Introduction to Chemical Engineering Thermodynamics
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN: 9781259696527
Author: J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher: McGraw-Hill Education
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Chapter 13, Problem 13.68P

Use Eq. (13.13) to reduce one of the following isothermal data sets, and compare the result with that obtained by application of Eq. (13.19). Recall that reduction means developing a numerical expression for GE/RT as a function of composition.
(a) Methylethylketone(1)/toluene(2) at 50°C: Table 13.1.

  1. Acetone(1)/methanol( 2) at 55°C: Prob. 13.34.
  2. Methyl tert-butyl ether( l)/dichloromethane( 2) at 35°C: Prob. 13.37.
  3. Acetonitrile(1)/benzene(2) at 45°C: Prob. 13.40.

Second-virial-coefficient data are as follows:

    Part (a) Part (b) Part (c) Part (d)
    B11/cm3?mol-1 -1840 -1440 -2060 -4500
    B12/cm3?mol-1 -1800 -1150 -860 -1300
    B22/cm3?mol-1 -1150 -1040 -790 -1000

Table 13.1: VLE Data for Methyl Ethyl Ketone(l)/Toluene(2) at 50°C

    P/kPa x1y1
    f ^ 1 t = y 1 P

    f ^ 2 t = y 2 P
    γ 1 γ 2
    12.30 ( P 2 s a t ) 0.0000 0.0000 0.000 12.300 ( P 2 s a t ) 1.000
    15.51 0.0895 0.2716 4.212 11.298 1.304 1.009
    18.61 0.1981 0.4565 8.496 10.114 1.188 1.026
    21.63 0.3193 0.5934 12.835 8.795 1.114 1.050
    24.01 0.4232 0.6815 16.363 7.697 1.071 1.078
    25.92 0.5119 0.7440 19.284 6.636 1.044 1.105
    27.96 0.6096 0.8050 22.508 5.542 1.023 1.135
    30.12 0.7135 0.8639 26.021 4.099 1.010 1.163
    31.75 0.7934 0.9048 28.727 3.023 1.003 1.189
    34.15 0.9102 0.9590 32.750 1.400 0.997 1.268
    36.09 ( P 1 s a t ) 1.0000 1.0000 36.090 ( P 1 s a t ) 0.000 1.000

13.34. The following is a set of VLE data for the system acetone(1)/methanol(2) at 55°C:

    P/kPa x1 y1 P/kPa x1 y1
    68.728 0.0000 0.0000 97.646 0.5052 0.5844
    72.278 0.0287 0.0647 98.462 0.5432 0.6174
    75.279 0.0570 0.1295 99.811 0.6332 0.6772
    77.524 0.0858 0.1848 99.950 0.6605 0.6926
    78.951 0.1046 0.2190 100.278 0.6945 0.7124
    82.528 0.1452 0.2694 100.467 0.7327 0.7383
    86.762 0.2173 0.3633 100.999 0.7752 0.7729
    90.088 0.2787 0.4184 101.059 0.7922 0.7876
    93.206 0.3579 0.4779 99.877 0.9080 0.8959
    95.017 0.4050 0.5135 99.799 0.9448 0.9336
    96.365 0.4480 0.5512 96.885 1.0000 1.0000

Extracted from D. C. Freshwater and K. A. Pike, J. Chem. Eng. Data. vol. 12, pp. 179-183. 1967.

  1. Basing calculations on Eq. (13.24), find parameter values 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.
  2. Repeat (a) for the van Laar equation.
  3. Repeat (a) for the Wilson equation.
  4. Using Barker’s method, find parameter values for the Margules equation that provide the best fit of the P- x1data. Prepare a diagram showing the residuals δ P and δ y 1 plotted vs. x1.
  5. Repeat (d) for the van Laar equation.
  6. Repeat (d) for the Wilson equation.

13.37. VLE data for methyl tert-butyl ether(1)/dichloromethane(2) at 308.15 K are as follows:

    P/kPa x1y1 P/kPa x1 y1
    85265 0.0000 0.0000 59.651 0.5036 0.3686
    83.402 0.0330 0.0141 56.833 0.5749 0.4564
    82.202 0.0579 0.0253 53.689 0.6736 0.5882
    80.481 0.0924 0.0416 51.620 0.7676 0.7176
    76.719 0.1665 0.0804 50.455 0.8476 0.8238
    72.422 0.2482 0.1314 49.926 0.9093 0.9002
    68.005 0.3322 0.1975 49.720 0.9529 0.9502
    65.096 0.3880 0.2457 49.624 1.0000 1.0000

Extracted from F. A. Mato, C. Bcrru. and A. Pcncloux, J. Cheni. Eng. Data. Vol. 36, pp. 259-262. 1991.

