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09.08 - Calculation of Fugacity (Liquids) Click here. 90 2

Liquid fugacity relative to vapor fugacity. (LearnChemE, 5 min) This screencast shows a sample derivation and sample calculation for the vapor equation of state given by: Z = 1-0.01P, solve for: (a) the vapor fugacity at 500K and 30 bar (b) the liquid fugacity in equilibrium with the same vapor at 500K and 30bar (c) the liquid fugacity at 500K and 60 bar. Data: VL = 25 cm3/mol.

Comprehension Questions:

1. How much did raising the pressure to 60 bar change the liquid fugacity (bars) (+/- 1%)?
2. Estimate the fugacity (bars) of the vapor at 500 K and 60 bar and compare it to the liquid. Which is smaller? Which state do you think best characterizes the fluid (ie. V or L)?
3. Estimate the fugacity (bars) of n-pentane vapor at 30 bar and 460 K by Eqn. 7.5.
4. Assuming VL=229cm3/mol, estimate the fugacity of liquid n-pentane at 460K and 600bar.
5. Compare your answers for 3 and 4 to the PREOS.

08.08 - Reference States Click here. 90 2

Departure Functions: PREOS.xls Compressor and OVC Design (11min) ( Redesign the ordinary vapor compression cycle (OVC) using propane as discussed in Chapter 5, this time applying PREOS.xls instead of the chart. In this sample calculation, the cycle operates from -100F in the evaporator with a compressor that takes the saturated vapor from the evaporator to 10 bars and 180F. With this procedure, applying PREOS.xls could be adapted to any compound in the database, not just propane. So PREOS.xls represents the equivalent of charts for roughly 200 compounds, and that's just what it can do for pure fluids.
Comprehension Questions: Assume a reference state of the saturated liquid at 1 bar. Use Eqn. 2.47 (SCVP eq) to estimate saturation conditions.
1. Compute the enthalpy (J/mol) of saturated vapor N2O at -100F.
2. Compute the enthalpy (J/mol) of saturated liquid N2O at 80F.
3. Compute the enthalpy (J/mol) of N2O at 60 bars and 350F.
4. Compute the COP for this OVC cycle.

01.5 Real Fluids and Tabulated Properties Click here. 90 2

P-V and P-T diagrams ( (5:52) Describes distinctions and trends between solid, vapor, liquid, gas.

11.02 - Calculations with Activity Coefficients Click here. 87.5 8

Activity Coefficient Calculations in Matlab (6:12) (

An overview of the strategy of placing the activity coefficient models in a single folder, how the gammaModels .m files are used with scalars and vectors, and how to use the Matlab 'addpath' command to run the code from any folder on your computer.

11.02 - Calculations with Activity Coefficients Click here. 85.4545 11

Dew Pressure (7:41) (

The culmination of the activity coefficient method is application of the fitted activity coefficients to extrapolate from limited experiments in a Stage III calculation. The recommended order of study is 1) Bubble Pressure; 2) Bubble Temperature; 3) Dew Pressure; 4) Dew Temperature. Note that an entire Pxy diagram can be generated with bubble pressure calculations; no dew calculations are required. However, many applications require dew calculations, so they cannot be avoided. The dew calculations are more complicated than bubble calculations, because the liquid activity coefficients are not known until the unknown liquid mole fractions are found. This screencast describes the procedure and how to implement the method in Matlab or Excel.

01.2 Molecular Nature of Temperature, Pressure, and Energy Click here. 85 12

Molecular Nature of Energy, Temperature, and Pressure By Etomica(, 17min). We can use a free website ( to visualize the ways that molecules interact, resulting in the average properties that we see at the macroscopic level. The oversimplified nature of the ideal gas model becomes really obvious and the improvement of the hard sphere model is easily understood. Including both attractive and repulsive forces, as in the square well potential model, leads to more surprising behavior. The two effects may cancel and make the Z factor (Z=PV/RT) look like an ideal gas even though it is not. Also, the adiabatic transformation between potential energy and kinetic energy leads to spikes in temperature as molecules enter each other's attractive wells. In certain cases, you might see molecules get stuck in each others' wells. This is effectively "bonding." This bonding is limited at very low density because it requires a third interaction to occur during the collision in order to stay bonded. This requirement lies at the fundamental basis of what is known as "unimolecular reaction," a fairly advanced concept that is easily understood by watching the video. Note: if the etomica applet causes problems with your browser, check the instructions in section 7.10 to download all the apps and run locally. We use the apps for homework in Chapter 7, so it's money in the bank.

Comprehension Questions:
1. What is the average temperature (K) illustrated in the screencast? Is it higher or lower than the initial temperature? Explain.
2. What is the average pressure (bar) illustrated in the screencast?
3. Go to the website and perform your own simulation with the piston-cylinder applet starting with 100 molecules and assuming the square well poential model. You can run the simulation in fast mode, but let the molecules collide for 2500 ps. Then report the average value of T,P,U,Z. (Hint: compute Z from its definition, and be careful with units.)

04.02 The Microscopic View of Entropy Click here. 85 4

Principles of Probability.

This is supplemental Material from "Molecular Driving Forces, K.A. Dill, S. Bromberg", Garland Science, New York:NY, 2003, Chapter 1. See the next three screencasts. This content is useful for graduate level courses that go into more depth or for students interested in more background on probability.

Download Handout Notes to Accompany Screencasts (

01.4 Basic Concepts Click here. 85 8

Molecular Nature of U and PV=RT ( (5:04)

Internal energy is the sum of molecular kinetic energy and intermolcular potential energy, which leads to the relation between internal energy and temperature for an ideal gas. Also, the ideal gas law can be derived by incoporating the relation between kinetic energy and temperature with the force due to the molecules bouncing off the walls.

Comprehension question:
One mole of Xenon molecules (MW=131g/mol) is flying back and forth in the x-direction of a three-dimensional cube of 1m³ volume with zero velocity in the y- or z- directions. The velocity of every molecule is 300 m/s. Estimate the pressure (MPa) in the x- and y- directions.

10.01 - Introduction to Phase Diagrams Click here. 84 5

Bubble, Dew, Flash Concepts and the Lever Rule (4:01) (

Understanding what is present (known) and not present (unkown) for a given state of a system will help you decide which routine to use. Notation is introduced for liquids, vapor, and overall compositions. Also, the lever rule concept is used throughout the chemical engineering curriculum, but it is important to see how to use compositions for the lever rule.

Comprehension Questions:

1. Which variables are fixed and which do you need to find in each of the following:
a. Bubble temperature
b. Bubble pressure
c. Dew temperature
d. Dew pressure
e. Isothermal flash
f. Adiabatic flash

01.2 Molecular Nature of Temperature, Pressure, and Energy Click here. 83.3333 12

Intermolecular Potential Energy ( (7:11)

The intermolecular potential energy is distinct from the gravitational potential energy of the center of mass. Further, understanding of the potential energy relation with intermolecular force is important.

Comprehension Questions:

1. 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.)

2. The potential, u(r), represents the work of bringing two molecules together from infinite distance to distance r. So, what is the force law between two molecules according to the Lennard-Jones potential model? Hint: W=∫F*dx

3. 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?