### Textbook Examples:

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**13.01 Specific Vapor Volume of Acetic Acid Using the Chemical Theory (p. 560)**

Mathcad (2001) – Solution (zip)

Mathcad (2001) – Solution as XPS

**13.02 Specific Vapor Volume of the Mixture Formic Acid – Nitrogen Using the Chemical Theory (p. 565)**

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 566)**

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. 567)**

Mathcad (2001) – Solution (zip)

Mathcad (2001) – Solution as XPS

### Additional Problems:

**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(P

^{S}/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 K

_{D}= 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 2

^{nd }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 α

_{ij}can be approximated by α

_{ij}= P

_{i}

^{S}/P

_{j}

^{S}· g

_{i}/g

_{j}.

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: Δu_{12} = 12.0164 cal/mol Δu_{21} = 68.3212 cal/mol

r_{1} = 0.9200

q_{1} = 1.4000

r_{2} = 2.2024

q_{2} = 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 g

^{E}-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 y

_{1}= 0.5. Use the association model and the corresponding constants from Table 13.6.

Mathcad (2001) – Solution (zip)

Mathcad (2001) – Solution as XPS