The data are well correlated by the three-parameter Margules equation [an extension of Eq. (13.39)]:

G E R T = A 21 x 1 + A 12 x 2 C x 1 x 2 x 1 x 2

Implied by this equation are the expressions:

I n γ 1 = x 2 2 A 12 + 2 A 21 A 12 C x 1 + 3 C x 1 2

I n γ 2 = x 1 2 A 12 + 2 A 12 A 21 C x 2 + 3 C x 2 2

  1. Basing calculations on Eq. (13.24), find the values of parameters Aj2, A2|. and C that provide the best fit of GE/RT to the data.
  2. Prepare a plot of In γ 1 In γ 2 , and G E / x 1 x 2 R T vs. x 1 showing both the correlation and experimental values.
  3. Prepare a Pxy diagram [see Fig. 13.8(a)] that compares the experimental data with the correlation determined in (a).
  4. Prepare a consistency-test diagram like Fig. 13.9.
  5. Using Barker’s method, find the values of parameters A12. A21, and C that provide the best fit of the P-x1data. Prepare a diagram showing the residuals δ P and δ y 1 plotted vs. x1

Chapter 13, Problem 13.68P, Use Eq. (13.13) to reduce one of the following isothermal data sets, and compare the result with , example  1

Chapter 13, Problem 13.68P, Use Eq. (13.13) to reduce one of the following isothermal data sets, and compare the result with , example  2

Figure 13.8: The diethyl ketone(l)/n-hexane(2) system at 65°C. (a) Pxy data and their correlations.

13.40. Following are VLE data for the system acetonitrile(1)/benzene(2) at 45°C

    P/kPa x1 y1 P/kPa x1y1
    29.819 0.0000 0.0000 36.978 0.5458 0.5098
    31.957 0.0455 0.1056 36.778 0.5946 0.5375
    33.553 0.0940 0.1818 35.792 0.7206 0.6157
    35.285 0.1829 0.2783 34.372 0.8145 0.6913
    36.457 0.2909 03607 32.331 0.8972 0.7869
    36.996 0.3980 0.4274 30.038 0.9573 0.8916
    37.068 0.5069 0.4885 27.778 1.0000 1.0000

The data are well correlated by the three-parameter Margules equation (see Prob. 13.37).
(?)
Basing calculations on Eq. (13.24), Find the values of parameters A12, A21, and C that provide the best fit of GE/RT to the data.
(b)
Prepare a plot of In γ 1 , In γ 2 , and G E / x 1 x 2 R T vs. x 1 showing both the correlation and experimental values.

  1. Prepare a Pxy diagram [see Fig. 13.8(a)] that compares the experimental data with the correlation determined in (a).
  2. Prepare a consistency-test diagram like Fig. 13.9.
  3. Using Barker’s method, find the values of parameters A12, A21, and C that provide the best Fit of the P- x1data. Prepare a diagram showing the residuals δ P and δ y 1 plotted vs. x1.

13.37. VLE data for methyl tert-butyl ether(1)/dichloromethane(2) at 308.15 K are as follows:

    P/kPa x1y1 P/kPa x1 y1
    85265 0.0000 0.0000 59.651 0.5036 0.3686
    83.402 0.0330 0.0141 56.833 0.5749 0.4564
    82.202 0.0579 0.0253 53.689 0.6736 0.5882
    80.481 0.0924 0.0416 51.620 0.7676 0.7176
    76.719 0.1665 0.0804 50.455 0.8476 0.8238
    72.422 0.2482 0.1314 49.926 0.9093 0.9002
    68.005 0.3322 0.1975 49.720 0.9529 0.9502
    65.096 0.3880 0.2457 49.624 1.0000 1.0000

Extracted from F. A. Mato, C. Bcrru. and A. Pcncloux, J. Cheni. Eng. Data. Vol. 36, pp. 259-262. 1991.

