If you have any questions related to the first test, please post them here instead of using email.

Best of luck on Tuesday !

## Sunday, February 18, 2007

## Thursday, February 15, 2007

### HW #5, P12.3 - Fitting VLE Data Using the Margules, van Laar & Wilson Equations - 18 pts

The following is a set of VLE data for the system acetone(1) / methanlo(2) at 55oC :

P (kPa) x1 y1 P (kPa) x1 y1 P (kPa) x1 y1

68.728 0.0000 0.0000 93.206 0.3579 0.4779 100.278 0.6945 0.7124

72.278 0.0287 0.0647 95.017 0.405 0.5135 100.467 0.7327 0.7383

75.279 0.0570 0.1295 96.365 0.448 0.5512 100.999 0.7752 0.7729

77.524 0.0858 0.1848 97.646 0.5052 0.5844 101.059 0.7922 0.7876

78.951 0.1046 0.2190 98.462 0.5432 0.6174 99.877 0.9080 0.8959

82.528 0.1452 0.2694 99.811 0.6332 0.6772 99.799 0.9448 0.9336

86.762 0.2173 0.3633 99.950 0.6605 0.6926 96.885 1.0000 1.0000

90.088 0.2787 0.4184

d.) Basing calculations on the Modified Raoult's Law, find parameters for the margules Equation that provide the best fit of GE/RT to the data and prepare a Pxy Diagram that compares the experimental points with curves determined from the correlation.

e.) Repeat part (c) for the van Laar Equation.

f.) Repeat part (c) for the Wilson Equation.

P (kPa) x1 y1 P (kPa) x1 y1 P (kPa) x1 y1

68.728 0.0000 0.0000 93.206 0.3579 0.4779 100.278 0.6945 0.7124

72.278 0.0287 0.0647 95.017 0.405 0.5135 100.467 0.7327 0.7383

75.279 0.0570 0.1295 96.365 0.448 0.5512 100.999 0.7752 0.7729

77.524 0.0858 0.1848 97.646 0.5052 0.5844 101.059 0.7922 0.7876

78.951 0.1046 0.2190 98.462 0.5432 0.6174 99.877 0.9080 0.8959

82.528 0.1452 0.2694 99.811 0.6332 0.6772 99.799 0.9448 0.9336

86.762 0.2173 0.3633 99.950 0.6605 0.6926 96.885 1.0000 1.0000

90.088 0.2787 0.4184

d.) Basing calculations on the Modified Raoult's Law, find parameters for the margules Equation that provide the best fit of GE/RT to the data and prepare a Pxy Diagram that compares the experimental points with curves determined from the correlation.

e.) Repeat part (c) for the van Laar Equation.

f.) Repeat part (c) for the Wilson Equation.

### HW #5, WB.1 - Pxy Diagram and Henry's Law Constants for Dichloromethane and Methanol - 14 pts

VLE data for the system dichloromethane(1) and methanol(2) at 50oC appear in the table below.

a.) Make a Pxy Diagram in Excel based on this data. No curve fit is necessary. Describe any unusual features in this diagram. Be specific and quantitative in your description.

b.) Make a fugacity or partial pressure plot (plot y1 P vs x1 and y2 P vs x1 on the same figure) in Excel. SVN Figure 12.2 is an example of such a plot.

c.) Determine the Henry's Law Constant at 50oC for each species from the partial pressure curves constructed in part b. Draw a line on each graph from part b, by hand or using Excel's drawing tools, that shows the graphical interpretation of the Henry's Law Constant for each species. (Ans.: Low-tech method (use last 2 data points and draw a line): k2 = 334 kPa/(mole 2/mol), High-tech method (fit the last 3 data points to a quadratic eqn and determine the slope as xi approaches 0): k2 = 437 kPa/(mole 2/mol) )

d.) Estimate the range of x1 values over which H1 is applicable and the range of x2 values over which H2 is applicable. Consider H values applicable as long as the error incurred is less than 5% of the partial pressure of the species.

