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07.11 - The molecular basis of equations of state: analytical theories Click here. 100 1

Nature of Molecular Parking Lots - RDFs(20min, uakron.edu) Molecules occupy space and they move around until they find their equilibrium pressure at a given density and temperature. Cars in a parking lot behave in a similar fashion except the parking lot is in 2D vs. 3D. Despite this exception, we can understand a lot about molecular distributions by thinking about how repulsive and attractive forces affect car parking. For example, one important consideration is that you should not expect to see two cars parked in the same space at the same time! That's entirely analogous for molecular parking. Simple ideas like this lead to an intuitive understanding of the number of molecules distributed at each distance around a central molecule. From there, it is straightforward to multiply the energy at a given distance (ie. u(r) ) by the number of molecules at that distance (aka. g(r) ), and integrate to obtain the total energy. A similar integral over intermolecular forces leads to the pressure. And, voila! we have a new conceptual route to developing engineering equations of state.
Comprehension questions:
1. Sketch u(r)/epsilon and g(r) vs. r/sigma for square well spheres at a very low density. Use a solid line for g(r) and a dashed line for u(r)/epsilon.
2. Sketch u(r)/epsilon and g(r) vs. r/sigma for hard spheres at a high density. Use a solid line for g(r) and a dashed line for u(r)/epsilon.
3. Sketch u(r)/epsilon and g(r) vs. r/sigma for square well spheres at a high density. Use a solid line for g(r) and a dashed line for u(r)/epsilon.

17.05 - Effect of Pressure, Inerts, Feed Ratios Click here. 100 1

Partial pressures and reactor sizing are among the keys to chemical engineering calculations (uakron.edu, 7 min, review from Section 1.6). Partial pressures (uakron.edu, 7 min) also play an essential role in reaction equilibrium calculations. Partial pressure calculations basically involve straightforward mass balances, but specific vocabulary and a need for systematic precision can cause difficulty. The calculations involve six elements that must be carefully computed:

(1) Stoichiometry - the reaction equation must be stoichiometrically balanced such that the number of atoms of each element are the same on both sides of the equation. This balance is achieved by adjusting the stoichiometric coefficients. The change in the number of moles of each component must be in correct stoichiometric proportions relative to the "key component." Inert compounds (see below) are NOT included in the stoichiometric equation. For the example in this presentation, the objective of the reactor is to oxidize carbon monoxide (CO) in a catalytic converter by reacting it with oxygen (O2). So, CO + 0.5 O2 = CO2.
(2) Limiting reactant (aka. "key component") - It is common to feed an excess of one of the components in order to promote complete conversion of the other components. The limiting reactant is the component that is NOT in excess. For this example, O2 is fed in excess so that CO conversion can be promoted. CO becomes the limiting reactant in that case and conversion must be computed relative to CO, NOT O2. If you think about it, expressing the conversion with respect to the excess component would mean that 100% conversion could result in a negative mole number for the limiting reactant. Such an implication is obviously physically impossible (and potentially embarrassing if you appear not to know that).
(3) %Excess - The number of moles of an excess component in the feed is (1+Xs) times the stoichiometric amount relative to the key component, where the stoichiometric amount is the number of moles necessary to perfectly balance the key component, and Xs is the fractional form of the %excess. For this example,  the stoichiometric ratio of CO:O2 would be 1:0.5 and for 50% excess, Xs = 0.50, and the actual ratio would be 1:0.75.
(4) %Conversion - the %conversion is the fraction of the entering amount of the limiting reactant that is transformed into product(s). Note that this might be different from the "extent of reaction," ξ. For example, if 50 moles/h of CO enter the reactor and the conversion is 90%, then 5 moles of CO exit the reactor. If you express the number of moles of CO as 50-ξ, you might conclude that the moles of CO exiting the reactor is 49.1. Take a minute to think about what the words mean before you start to calculate, then make a mental estimate of what the results should be, then get out your calculator. Another common mistake is to apply the % conversion to all the components, wrongly including the excess component. For example, if 45 moles of CO react, then 22.5 moles of O2 react. With 50% excess O2 in the feed, the O2 exiting should be 37.5-22.5=15, NOT 3.75. This is what it means to be careful and systematic. You must compute the conversion of limiting reactant first, then compute the conversion of other components relative to the limiting reactant.
(5) Inerts - These are components that may enter the reactor by coincidence or convenience but do not participate in the reaction. Therefore, their number of moles exiting the reactor is simply equal to their number of moles entering the reactor. A common mistake is to apply the %conversion to all components entering the reactor, including the inerts. In this example, the source of O2 is air, with roughly 4:1 ratio of nitrogen (N2) to O2. The N2 is inert.
(6) Total Pressure - Once the mole numbers and mole fractions have been computed, don't forget to multiply the mole fractions by the total pressure to get the partial pressure. The partial pressure is equal to the mole fraction only in the case that the reactor operates at 1.00 bar.

Comprehension Questions:

1. What is the value of the total pressure (bar) applied in the presentation of this example?
2. What equation is used to compute the mole number of O2? What is the final overall equation used to compute PO2?
3. Suppose 100 moles/h of ammonia (NH3) at 100bars is to be produced from N2 and hydrogen (H2) with 10% excess N2. Methane (CH4) is included with the N2+H2 as a result of the synthesis process with a ratio of 1:10 CH4:H2. (a) Write a stoichiometrically balanced equation (b) Identify the limiting reactant (c) Calculate the number of moles and partial pressures of each component entering the reactor. (d) Calculate the number of moles and partial pressures of each component exiting the reactor assuming 25% conversion.

