﻿ Problems and Solutions Chapter 2

## Problems and SolutionsChapter 13 Special Applications

### Textbook Examples:

XPS-file display is available in Internet Explorer. In case of Firefox, select Internet Explorer when asked for the software to open the file.

13.01           Specific Vapor Volume of Acetic Acid Using the Chemical Theory (p. 558)

13.02           Specific Vapor Volume of the Mixture Formic Acid - Nitrogen Using the Chemical Theory (p. 563)

Mathcad (2001) - Solution (zip)
Mathcad (2001) - Solution as XPS

13.03           Vapor Fugacity Coefficients of the Mixture Water – Acetic Acid Using the Chemical Theory (p 563)

Mathcad (2001) - Solution (zip)
Mathcad (2001) - Solution as XPS

13.04           Activity Coefficients from VLE Data for the System Water – Acetic Acid Using the Chemical Theory for the Vapor Phase (p. 566)

Mathcad (2001) - Solution (zip)
Mathcad (2001) - Solution as XPS

P13.01       Compressibility Factor of Formic Acid Vapor Using the Chemical Theory

Calculate the compressibility factor of formic acid vapor at 420 K and 0.5 bar using the chemical theory. The required dimerization and tetramerization constants can be calculated from the parameters given in Table 13.6.

Mathcad (2001) - Solution (zip)
Mathcad (2001) - Solution as XPS

P13.02       Heat Capacity of Acetic Acid Along the Vapor-Liquid Coexistence Curve Using the Chemical Theory

Estimate the heat capacity of acetic acid along the vapor-liquid coexistence curve for both phases using the vapor pressure and ideal gas heat capacity correlations given in Appendix A and the dimerization and tetramerization constants from Table 13.6.

Mathcad (2001) - Solution (zip)
Mathcad (2001) - Solution as XPS

P13.03       Entropy and Enthalpy Change Upon Isothermal Compression of Propionic Acid Using the Chemical Theory

Estimate the entropy and enthalpy change upon isothermal compression of propionic acid from 0.01 to 1 atm at a temperature of 145°C using the chemical theory with dimerization constants given in Table 13.6.

Mathcad (2001) - Solution (zip)
Mathcad (2001) - Solution as XPS

P13.04        Change of the Degree of Association Along the Vapor Pressure Curve for Different Carboxylic Acids

Estimate the change of the degree of dimerization along the vapor pressure curve for formic acid, acetic acid and propionic acid using the dimerization constants and a simplified vapor pressure equation (log(PS/1atm) = A-B/T). Calculate the values of the parameters A and B from the boiling temperatures at 0.5 and 2 atm.

Vapor pressure equation constants can be found in Appendix A. Dimerization constants can be calculated from the parameters given in Table 13.6. In case of acetic acid, the dissociation constant should be described by the equation KD = exp(-17.374 + 7290/T) bar-1 (Gmehling, J., Onken, U., Arlt, W., Grenzheuser, P., Kolbe, B., Weidlich, U., Rarey, J. Vapor-Liquid Equilibrium Data Collection, 37 parts, DECHEMA Chemistry Data Series, Frankfurt (1977–2011).)
This equation was regressed without taking into account tetramerization.

Mathcad (2001) - Solution (zip)
Mathcad (2001) - Solution as XPS

P13.05        Vapor Pressure and Fugacity of Associating and Non-Associating Components

Calculate the saturated vapor pressure and fugacity along the vapor-liquid coexistence curve for benzene, water and acetic acid between 25°C and the critical temperature of the components. For the real vapor phase behavior, use the virial equation truncated after the 2nd virial coefficient in case of water and benzene and the chemical theory in case of acetic acid. Discuss the results. Inside which temperature range are the results reliable? Do the calculations lead to under- or overprediction of the fugacity outside the reliable temperature range?

Vapor pressure equation coefficients and second virial coefficient correlations as function of temperature are given in Appendix A. Dimerization and tetramerization constant parameters are given in Table 13.6.

Mathcad (2001) - Solution (zip)
Mathcad (2001) - Solution as XPS

P13.06        Effect of the Real Gas Factor on the Separation Factor

In case of mixtures of components, which do not strongly or differently associate in the vapor phase, the separation factor αij can be approximated by  αij= PiS/PjS · gi/gj. In other cases the ratio of the real gas factors has to be taken into account. Calculate the ratio of the pure component vapor pressures, the activity coefficients (calculated using the UNIQUAC model) and the real gas factors for the system water (1) – acetic acid (2) at 80°C as function of concentration. Discuss the results.
Vapor pressure equation constants can be found in Appendix A. Calculate the dimerization and tetramerization constant of acetic acid using the parameters given in Table 13.6.

UNIQUAC parameters:
Δu12 = 12.0164 cal/mol                  Δu21 = 68.3212 cal/mol
r1      = 0.9200                                      q1     = 1.4000
r2      = 2.2024                                      q2     = 2.0720

Mathcad (2001) - Solution (zip)
Mathcad (2001) - Solution as XPS

P13.07        Heat of Vaporization Data for Acetic Acid (DDB)

Search for experimental heats of vaporization data for acetic acid in the free DDBSP Explorer Edition. Interpret the behavior as function of temperature. Compare the values to those of a non-associating component of similar molecular weight (acetone).

P13.08        Regression of VLE Data of Water - Acetic  Acid Using DDB, DDBSP

In the free DDBSP Explorer Edition, search for all data for the system water – acetic acid and regress these data simultaneously using the Three-Suffix Margules equation and binary parameters with quadratic temperature dependence. The Three-Suffix Margules gE-model is very seldom used today but is the only simultaneous regression model available in the free DDBSP Explorer Version.  In the x-y diagram, the equilibrium curves are nearly parallel to the diagonal line at mole fractions of water greater than 0.7. What is the reason for this strange behavior?

P13.09        Fugacity Coefficients of Acetic Acid and Water Using the Chemical Theory

Calculate the fugacity coefficients of both components in the system acetic acid (1) – water (2) at T = 393.15 K and P = 1 bar for a mole fraction y1 = 0.5. Use the association model and the corresponding constants from Table 13.6.

Mathcad (2001) - Solution (zip)
Mathcad (2001) - Solution as XPS