Data :

P (kPa) x1 y1

55.55 0.000 0.000

58.79 0.042 0.093

61.76 0.097 0.174

64.59 0.189 0.265

65.66 0.292 0.324

65.76 0.349 0.349

65.59 0.415 0.367

65.15 0.493 0.386

63.86 0.632 0.418

62.36 0.720 0.438

59.03 0.835 0.484

54.92 0.893 0.537

48.41 0.945 0.620

31.10 1.000 1.000

a.) Make a Pxy Diagram in Excel based on this data. No curve fit is necessary. Describe any unusual features in this diagram. Be specific and quantitative in your description.

b.) Make a fugacity or partial pressure plot (plot y1 P vs x1 and y2 P vs x1 on the same figure) in Excel. SVN Figure 12.2 is an example of such a plot.

c.) Determine the Henry's Law Constant at 50oC for each species from the partial pressure curves constructed in part b. Draw a line on each graph from part b, by hand or using Excel's drawing tools, that shows the graphical interpretation of the Henry's Law Constant for each species. (Ans.: Low-tech method (use last 2 data points and draw a line): k2 = 334 kPa/(mole 2/mol), High-tech method (fit the last 3 data points to a quadratic eqn and determine the slope as xi approaches 0): k2 = 437 kPa/(mole 2/mol) )

d.) Estimate the range of x1 values over which H1 is applicable and the range of x2 values over which H2 is applicable. Consider H values applicable as long as the error incurred is less than 5% of the partial pressure of the species.

Data :

P (kPa) x1 y1

55.55 0.000 0.000

58.79 0.042 0.093

61.76 0.097 0.174

64.59 0.189 0.265

65.66 0.292 0.324

65.76 0.349 0.349

65.59 0.415 0.367

65.15 0.493 0.386

63.86 0.632 0.418

62.36 0.720 0.438

59.03 0.835 0.484

54.92 0.893 0.537

48.41 0.945 0.620

31.10 1.000 1.000

### HW #5, WB.2 - Determination of Azeotropes Using Margules and van Laar Equations - 12 pts

For each of the following systems, determine the azeotropic pressure and composition.

a.) Benzene(1) / acetonitrile(2) at 40oC. Margules parameters: A12 = 1.780, A21 = 1.055. Vapor pressures at 40oC: P1* = 29.82 kPa, P2* = 22.78 kPa.

Ans.: P ≈ 37 kPa

b.) Acetone(1) / chloroform(2) at 50oC. van Laar parameters: L12 = -0.936, L21 = -0.678. Vapor pressures at 50oC: P1* = 81.75 kPa, P2* = 69.38 kPa.

Ans.: P ≈ 61 kPa

Hints :

How can you recognize when an azeotrope exists ? Express this idea in terms of the Modified raoult's law and the Margules and van Laar Equations.

a.) Benzene(1) / acetonitrile(2) at 40oC. Margules parameters: A12 = 1.780, A21 = 1.055. Vapor pressures at 40oC: P1* = 29.82 kPa, P2* = 22.78 kPa.

Ans.: P ≈ 37 kPa

b.) Acetone(1) / chloroform(2) at 50oC. van Laar parameters: L12 = -0.936, L21 = -0.678. Vapor pressures at 50oC: P1* = 81.75 kPa, P2* = 69.38 kPa.

Ans.: P ≈ 61 kPa

Hints :

How can you recognize when an azeotrope exists ? Express this idea in terms of the Modified raoult's law and the Margules and van Laar Equations.

## Monday, February 12, 2007

### HW #5, WB.3 - Determination of Azeotropes Using the Wilson Equation - 8 pts

For the ethanol(1) / toluene(2) binary system at 1 atm, determine the azeotropic temperature and composition. The Wilson parameters for this system are given on page 474 of your textbook.

### HW #5, WB.4 - Bubble Point and Dew Point Calculations Using the Wilson Equation - 22 pts

For the system methanol(1) / acetonitrile(2), the Wilson parameters are given on page 474 of your textbook and the Antoine parameters are given below.

Ln[P1*] = 16.5938 - 3644.30 / ( t + 239.76 )

Ln[P2*] = 14.7258 - 3271.24 / ( t + 241.85 )

Where P* is in kPa and t is in oC.

a.) Calculate Pbub, given x1 = 0.73 and T = 70oC

b.) Calculate Tdew, given y1 = 0.63 and P = 101.325 kPa

Ln[P1*] = 16.5938 - 3644.30 / ( t + 239.76 )

Ln[P2*] = 14.7258 - 3271.24 / ( t + 241.85 )

Where P* is in kPa and t is in oC.

