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06.2 Derivative Relations Click here. 45 4

Assembling your derivative toolbox including the triple product rule, (, 13min) Beginning with the fundamental property relation, substitutions lead to Eqns. 6.4-6.7. Differentiating these and equating through exact differentials leads to Eqns. 6.29-6.32 (aka. Maxwell's Relations). Combining Maxwell's Relations with Eqns. 6.4-6.7 leads to Eqns. 6.37-6.41. With these tools in hand, and Eqn. 6.15 (aka. Triple Product Rule), you have all the tools you need to quickly transform any derivative into "expressions involving Cp, Cv, P, V, T, and their derivatives." This capability is fundamental to obtaining expressions for U, H, and S from any given equation of state for any chemical of interest. Four sample derivations are illustrated: (∂U/∂V)T, (∂T/∂S)V, (∂T/∂V)S, (∂S/∂V)A,

Comprehension Questions:

1. Transform the following into "expressions involving Cp, Cv, P, V, T, and their derivatives:" (∂T/∂V)S.

2. Transform the following into "expressions involving Cp, Cv, P, V, T, and their derivatives." Your expression may involve absolute values of S as long as they are not associated with any derivative. (∂T/∂U)P.

14.07 Plotting Ternary LLE Data Click here. 45 8

Plotting Ternary Data (6:25) (

This screencasts discusses equilateral and Cartesion plots, the one- and two-phase regions, Plait point, lever rule, interpolation of tie lines using the tie line plot, and the relation of the tie-line slope to the K ratio at small concentrations.

11.12 - Lewis-Randall Rule and Henry's Law Click here. 44 5

Henry's Law can be used to compute VLE of gases in solvents. We can estimate Henry's "constants" (, 12min) by Eqns. 11.64 and 11.68. Here we demonstrate the procedure for CO2+toluene and CO2+water. In some cases, the estimates can be good and in some cases they can be quite bad. The only way to know for sure is to validate your model with experimental data. Validation essentially involves finding data in the library and plotting on the same graph as the predictions. You should also compute the average deviations to provide a numerical measure of the goodness of fit.

Comprehension Questions:
1. Does the SCVP+ model predict higher or lower pure component fugacities than SCVP?
2. Why is it unusual for the deviations from Henry's Law to be positive?
3. Find experimental data for supercritical CO2+acetone. Identify the optimal value of A12 in the SCVP+M1 model to fit these data and compute the root mean square deviation (rmsd) of pressure: rmsd = sqrt(sum(Pcalc-Pexpt)^2).
4. Repeat 3 for N2+acetone. Compare the SCVP, SCVP+, and SCVP+MAB predictions as well as including experimental data.

10.02 - Vapor-Liquid Equilibrium (VLE) Calculations Click here. 44 5

Use VLookup and Eqn. 2.47 to tabulate shortcut estimates of Antoine coefficients. (6min, By calculating these in a distinct location, then referencing those estimates in the cells that will actually be used for later calculations, 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. This screencast includes sample calculations of the shortcut Antoine coefficients of methanol and benzene.

Comprehension Questions:

1. Estimate the Antoine "A" coefficient for methanol according to the shortcut method.
2. Estimate the Antoine "B" coefficient for benzene according to the shortcut method.
3. Estimate the Antoine "C" coefficient for ethanol according to the shortcut method. Compare to the "C" coefficient reported in Apx. E.
4. Estimate the Antoine "A" coefficient for ethanol according to the shortcut method. Compare to the "A" coefficient reported in Apx. E.
5. Estimate the Antoine "B" coefficient for water according to the shortcut method. Compare to the "A" coefficient reported in Apx. E.

11.12 - Lewis-Randall Rule and Henry's Law Click here. 42.8571 7

Characterizing gas solubility beyond Henry's Law concentrations (, 6min) This presentation shows how to use the M2 model to fit the gas solubility when the pressure deviates from the linear behavior indicated by Henry's Law. It is very similar to the procedure illustrated in Section 11.9, but we use a slightly customized format here.

