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|09.09 - Calculation of Fugacity (Solids)||Click here.||33.3333||6||
The fugacity of a solid (uakron, 19min) follows a similar trend to that of a liquid, but there can be unexpected implications. The impact of pressure requires careful consideration. NIST Webbook lists the melting temperature of xenon as 161.45K and the Antoine equation as log10Psat(bars) = 3.80675 - 577.661/(T(K)-13.0), CpV=22.7 J/mol-K, CpL=44.4 J/mol-K, ρL=2.9662 g/cm3. Wikipedia lists the solid density as 3.540 g/cm3 (and the liquid density as 3.084) and the heat of fusion as 2270 J/mol. You may assume CpL=CpS. Use Eq. 7.06 to describe the vapor phase. You may assume ω = 0 for the purpose of these calculations. This screencast shows a sample calculation to solve for: (a) the vapor fugacity at 162 K and 0.085 MPa (b) the liquid fugacity in equilibrium with the same vapor at 162 K and 0.085 MPa (c) the liquid fugacity at 162 K and 8.5 MPa (d) the solid fugacity at 161.45 K and 0.082 MPa (e) the solid fugacity at 162 K and 8.5 MPa. If you are still having trouble understanding the ways that all these fugacities relate, you might like to view the phase diagram implications of VLSE (uakron, 9min).
1. How much did raising the pressure to 8.5 MPa change the liquid fugacity (bars)?
|10.02 - Vapor-Liquid Equilibrium (VLE) Calculations||Click here.||32||5||
Use VLookup and shortcut estimates of Antoine coefficients (see above) to quickly generate the Pxy phase diagram for an ideal solution. (11min, uakron.edu) This video shows a sample calculation for methanol+benzene using Eqn. 10.8. It also shows how to reference the approximate estimates in the cells that will actually be used for later calculations, so you can type in precise estimates when you have them. When no precise values are available, recover the shortcut estimates by simply typing "=" and referencing the cell with the shortcut estimate. The predictive formulas are written in black and should not be edited. The cells for user modification by pasting more accurate values are indicated in blue. We use this approach a lot, and refer to it fondly as the "black and blue" method.
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."
1. Create a Pxy diagram for methanol+benzene at 90C based on the ideal solution SCVP model. Be sure to include all appropriate labels and label your sketch as quantitatively as possible. Compare your model to the data in HW 11.10 by including those points in the plot. Explain similarities and discrepancies.
|08.01 - The Departure Function Pathway||Click here.||32||5||
Demystifying The Departure Function (11min) (uakron.edu)
1. In the diagram of (A-Ac)/RTc, which state represents the closest point to an ideal gas: A, B, C, or D?
|12.05 - MOSCED and SSCED Theory||Click here.||30||6||
There are so many activity models, how can you keep them straight? This video shows how MAB, SSCED, and Scatchard-Hildebrand models are all closely related.(9min,uakron.edu) By changing the assumptions, one model can be transformed into the other. So focus on remembering one model very well, then remember the small adjustments to obtain the other models.
|08.03 - The Entropy Departure Function||Click here.||28||5||
The Entropy Departure Function (11:22) (uakron.edu)
Comprehension Questions: The RK EOS can be written as: Z = 1/(1-bρ) - aρ/(RT1.5).
|08.07 - Implementation of Departure Functions||Click here.||28||5||
Helmholtz Energy - Mother of All Departure Functions. (uakron.edu, 10min) This screencast begins with a brief perspective on energy and free energy as they relate to concepts from Chapter 1 and through to the end of the course. Then it focuses on how the Helmholtz departure function is one of the most powerful due to the relations that can be developed from it. The Helmholtz departure is relatively easy to develop from a density integral of the compressibility factor. Then the internal energy departure can be derived from a temperature derivative. Alternatively, if the internal energy departure is given, the Helmholtz energy can be inferred by integration, and the compressibility factor can be derived from a density derivative.
