
What type of components make an ideal solution that follows Raoult's Law? What does a diagram look like for a system that follows Raoult's Law? Can you identify the regions? What is the K-ratio for Raoult's Law? What simple principles must be followed for the K-ratios of the components in a binary mixture?
03.6 - Energy Balance for Reacting Systems Click here. 60 1

Heat Removal from a Chemical Reactor (uakron, 8min) determines heat removal so that a chemical reactor is isothermal following the pathway of Figure 3.5b using the pathway of Figure 2.6c if a heat of vaporization is involved. The reaction is: N2 + 3H2 = 2NH3 at 350C and 1 bar. The pathway to go from products to the reference condition is to correct for any liquid formation at the conditions of the product stream then cool/heat the products to 25C (the reference temperature), then "unreact" them back to their elements of formation. Summing up the enthalpy changes over these steps gives the overall enthalpy of the reactor outlet stream. The same procedure applied to the reactor inlet gives the overall enthalpy of reactor inlet stream. Then the heat duty of the reactor is simply the difference between the two stream enthalpies.

Comprehension Questions:
1. Use this approach to compute the heat of reaction for 2 CH3OH = CH3OCH3 + H2O at 250C and 1 bar. Compare to your answer when using the pathway of Figure 3.5a. 
2. Methanol is a liquid at 45C and 2bars. Compute the enthalpy of a stream that is 100 mol/h of pure methanol at 45 C and 2 bars according to the method of Figure 3.5b. Hint: this is different from the pathway of Figure 2.6c because it includes the heat of formation.
11.13 - Osmotic Pressure Click here. 60 5

Osmotic Pressure (7:23) (Learncheme.com)

A derivation of the relation for osmotic pressure, and an explanation of why the pressures are different on each side of the semi-permeable membrane.

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