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|09.10 - Saturation Conditions from an Equation of State||Click here.||60||2||
Solving for the saturation pressure using PREOS.xls simply involves setting the temperature and guessing pressure until the fugacities in vapor and liquid are equal. (5min, learncheme.com) It is not shown, but it would also be easy to set the pressure and guess temperature until the fugacities were equal in order to solve for saturation temperature. One added suggestion would be to type in the shortcut vapor pressure (SCVP) equation to give an initial estimate of the pressure. Rearranging the SCVP can also give an initial guess for Tsat when given P. This presentation illustrates a sample calculation for toluene to explore when the vapor is the stable, when the liquid is the stable phase, and when the phases are roughly in equilibrium.
1. Estimate the vapor pressure (MPa) of n-pentane at 450K according to the PREOS. Compare your result to the value from Eq. 2.47 (SCVP) and to the Antoine equation using the coefficients given in Appendix E. What do you think explains the observations that you make?
|10.03 - Binary VLE using Raoult's Law||Click here.||60||4||
Raoult's Law Calculation Procedures (11:45) (msu.edu)
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.
|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.
1. What equation can we use to estimate the fugacity of a compressed liquid relative to its saturation value?
|14.04 LLE Using Activities||Click here.||60||2||
Txy Phase Diagram Showing LLE and VLE Simultaneously (9min,uakron.edu)
The binary Txy phase diagram of methanol+benzene is visualized with sample calculations of the SSCED model with several values of the nonideality (kij) parameter. The calculations show the liquid-liquid equilibrium (LLE) phase boundary as well as the vapor-liquid equilibrium (VLE) boundary. As the estimated nonideality (kij) increases, the LLE boundary crashes into the VLE. It is so exciting that it makes a thermo nerd wax poetic about the "valley of Gibbs."
1. The LLE phase boundary moves up as the nonideality increases. Which way does the VLE contribution move? Explain how this relates to the molecules' escaping tendencies.
|07.08 Matching The Critical Point||Click here.||60||2|
|01.5 Real Fluids and Tabulated Properties||Click here.||60||2||
Steam Tables (LearnChemE.com) (5:59) calculate enthalpy of steam by interpolation
|11.12 - Lewis-Randall Rule and Henry's Law||Click here.||60||11||
Introduction to Henry's Law (10:16) (msu.edu)
Fugacities are calculated relative to standard state values, and the relations developed earlier in the chapter use a pure fluid standard state. What if the pure fluid does not exist as a liquid when pure? One choice is to use Henry's law.
|11.13 - Osmotic Pressure||Click here.||60||9||
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.
|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."
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.
|03.1 - Heat Engines and Heat Pumps: The Carnot Cycle||Click here.||56.6667||6||
Introduction to the Carnot cycle (Khan Academy, 21min). 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). Note that Khan uses the absolute value when referring to quantities of heat and work so his equations may look a little different from ours. By systematically adding up the heat and work increments through all stages of the process, we can infer an approximate equation for thermal efficiency (Khan Academy, 14min) The steps are isothermal and reversible expansion, adiabatic and reversible expansion, isothermal and reversible compression, and adiabatic/reversible compression. We know how to compute the heat and work for ideal gases of each step based on Chapter 2. In this presentation by KhanAcademy, an additional proof is required (17min) to show that the volume ratio during expansion is equal to the volume ratio during compression. (Note that the presentation by KhanAcademy uses arbitrary sign conventions for heat and work. They prefer to change the sign to minimize the use of negative numbers but it doesn't always work out.) When we put it all together, the equation we get for "Carnot efficiency" is remarkably simple: ηθ = (TH - TC)/TH, where TH is the hot temperature and TC is the cold temperature. We can use this formula to quickly estimate the thermal efficiency for many processes. We will show in Chapter 5 that this formula remains the same, even when we use working fluids other than ideal gases (e.g. steam or refrigerants).
Visualizing the vdW EOS (uakron.edu, 16min) Building on solving for density, describes plotting dimensionless isotherms of the vdW EOS for methane at 5 temperatures, two subcritical, two supercritical, and one at the critical condition. From these isotherms in dimensionless form, it is possible to identify the critical point as the location of the inflection point where the temperature first exits the 3-root region. This method can be adapted to any equation of state, whether it is cubic or not. The illustration was adapted from a sample test problem. This screencast also addresses the meaning of the region where the pressure goes negative, with a (possibly disturbing) story about a blood-sucking octopus.
1. What are the dimensions of the quantity (bP/RT)?
2. Starting with the expression for Z(ρ,T), rewrite the vdW EOS to solve for the quantity (bP/RT) in terms of (bρ) and (a/bRT).
3. Consider the following EOS: Z = 1 + 2bρ/(1-2bρ) - (a/bRT) /(1-bρ)2. Estimate the value of bPc/(RTc) for this EOS.
4. Consider the following EOS: Z = 1 + 2bρ/(1-2bρ) - (a/bRT) /(1-bρ)2. Estimate the value of (a/bRTc) for this EOS.
5. Compute the values of a(J-cm3/mol2) and b(cm3/mol) for methane according to this new EOS.