## Problems and Solutions

Chapter 13

Special Applications

### Textbook Examples:

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

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. 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

### 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