Homework Problems

12.1. The compositions of coexisting phases of ethanol(1) + toluene(2) at 55°C are x₁ = 0.7186, and y₁ = 0.7431 at P = 307.81 mmHg, as reported by Kretschmer and Wiebe, 1949. J. Amer. Chem. Soc., 71:1793. Estimate the bubble pressure at 55°C and x₁ = 0.1, using

a. The Scatchard-Hildebrand model with k₁₂ = 0

b. The SSCED model with a default value of k₁₂

c. The SSCED model with k₁₂ matched to the data

d. The van Laar equation

12.2. A vapor/liquid experiment for the carbon disulfide(1) + chloroform(2) system has provided the following data at 298 K: , , x₁ = 0.2, y₁ = 0.363, and P = 34.98 kPa. Estimate the dew pressure at 298 K and y₁ = 0.6, using

a. The Scatchard-Hildebrand model with k₁₂ = 0

b. The SSCED model with a default value of k₁₂

c. The SSCED model with k₁₂ matched to the data

d. The van Laar equation

12.3. The (1) + (2) system forms an azeotrope at x₁ = 0.75 and 80°C. At 80°C, , . The liquid phase can be modeled by the van Laar model.

a. Estimate the activity coefficient of component 1 at x₁ = 0.75 and 80°C. [Hint: The relative volatility (given in Eqn 10.32) is unity at the azeotropic condition.]

b. Qualitatively sketch the P-x-y and T-x-y diagrams that you expect.

12.4. Ethanol(1) + benzene(2) form azeotropic mixtures. Compare the specified model to the experimental data of Brown and Smith cited in problem 10.2.

a. Prepare a y-x and P-x-y diagram for the system at 45°C assuming the van Laar model and using the experimental pressure at x_E = 0.415 to estimate A₁₂ and A₂₁.

b. Prepare a y-x and P-x-y diagram for the system at 45°C with the predictions of the Scatchard-Hildebrand theory with k₁₂ = 0.

c. Prepare a y-x and P-x-y diagram for the system at 45°C assuming the SSCED model and using the standard guideline to estimate k₁₂.

d. Prepare a y-x and P-x-y diagram for the system at 45°C assuming the SSCED model and using the experimental pressure at x_E = 0.415 to estimate k₁₂.

12.5. The CRC Handbook lists the azeotrope for the acetone + chloroform system as 64.7°C and 20 wt% acetone.

a. Use the van Laar model to estimate the T-x-y diagram at 1 bar.

b. Use the SSCED model to estimate the T-x-y diagram at 1 bar with predicted k₁₂.

c. What value of V₂/V₁ is implied by the van Laar parameters?

12.6. Using the van Laar model and the data from problem 11.3, estimate the total pressure and composition of the vapor in equilibrium with a 20 mol% ethanol(1) solution in water(2) at 78.15°C.

12.7. A liquid mixture of 50 mol% chloroform(1) and 50% 1,4-dioxane(2) at 0.1013 MPa is metered into a flash drum through a valve. The mixture flashes into two phases inside the drum where the pressure and temperature are maintained at 24.95 kPa and 50°C. The compositions of the exiting phases are x₁ = 0.36 and y₁ = 0.62.

Your supervisor asks you to adjust the flash drum pressure so that the liquid phase is x₁ = 0.4 at 50°C. He doesn’t provide any VLE data, and you are standing in the middle of the plant with only a calculator and pencil and paper, so you must estimate the new flash drum pressure. Fortunately, your supervisor has a phenomenal recall for numbers and tells you that the vapor pressures for the pure components at 50°C are  and . What is your best estimate of the pressure adjustment that is necessary without using any additional information?

12.8. Fit the data from problem 11.11 to the following model by regression over all points, and compare with the experimental data on the same plot, using

a. The Scatchard-Hildebrand model with k₁₂ = 0

b. The SSCED model with a default value of k₁₂

c. The SSCED model with k₁₂ matched to the data

d. The van Laar equation

e. Plot the P–x–y diagram at 80°C, based on the fits specified by your instructor.

12.9. Fit the data from problem 11.10 to the following model by regression over all points, and compare with the experimental data on the same plot, using

(a) – (d) as in problem 12.8.
(e) Plot the T–x–y diagram at 1 bar, based on the fits specified by your instructor.

12.10. Fit the data from problem 11.26 to the following model by regression over all points, and compare with the experimental data on the same plot, using

(a) – (e) as in problem 12.8.

12.11. Fit the data from problem 11.27 to the following model by regression over all points, and compare with the experimental data on the same plot, using

(a) – (e) as in problem 12.8.

12.12. Starting from the excess Gibbs energy formula for Flory’s equation, derive the formula for the activity coefficient of component 1 in a binary mixture.

12.13. Crime scene investigators have determined that an acrylic spray paint (polymethylmethacrylate, PMMA) was used to deface the Mona Lisa. Leonardo used linseed oil. We would like a solvent that interacts more strongly with acrylic than with linseed oil. Based on their chemical structures, we can approximate the SSCED parameters of linseed oil as n-hexadecane and acrylic paint as methylethylketone. Do you recommend CHCl₃, toluene, or acetone as the solvent? Explain.

12.14. R410a is a replacement for R22 in air conditioners and heat pumps. Air conditioners require a different refrigerant because they operate in a different temperature range. R410a avoids the problems with the ozone layer caused by chlorofluorocarbons, but its longevity may be limited because it has a relatively high global warming factor (1725 times the effect of CO₂). Roughly, it is a 50wt% mixture of difluoromethane (D) and pentafluoroethane (P) (i.e., 70mol% D). Kobayashi and Nishiumi (1998) report a pressure of 1.098 MPa at 283.05K.¹¹ You may assume the SCVP equation

a. Assuming k_ij = 0 for the binary interaction parameter of the SSCED equation, predict whether an azeotrope should be expected in this system at 283.05 K. Tabulate the relative volatilities at x_D = 0.01 and 0.99.

b. Solve for the value of k₁₂ that matches the reported pressure.

c. What acidity value for pentafluoroethane matches the value of k_ij determined in part (b)?

12.15. As part of a biorefining effort, butanediols are being produced by fermentation. The problem is that the isomers are all mixed up. Furthermore, 1,3-propanediol comprises roughly 30mol% of the mixture on a dry basis (i.e., water has been removed). The problem is to assess the prospects for azeotrope formation and avoidance. The following steps should shed some light on the problem.

a. Plot log₁₀(P^sat) versus 1000/T(K) in the range of T°C = [100,400] for 1,3-propanediol, 1,3-butanediol, and 1,4-butanediol on the same axes. Are there Bancroft points?

b. Compile a table of  for each component in each solvent based on the SSCED model. Which combinations show the greatest tendency to form azeotropes?CopycopyHighlighthighlightAdd NotenoteGet Linklink