|03.5 Mixture Properties for Ideal Solutions||Click here.||25||4||
Stream enthalpies for the DME process (uakron, 7min) can be estimated using the "heat of reaction" pathway (Fig 3.5a) or the "heat of formation" pathway (Fig 3.5b). This presentation is based on Fig 3.5b, which is very similar to Fig 2.6c. The main difference is the inclusion of the heat of formation for each compound relative to its elements. Including the heat of formation puts the reference state for each compound on the same basis of comparison (ie. the elements). If one stream (e.g. "products") possesses more enthalpy than another stream (e.g. "reactants") then the energy difference between the streams (e.g. "heat of reaction") would be accounted for by simply subtracting the two stream enthalpies. Reactions inherently involve multiple components, so including the heats of formation in the stream enthalpies, as well as the other enthalpic contributions represented in Fig 2.6c, is inevitable. These sample calculations are illustrated for all the streams appearing in the DME process. The presentation follows up on the discussion of Fig 2.6c for pure fluids. Once you understand the calculations for each pure fluid, the mixture property simply involves taking the molar average, so: H ≈ ∑(xi*Hfi+CpiigΔT+(qi-1)*Hivap). In this equation, (qi-1)*Hivap accounts crudely for departures from ideal gas behavior. For example, if a stream is a vapor, then q=1 and Hvap doesn't matter. If q=0, then the stream is a liquid and Hvap must be subtracted. We will study more accurate models of ideal gas departures in Unit II.
1. Compute the enthalpy, H(J/mol), of methanol at 250C and 2 bars relative to its ideal gas standard state elements.
2. Compute the enthalpy, H(J/mol), of DME at 250C and 2 bars relative to its ideal gas standard state elements.
3. Compute the enthalpy, H(J/mol), of water at 250C and 2 bars relative to its ideal gas standard state elements.
4. Compute the enthalpy, H(J/mol), of a stream that is 50% methanol, 25% DME, and 25% water at 250C and 2 bars relative to its ideal gas standard state elements.
|12.05 - MOSCED and SSCED Theory||Click here.||24||5||
This video walks you through the process of transforming the Scatchard-Hildebrand model into the SSCED model using Excel (6min, uakron.edu) It steps systematically through the modifications to the spreadsheet to obtain the new model. You should implement the Scatchard-Hildebrand model before implementing this procedure.
|02.01 Expansion/Contraction Work||Click here.||22.2222||9||
Closed System Energy Balance: Ideal Gas Expansion (uakron.edu, 9min) An ideal gas is on the left side of a frictionless piston that expands to produce work energy. Beginning with the work energy of expansion and contraction, then contemplating the manners in which other forms of energy could impact this closed system, a checklist is developed for analyzing all the ways that energy can change in the system. This checklist is known as the energy balance, and in this particular case, for a closed system. This system forms the basis for three sample calculations (18min): (1) Adiabatic, reversible expansion from 1000C, 100 bars, and 0.1 L to 0.6L. (2) Isothermal, reversible expansion from 1000C, 100 bars, and 0.1 L to 0.6L. (3) Adiabatic, irreversible expansion from 1000C, 100 bars, and 0.1 L to 0.6L against a perfect vacuum. Calculate the temperature, pressure, work and change in internal energy at the final conditions. The gas can be assumed as pure air. NOTE: Case (1) leads to a very important equation that should be memorized ASAP! Quick answers to common questions (UA, 12min) illustrate easy ideal gas calculations.
|08.07 - Implementation of Departure Functions||Click here.||20||1||
Helmholtz Example - Scott+TPT EOS. (uakron.edu) A sample derivation (8min) for the compressibility factor given that (A-Aig)TV/RT = -2ln(1-2ηP) - 18.7ηPβε/[1+0.36βεexp(-5ηP)]. This equation of state is a little complicated, but the derivation is no problem if you just go slow and steady. The remainder of this screencast shows a sample calculation (21min) to solve the resulting equation of state at a given value of pressure and temperature following the methodology of "visualizing the vdW EOS." This problem was adapted from an actual test problem. This screencast is live so the audio is inferior, but it gives insight into questions that real students have.