a.) Calculate Pbub, given x1 = 0.73 and T = 70oC

b.) Calculate Tdew, given y1 = 0.63 and P = 101.325 kPa

### HW #5, P12.22 - Multicomponent Flash Using the Wilson Equation - 20 pts

For the acetone(1) / methanol(2) / water(3) system, based on the Modified raoult's law and the Wilson Equation, make the following calculations :

a.) Bubble point temperature for P = 101.33 kPa, x1 = 0.30 and x2 = 0.40.

b.) Dew point temperature for P = 101.33 kPa, y1 = 0.30 and y2 = 0.40.

c.) PT Flash: Given P = 101.33 kPa, T = (Tbub+Tdew)/2, and z1 = 0.30 and z2 = 0.20.

a.) Bubble point temperature for P = 101.33 kPa, x1 = 0.30 and x2 = 0.40.

b.) Dew point temperature for P = 101.33 kPa, y1 = 0.30 and y2 = 0.40.

c.) PT Flash: Given P = 101.33 kPa, T = (Tbub+Tdew)/2, and z1 = 0.30 and z2 = 0.20.

### HW #5, P12.27 - Volume Change of Mixing Two Liquids - 6 pts

The volume change of mixing (in cm3/mol) for the system ethanol(1) / methyl butyl ether (2) at 25oC is given by the equation:

Given that V1 = 58.63 cm3/mol and V2 = 118.46 cm3/mol, what volume of mixture is formed when 750 cm3 of pure species 1 is mixed with 1500 cm3 of pure species 2 at 25oC ? What would be the volume of the mixture if an ideal solution were formed ?

Given that V1 = 58.63 cm3/mol and V2 = 118.46 cm3/mol, what volume of mixture is formed when 750 cm3 of pure species 1 is mixed with 1500 cm3 of pure species 2 at 25oC ? What would be the volume of the mixture if an ideal solution were formed ?

## Wednesday, February 07, 2007

### HW #4, P11.25 - Fugacity of a Mixture: Real vs. Ideal Solution - 8 pts

For the system ethlyene(1) / propylene(2) as a gas, estimate: f1^, f2^, phi1^ and phi2^ at T = 150 degC, P = 30 bar and y1 = 0.35.

a.) Through application of Eqs.(11.59) and (11.60).

(Actually, use the SRK EOS, like in class.)

b.) Assuming that the mixture is an ideal solution.

a.) Through application of Eqs.(11.59) and (11.60).

(Actually, use the SRK EOS, like in class.)

b.) Assuming that the mixture is an ideal solution.

### HW #4, P10.25+ - Bubble and Dew Point Calculations Using the SRK EOS - 16 pts

Assuming the validity of the DePriester Charts, make the following VLE calculations for the methane(1) / ethylene(2) / ethane(3) system:

a.) Pbub, given x1 = 0.10, x2 = 0.50 and t = -60oF.

b.) Pdew, given y1 = 0.50, y2 = 0.25 and t = -60oF.

c.) Tbub, given x1 = 0.12, x2 = 0.40 and P = 250 psia.

d.) Tdew, given y1 = 0.43, y2 = 0.36 and P = 250 psia.

Hints:

Do parts b and c only.

Use the results from my solution to this problem in HW#2, based on the DePriester Charts, as a starting point for SRK.

Use the SRK equations for mixtures to answer this question. The equations are the 2 SRK eqns in terms of Zliq and Zvap and three equilibrium eqns. The unknowns are The two Z's, two of the three yi's and the total pressure.

You will need to run Solver several times, tweaking your guesstimates of the unknown variables each time, in order to get Excel to converge to the correct answer. The correct answer is the one that yields the lowest value of the Σerror^2.

a.) Pbub, given x1 = 0.10, x2 = 0.50 and t = -60oF.

b.) Pdew, given y1 = 0.50, y2 = 0.25 and t = -60oF.

c.) Tbub, given x1 = 0.12, x2 = 0.40 and P = 250 psia.

d.) Tdew, given y1 = 0.43, y2 = 0.36 and P = 250 psia.

Hints:

Do parts b and c only.

Use the results from my solution to this problem in HW#2, based on the DePriester Charts, as a starting point for SRK.

Use the SRK equations for mixtures to answer this question. The equations are the 2 SRK eqns in terms of Zliq and Zvap and three equilibrium eqns. The unknowns are The two Z's, two of the three yi's and the total pressure.

