# 07.06 Solving The Cubic EOS for Z

### Solving the PR EOS for Z . (8

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.

### Using Preos.xlsx and Interpreting

3. Using Preos.xlsx and Interpreting Output (11:38) (msu.edu)
This screencast includes discussion of what we mean by the casual terminology 'three root region' and 'one root region', and how to interpret screen output. Also, the screencast spends time dicussing selection of stable roots using fugacity.

Comprehension Questions:

1. Is it possible to have a 1-root region below the critical temperature?

2. Is it possible to have a 3-root region above the critical temperature?

3. How does fugacity help us to identify the proper root to select?

4. Would argon at 5 MPa be in the 1-root or 3-root region?

### Peng-Robinson PVT Properties

1. Peng-Robinson PVT Properties - Excel (3:30) (msu.edu)

Introduction to PVT calculations using the Peng-Robinson workbook Preos.xlsx. Includes hints on changing the fluid and determining stable roots.

Comprehension Questions:

1. At 180K, what value of pressure gives you the minimum value for Z of methane? Hint: don't call solver.

2. At 30 bar, what value of pressure gives Z=0.95 for methane?

3. Compute the molar volume(s) (cm3/mol) for argon at 100K for each of the following?
(a) 3.000 bars (b) 4.000 bars (c) 3.26903 bars.

### Peng Robinson Using Solver fo

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.

### Selecting Stable Roots

4. Selecting Stable Roots (1:11) (msu.edu)

Selecting stable roots is often one of the confusing aspects in working with cubic equations of state. This screencasts gives a visual picture of how the roots and stability are related to the vapor pressure and EOS humps at subcritical temperatures.

### Solving vdW EOS for density

6. Solving for density (uakron.edu, 9min) An alternative to solving directly for Z is to solve for density then compute Z=P/(ρRT). This requires iterative solution and it is not very expedient for repetitive calculations, but it requires no rearrangement of the EOS and it is easy to visualize. This sample calculation is illustrated here for the vdW EOS, solving for the density of propane as: (a) liquid 25C,11bars (b) liquid 62C,35bars (c) vapor at 80C and 30bars.

Comprehension Questions:

1. Solve for the liquid density (mol/cm3) of n-pentane at 62C and 2.5 bars using the vdW EOS.
2. Solve for the Z-factor of liquid n-pentane at 62C and 2.5 bars using the vdW EOS.
3. What's the value of the Z-factor at 80C and 30 bars according to this presentation?