Comprehension questions:

1. Find experimental data for supercritical CO2+acetone. Identify the optimal value of A12 and A21 in the SCVP+M2 model to fit these data and compute the root mean square deviation (rmsd) of pressure: rmsd = sqrt(sum(Pcalc-Pexpt)^2/NPTS). Also tabulate the %AAD for this system.
2. Repeat 1 for ethylene+water at 100F. (Hint: cf. DECHEMA for reference to Anthony and McKetta, 1967)

09.07 - Calculation of Fugacity (Gases) Click here. 40 3

We occasionally require the fugacity in the vapor phase by an EOS other than the PR EOS. (learncheme, 3min) This becomes especially common in Unit 3 when we extend our methods to mixtures. Another skill demonstrated in this screencast is a sample derivation using the pressure dependent formulas. Note that there is a typo in the initial problem statement. The equation of state should be: PV = (1-0.05 P)RT.

Comprehension Questions:

1. Rearrange the given EOS to solve for Z and apply Eq. 9.23 to solve for the change in fugacity. Compare your answer to that given in the screencast. Which method seems easier to you?
2. Use Eq. 7.5 with Eq. 9.23 to derive an expression for the fugacity.
3. Apply the result of #2 to evaluate the fugacity of n-pentane at 398 K and 1 MPa.
4. Does this condition for pentane satisfy Eq. 7.10? Explain.

11.02 - Calculations with Activity Coefficients Click here. 40 4

This example shows how to quickly generate a Txy diagram in Excel using the Margules Acid-Base (MAB) model and the Excel solver.(14min, It is a bit of a sneaky trick that sometimes needs good initial guesses, but it is a lot more convenient than solving for each temperature individually by trial and error.

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."

Comprehension Questions
VLE data at constant pressure are much more relevant to distillation. Generate the Txy diagram for ethanol+benzene using the MAB model (a) at 1 bar (b) at 20 bars. Does the azeotrope change? How might you use these observations to "bust" the azeotrope and obtain pure ethanol and pure benzene? (Hint: use more than one distillation column?)

03.6 - Energy Balance for Reacting Systems Click here. 40 1

Heat Removal from a Chemical Reactor (, 8min) determines heat removal so that a chemical reactor is isothermal following the pathway of Figure 3.5a. The reaction is N2 + 3H2 = 2NH3 at 350C and 1 bar. The pathway to go from products to reactants is to cool the products to 25C (the reference temperature), then "unreact" them back to their initial feed state (reactants), then to heat the reactants back to the inlet condition of the reactor (350C,1bar). Summing up the enthalpy changes over these three steps gives the overall change in enthalpy at the reactor conditions.

Comprehension Questions:
1. Suppose the reaction had been carried out at 2 bars. How would we compute the enthalpy change then?
2. Use this approach to compute the heat of reaction for 2 CH3OH = CH3OCH3 + H2O at 250C and 1 bar.
3. Methanol, dimethyl ether, and water are all liquids at 25C and 1 bar. Did you account for the heat of vaporization when answering Question #2 above? Explain.

09.01 - Criteria for Phase Equilibrium Click here. 40 4

Phase equilibrium in a pure fluid (uakron, 11min) can be contemplated in terms of the following question: Suppose propane exists at a set temperature in an uninsulated piston/cylinder with half the volume as vapor and half as liquid. What is the final pressure when the piston is pressed down. A proper thermodynamic answer leads to the consideration of the Gibbs energy, with implications that open up an entire new world of problems to be solved related to equilibrium partitioning for pure fluids and mixtures.

Comprehension Questions:

1. Write dG for the total piston/cylinder system in terms of the individual phases.
2. What is the criterion for equilibrium in a pure fluid?
3. What is the stable state (L,V,L=V) when GL > GV ?
4. For the vdW fluid at 62C, 0.35 MPa, the following roots were obtained: ZL = 0.02598,
= 0.92718, A=0.08608, B=0.01820. What is the stable state (L,V,L=V)?
5. For the vdW fluid at 62C, 0.25 MPa, the following roots were obtained: ZL = 0.01859,
= 0.94910, A=0.061487, B=0.013000. What is the stable state (L,V,L=V)?

Hint: (G-Gig)/RT = -ln(Z-B)-A/Z + Z - 1 - ln(Z) where A=a*P/(R2T2); B=bP/RT; b=0.125*RTc/Pc

09.11 - Stable Roots and Saturation Conditions Click here. 40 1

Selecting Stable Roots (5:41) (

Understanding the relation between stable roots and the vapor pressure is a confusing aspect of working with cubic equations of state. When solving problems with enthalpy or entropy matching, it is important to remember to check for stability of the roots. See also the screencast for section 7.6.