07.02 Corresponding States Click here. 100 1

Principles of Corresponding States (10:02) (msu.edu)
An overview of use of Tc and Pc and acentric factor to create corresponding states correlation. The relation between acentric factor and deviations from spherical fluids is highlighted.

Comprehension Questions:

1. What is the value of the reduced vapor pressure for Krypton at a reduced temperature of 0.7? How does this help us to characterize the vapor pressure curve?

2. Sketch the graph of vapor pressure vs. temperature as presented in this screencast for the compounds: Krypton and Ethanol. Be sure to label your axes completely and accurately. Draw a vertical line to indicate the condition that defines the acentric factor.

08.02 - The Internal Energy Departure Function Click here. 100 1

Departure Function Derivation Principles (8:03) (msu.edu)
This screencast covers sections 8.2 - 8.8. Concepts of using the equation of state to evaluate departure functions. The screencasts also discusses the choice of density integrals or pressure integrals. The use of a reference state is discussed.

03.3 - Introduction to Mixture Properties Click here. 100 1

Props.xlsx has a lot of data, but usually we are only interested in a few components at a time. Adding a few lines at the top and applying the VLookup function makes it easy to tabulate the properties you need. (8min, uakron.edu)

Comprehension questions

1. Download the latest version of Props.xlsx from sourceforge. Add lines to support 8 components of interest and cells to compute Psat given T as input and Tsat given P as input by appropriately arranging Eqn. 2.47. Add a column for computing Hvap at Tsat for each component by Eqn. 2.45.

2. Insert a sheet(tab) called Hrxn in Props.xlsx. Types the names for components in the reaction CO+0.5O2=CO2. Use VLookup to tabulate the Hf values for each component. To the left of the name column, insert cells to represent the stoichiometric coefficients. Then calculate the heat of reaction by using the sumproduct() function applied to the stoichiometric coefficients and Hf values. Check your result with a hand calculation.

3. Download the latest versions of PREOS.xls and Props.xlsx from sourceforge. Update the Props tab appropriately. Then implement the VLookup function on the ThermoProps tab of PREOS so all you need to do is type the name of the compound of interest in order to update the ThermoProps sheet to all properties of interest. We discuss how to use PREOS.xls to solve problems in Unit II.

07.11 - The molecular basis of equations of state: analytical theories Click here. 100 1

Nature of Molecular Energy - Example Calculation(8min, uakron.edu) Given an estimate for the radial distribution function (RDF) integrate to obtain an estimate of the internal energy. The result provides an alternative to the attractive term of the vdW EOS.

09.04 - Changes in Gibbs Energy with Pressure Click here. 100 1

Gibbs Energy - Nuts to Soup. (learncheme.com, 8min) It is straightforward to start from the definition of Gibbs Energy and derive all the changes in Gibbs energy. These can be graphed for H2O to see how familiar quantities from the steam tables relate to changes in this unfamiliar property.

14.09 - Numerical procedures for binary, ternary LLE Click here. 100 1

LLE flash using Matlab/Chap14/LLEflash.m (5:54) (msu.edu)

An overview of the LLE flash routine in Matlab, including an overview of the program logic and then an example of how to run the program.

See also - Supplement on Iteration of LLE with Excel and Matlab.

09.05 - Fugacity and Fugacity Coefficient Click here. 100 1

What is fugacity? (10min) (learncheme.com) Defines fugacity in terms of Gibbs Energy and describes the need for defining this new property as a generalization of how pressure affects ideal gases.
Comprehension Questions
1. The phases in this video start with concentrations 0.0007kg/L and 1.0 kg/L, when not at equilibrium. What are the equilibrium concentrations?
2. Why is concentration an unreliable indicator for the direction of mass transfer?
3. Name two indicators for the direction of mass transfer that are superior to concentration.  

09.05 - Fugacity and Fugacity Coefficient Click here. 100 1

In a contest for "the most hated word in Chemical Engineering," fugacity won by a landslide. This video (15min, uakron.edu) reviews how the term was developed and why it's not really as bad as all that. In fact, it's a nice word that sets the stage for all of phase and reaction equilibrium with a straightforward extension of the same conceptual basis to mixtures. On second thought, perhaps the power of that conceptual basis and all that it implies is what really intimidates new students. Many perspectives have been offered to help overcome the frustration that students feel toward fugacity. If you like a comic book perspective, even that is available.

Comprehension Questions:

1.What is the fugacity of a vapor phase component in a mixture according to Raoult's law?
2.What is the fugacity of a liquid phase component in a mixture according to Raoult's law?
3. What word is modern usage is closely related to the latin root "fuga-"?
4. Water is in VLE at 0.7 bars in a fixed volume vessel. Five cm3 of air are injected into the vessel and the temperature is allowed to return to its original value. Does the water in the vapor phase increase, decrease, or remain the same? (Learncheme.com, 2min) (Hint: you may assume that air does not dissolve in the liquid water and the pressure is sufficiently low that the vapor can be assumed to behave as an ideal gas.)

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