The data are well correlated by the three-parameter Margules equation [an extension of Eq. (13.39)]:

G E R T = A 21 x 1 + A 12 x 2 C x 1 x 2 x 1 x 2

Implied by this equation are the expressions:

I n γ 1 = x 2 2 A 12 + 2 A 21 A 12 C x 1 + 3 C x 1 2

I n γ 2 = x 1 2 A 12 + 2 A 12 A 21 C x 2 + 3 C x 2 2

  1. Basing calculations on Eq. (13.24), find the values of parameters Aj2, A2|. and C that provide the best fit of GE/RT to the data.
  2. Prepare a plot of In γ 1 In γ 2 , and G E / x 1 x 2 R T vs. x 1 showing both the correlation and experimental values.
  3. Prepare a Pxy diagram [see Fig. 13.8(a)] that compares the experimental data with the correlation determined in (a).
  4. Prepare a consistency-test diagram like Fig. 13.9.
  5. Using Barker’s method, find the values of parameters A12. A21, and C that provide the best fit of the P-x1data. Prepare a diagram showing the residuals δ P and δ y 1 plotted vs. x1

Chapter 13, Problem 13.68P, Use Eq. (13.13) to reduce one of the following isothermal data sets, and compare the result with , example  3

Chapter 13, Problem 13.68P, Use Eq. (13.13) to reduce one of the following isothermal data sets, and compare the result with , example  4

Figure 13.8: The diethyl ketone(l)/n-hexane(2) system at 65°C. (a) Pxy data and their correlations.

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Chapter 13 Solutions

Introduction to Chemical Engineering Thermodynamics

Ch. 13 - A binary mixture of mole fraction z1is flashed to...Ch. 13 - Humidity, relating to the quantity of moisture in...Ch. 13 - A concentrated binary solution containing mostly...Ch. 13 - Air, even more than carbon dioxide, is inexpensive...Ch. 13 - Helium-laced gases are used as breathing media for...Ch. 13 - A binary system of species 1 and 2 consists of...Ch. 13 - For the system ethyl ethanoate(l)/n-heptane(2) at...Ch. 13 - A liquid mixture of cyclohexanone(1)/phenol(2) for...Ch. 13 - A binary system of species 1 and 2 consists of...Ch. 13 - For the acetone(l)/methanol(2) system, a vapor...Ch. 13 - The following is a rule of thumb: For a binary...Ch. 13 - A process stream contains light species 1 and...Ch. 13 - If a system exhibits VLE, at least one of the...Ch. 13 - Flash calculations are simpler for binary systems...Ch. 13 - Prob. 13.25PCh. 13 - (a) A feed containing equimolar amounts of...Ch. 13 - A binary mixture of benzene(1) and toluene(2) is...Ch. 13 - Ten (10) kmolhr-1 of hydrogen sulfide gas is...Ch. 13 - Physiological studies show the neutral comfort...Ch. 13 - Prob. 13.30PCh. 13 - Prob. 13.31PCh. 13 - Prob. 13.32PCh. 13 - If Eq. (13.24) is valid for isothermal VLE in a...Ch. 13 - Prob. 13.34PCh. 13 - The excess Gibbs energy for binary systems...Ch. 13 - For the ethanol(l )/chloroform(2) system at 50°C,...Ch. 13 - VLE data for methyl tert-butyl...Ch. 13 - Prob. 13.38PCh. 13 - Prob. 13.39PCh. 13 - Following are VLE data for the system...Ch. 13 - Prob. 13.41PCh. 13 - Prob. 13.42PCh. 13 - Problems 13.43 through 13.54 require parameter...Ch. 13 - Problems 13.43 through 13.54 require parameter...Ch. 13 - Prob. 13.45PCh. 13 - Problems 13.43 through 13.54 require parameter...Ch. 13 - Prob. 13.47PCh. 13 - Prob. 13.48PCh. 13 - Prob. 13.49PCh. 13 - Prob. 13.50PCh. 13 - Problems 13.43 through 13.54 require parameter...Ch. 13 - Prob. 13.52PCh. 13 - The following expressions have been reported for...Ch. 13 - Possible correlating equations for In 1 in a...Ch. 13 - Prob. 13.57PCh. 13 - Binary VLE data are commonly measured at constant...Ch. 13 - Consider the following model for GE/RT of a binary...Ch. 13 - A breathalyzer measures volume-% ethanol in gases...Ch. 13 - Table 13.10 gives values of parameters for the...Ch. 13 - Prob. 13.62PCh. 13 - A single P-x1- y1data point is available for a...Ch. 13 - A single P- x1, data point is available for a...Ch. 13 - The excess Gibbs energy for the system...Ch. 13 - Prob. 13.66PCh. 13 - A system formed of methane(l) and a light oil(2)...Ch. 13 - Use Eq. (13.13) to reduce one of the following...Ch. 13 - For one of the following substances, determine...Ch. 13 - Departures from Raoult's law are primarily from...Ch. 13 - The relative volatility a12is commonly used in...Ch. 13 - Prob. 13.74PCh. 13 - Prob. 13.75PCh. 13 - Prob. 13.76P
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