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18.09 - Sillen Diagram Solution Method Click here. 80 1

 Sillen Diagram for Electrolyte Calculations (10:14) (msu.edu)

Construction of a Sillien diagram involves several steps that are hard to follow from a textbook. This screencast goes through the steps of solving Example 18.5 from the Elliott and Lira textbook using the Sillen diagram. The problem asks for the pH of a solution that is 0.01 M NaOAc.

01.2 Molecular Nature of Temperature, Pressure, and Energy Click here. 78 20

Molecular Nature of Internal Energy: Thermal Energy
This introduction to "thermal energy" elaborates on the ideal gas definition of temperature, which derives from the way that PV is related to kinetic energy. This PV relation can be easily understood in terms of an ultrasimplified model of ideal gas pressure. (uakron, 6min). Noting empirically from the ideal gas law that PV=nRT, we are led to the derivation of Eqn. 1.1 (uakron, 5min, same as above). This result suggests counter-intuitive implications about the the ways that solid, liquid, and gas molecular velocities must be related. When applying Eqn. 1.1, you must be careful to keep your units straight, as illustrated in this sample calculation of molecular temperature for Xenon (Mw=131g/mol) (uakron, 5min). On a closely related note, we could perform a sample calculation of molecular pressure for Xenon using Eqn. 1.21.

Comprehension Questions:
1. If two phases are in equilibrium (e.g. a vapor with a solid), then their temperatures are equal and the rate at which molecules leave the solid equals the rate at which molecules enter the solid. Which molecules are moving faster, solid or vapor? For simplicity, assume that the vapor is xenon and the solid is xenon. Hint: think about the exchange of momentum when the vapor molecules collide with the solid.
2. Compute the average (root mean square) velocity (m/s) of molecules at room temperature and pressure and compare to their speeds of sound. You can search the internet to find the speed of sound.
a. Argon
b. Xenon
3. Three xenon atoms are moving with (x,y,z) velocities in m/s of (300,-450,100), (-100,300,-50), (-200,-150,-50). Estimate the temperature (K) of this fluid.
4. Estimate the pressure of the xenon atoms in Q3 above in a vessel that is 4nm3 in size. 

01.2 Molecular Nature of Temperature, Pressure, and Energy Click here. 77.2308 65

Molecular Nature of Energy and Temperature (msu.edu) (3:34)
This introduction shows the connection with temperature and kinetic energy.  When applying Eqn. 1.1, you must be careful to keep your units straight, as illustrated in this sample calculation of the molecular temperature for xenon (Mw=131). (uakron, 5min).

Comprehension Questions:

1. A 1m3 vessel contains 0.5m3 of saturated liquid in equilibrium with 0.5 m3 of saturated vapor. Which molecules are moving slower? (a) the vapor (b) the liquid (c) they are all the same.

2. A glass of ice water is sitting in your freezer, set to 0C and fully equilibrated. Which molecules are moving slower? (a) the gas (b) the liquid (c) the solid (d) they are all the same.

3. You walk into the kitchen in the morning to get some breakfast. The ceiling fan is on. You forgot your slippers. Which one is "hotter?" (a) the floor (b) the ceiling (c) the granite counter top (d) the air in the room (e) they are all the same.

10.03 - Binary VLE using Raoult's Law Click here. 73.3333 3

Raoult's Law Calculation Procedures (11:45) (msu.edu)
Details on how to implement bubble, dew, and flash calculations for Raoult's Law. This screencast shows sample calculations for the bubble pressure and dew pressure of methanol+ethanol.

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.
2. Estimate the dew temperature (K) of 30% acetone + 70% benzene at 1 bar.
3. Estimate the fraction vapor and phase compositions ethylamine+ethanol at 298K, 400mmHg and a feed of 60%amine.

07.05 Cubic Equations of State Click here. 73.3333 3

Virial and Cubic EOS (11:18) (msu.edu)
Discusses the strategy of the virial EOS and the cubic EOS and the strategy used to solve as a cubic in Z. Gives formulas for calculating the a and b parameters of both the vdW and Peng-Robinson EOS's, as well as the virial EOS. You might want to watch the video on "Visualizing the vdW EOS" if you want to understand where the equations for a and b come from or how to make quantitative plots of isotherms.