You will need to run Solver several times, tweaking your guesstimates of the unknown variables each time, in order to get Excel to converge to the correct answer. The correct answer is the one that yields the lowest value of the Σerror^2.

### HW #4, P10.31+ - Equilibrium Flash Distillation Using the SRK EOS - 20 pts

A mixture consisting of 1 mol% ethane, 5 mol% propane, 44 mol% n-butane and 50 mol% isobutane is brought to a condition of 70oF at pressure P. If the molar fraction of the system that is vapor is 0.20, what is the pressure P, and what are the compositions of the vapor and liquid phases ?

Hints:

Use the results from my solution to this problem in HW#2, based on the DePriester Charts, as a starting point for SRK. Solve for P, the 4 xi's, the 4 yi's and the two Z's (compressibility of the vapor and liquid phases). That is a whopping 11 unks. I reduced the problem to 9 unks by forcing the Σxi = 1 and Σyi = 1. The 9 eqns include 3 independent material balance eqns, 4 equilibrium eqns and 2 SRK eqns in terms of two Z's, A's and B's. Remember that A, B and Z are not the same in the liquid phase as they are in the vapor phase.

Hints:

Use the results from my solution to this problem in HW#2, based on the DePriester Charts, as a starting point for SRK. Solve for P, the 4 xi's, the 4 yi's and the two Z's (compressibility of the vapor and liquid phases). That is a whopping 11 unks. I reduced the problem to 9 unks by forcing the Σxi = 1 and Σyi = 1. The 9 eqns include 3 independent material balance eqns, 4 equilibrium eqns and 2 SRK eqns in terms of two Z's, A's and B's. Remember that A, B and Z are not the same in the liquid phase as they are in the vapor phase.

### HW #4, P11.28 - Excess Gibbs Free Energy of a Real Liquid Mixture - 16 pts

The excess Gibbs energy of a binary liquid mixture at T and P is given by:

a.) Find expressions for Ln g1 and Ln g2 at T and P.

b.) Show that when these expressions are combined in accord with Eq.(11.95) the given equation for GE/RT is recovered.

c.) Show that these expressions satisfy Eq.(11.96), the Gibbs/Duhem Equation.

d.) Show that (d Ln g1 / dx1)x1=1 = (d Ln g2 / dx1)x1=0 = 0.

e.) Plot GE/RT, Ln g1 and Ln g2 as calculated by the given equation for GE/RT and by the equations developed in part (a) vs. x1. Label points Ln g1∞ and Ln g2∞ and show their values.

### HW #4, P11.36 - Excess Gibbs Free Energy of a Real Liquid Mixture - 12 pts

The data in the table below are experimental values of HE for binary liquid mixtures of 1,2-dichloroethane(1) and dimethyl carbonate(2) at 313.15 K and 1 atm.

a.) Determine from the data numerical values of parameters a, b and c in the correlating equation:

b.) Determine from the results of part (a) the minimum value of HE. At what value of x1 does this occur ?

c.) Determine from the results of part (a) expressions for : partial molar HE1 and partial molar HE1. Prepare a plot of these quantities vs. x1 and discuss its features.

x1 HE~ (J/mol)

0.0426 -23.3

0.0817 -45.7

0.1177 -66.5

0.1510 -86.6

0.2107 -118.2

0.2624 -144.6

0.3472 -176.6

0.4158 -195.7

0.5163 -204.2

0.6156 -191.7

0.6810 -174.1

0.7621 -141.0

0.8181 -116.8

0.8650 -85.6

0.9276 -43.5

0.9624 -22.6

a.) Determine from the data numerical values of parameters a, b and c in the correlating equation:

b.) Determine from the results of part (a) the minimum value of HE. At what value of x1 does this occur ?

c.) Determine from the results of part (a) expressions for : partial molar HE1 and partial molar HE1. Prepare a plot of these quantities vs. x1 and discuss its features.

x1 HE~ (J/mol)

0.0426 -23.3

0.0817 -45.7

0.1177 -66.5

0.1510 -86.6

0.2107 -118.2

0.2624 -144.6

0.3472 -176.6

0.4158 -195.7

0.5163 -204.2

0.6156 -191.7

0.6810 -174.1

0.7621 -141.0

0.8181 -116.8

0.8650 -85.6

0.9276 -43.5

0.9624 -22.6

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