Comprehension Questions:

1. To what region of pressure is the virial EOS limited at a given temperature? Why?
2. Is the Pitzer EOS limited to the same conditions as the virial EOS?
3. Is the virial EOS a 2-parameter or 3-parameter EOS?
4. Is the Peng-Robinson (PR) EOS a 2-parameter or 3-parameter EOS?
5. What is the primary shortcoming of the vdW EOS, as described on slide 4 of this presentation?
6. Is the PR EOS limited to the same conditions as the virial EOS? Explain.
7. How does the "fugacity" help you to identify the stable root of a cubic EOS?
8. When there are 3 real roots to a cubic EOS, what do we do with the center root? Why?

08.02 - The Internal Energy Departure Function Click here. 73.3333 3

The Internal Energy Departure Function (11min, uakron.edu) Deriving departure functions for a variety of equations of state is simplified by transforming to dimensionless units and using density instead of volume. This also leads to an extra simplification for the internal energy departure function.

Comprehension Questions:

1. What is the value of T(∂P/∂T)V - P for an ideal gas?
2. What is the value of (∂U/∂V)T for an ideal gas and how can you explain this result at the molecular scale?
3. The Redlich-Kwong (RK) EOS is: P=RT/(V-b) -a/(V2RT1.5). Use Eqn. 8.13 to solve for (U-Uig)/RT of the RK EOS.
4. The RK EOS can be written as: Z = 1/(1-) - /(RT1.5). Use Eqn. 8.14 to solve for (U-Uig)/RT of the RK EOS.

13.04 - UNIQUAC Click here. 73.3333 3

UNIQUAC concepts (6:44) (msu.edu)

Concepts and assumptions used in developing the UNIQUAC activity coefficient method. This method introduced the use of surface area as an important quantity in calculation of activity coefficients.

04.02 The Microscopic View of Entropy Click here. 72 5

Principles of Probability III, Distributions, Normalizing, Distribution Functions, Moments, Variance. This screencast extends beyond material covered in the textbook, but may be helpful if you study statistical mechanics in another course. (msu.edu, 15min) (Flash)

06.1 The Fundamental Property Relation Click here. 70 2

From the physical world to the realm of mathematics (uakron.edu, 15min) In Unit I, students develop the skills to infer simplified energy and entropy balances for various physical situations. In order to facilitate that approach for applications involving chemicals other than steam and ideal gases, we need to transform that approach into a realm of pure mathematics. In this context it suffices to apply the energy and entropy balance of a very simple system (piston/cylinder) then focus on the state functions that are involved (U,H,S,...). The mathematical realm is relatively abstract, but it is ideally suited for the generalizations required to extend our principles from steam and ideal gases to any chemical.

Comprehension Questions:

1. In example 4.16, we noted that the estimated work to compress steam was less when treated with the steam tables than when treated as an ideal gas. Explain why while referring to the molecular perspective.

2. In Chapter 5, we noted that the temperature drops when dropping the pressure across a valve when treating steam or a refrigerant with thermodynamic tables, but the energy balance suggests that the temperature drop for an ideal gas should be zero. Explain how these two apparently contradictory observations can both be true while referring to the molecular perspective.

3. What is the relation of the state variable dU to the state variables S and V according to the fundamental property relation?

4. What is the relation of the state variable dH to the state variables S and P according to the fundamental property relation?

5. What is the significance of writing changes of state variables in terms of changes in other state variables?

6. Why is the compressibility factor (Z=PV/RT) less than one sometimes?

7. Is it possible for Z to be greater than one? Explain.

8. What is the significance of having a relation for P = P(V,T)? How will that help us to solve problems involving chemicals other than steam and ideal gases?

11.13 - Osmotic Pressure Click here. 70 2

MW of protein by osmotic pressure - (8:23) (learncheme.com)

An application of osmotic pressure measurement to determine MW of a protein.

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