## Problems and Solutions

Chapter 3

Correlation and Estimation of Pure Component Properties

### Textbook Examples:

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03.07
Enthalpy of Reaction and
Equilibrium Concentration of the Theoretically Possible n-Butane –
Isobutene Isomerization Reaction in the Gas Phase (p. 74)

Mathcad (2001) - Solution (zip)

Mathcad (2001) - Solution as XPS

### Additional Problems:

P03.01 ** ****Conversion
of cP-Coefficients for Carbon by Parameter Regression**

Regress a third order polynomial to
results of the equation for the heat capacity at constant pressure for
graphite reported in “Butland, A.T.D.; Maddison, R.J., The specific heat
of graphite: an evaluation of measurements, J. Nucl. Mater., 1973, 49,
45-56”:

Mathcad (2001) - Solution (zip)

Mathcad (2001) - Solution as XPS

** Calculation
of the Enthalpy of Evaporation at a Different Temperature Using the
Watson-Equation**

Calculate the enthalpy of vaporization of ethanol at 25°C and
200°C using the Watson-equation. The enthalpy of vaporization at the
normal boiling temperature of 351.41K is 39.183 kJ/mol. The critical
temperature of ethanol can be found in Appendix A.

Mathcad (2001) - Solution (zip)

Mathcad (2001) - Solution as XPS

P03.03
**Estimation of Critical Data of Hexene Using the Joback-Method**

Estimate the critical data T_{C}, P_{C} and v_{C}
of n-hexene using the Joback-method.

Mathcad (2001) - Solution (zip)

Mathcad (2001) - Solution as XPS

P03.04
**Estimation of Standard Enthalpy and Standard Gibbs Energy Using
the Joback Method **

Determine the enthalpy of formation as well as the Gibbs energy
of formation for hexane and benzene at 25°C and 1 atm (ideal gas) using
the Joback group contribution method.

Mathcad (2001) - Solution (zip)

Mathcad (2001) - Solution as XPS

P03.05
**Solid and Liquid Vapor Pressure Calculations Using the
Wagner-Equation (DDBSP, Excel)**

Retrieve the vapor pressure data of naphthalene from the free
DDBSP Explorer Edition and export the values to MS-Excel. Regress the
coefficients of the Wagner equation (Eq. 3.37) to the experimental data
using the Excel Solver Add-In. Use the Wagner equation to calculate the
vapor pressure of the hypothetical subcooled liquid. From the vapor
pressures of the hypothetical subcooled liquid and the sublimation
pressure data found in the free DDBSP Explorer Edition, estimate the
melting point and heat of fusion for naphthalene. Compare the results to
the values given in the DDB.

Mathcad (2001) - Solution (zip)

Mathcad (2001) - Solution as XPS

P03.06 **
Estimation of the Melting Temperature of Naphthalene Using the Joback
Method**

Estimate the melting temperature of naphthalene using the Joback
method and compare the result to the recommended value of 353.35 K. The
estimation can either be performed by hand using the group contributions
in Table 3.1 or with the help of the program Artist in the free DDBSP
Explorer Edition.

P03.07 **Retrieval
and Estimation of Liquid Density Data of THF (DDBSP) **

Retrieve the saturated liquid density data for tetrahydrofuran in
the free DDBSP Explorer Edition and plot the data together with the
prediction of the Campell/Thodos method. In Artist, estimate the liquid
density at the normal boiling point and compare the results to the data
and estimation above.

P03.08
**Regression of Trichloromethane Vapor Pressure Data Using DDBSP**

In the free DDBSP Explorer Edition, regress the liquid vapor
pressure data for trichloromethane using the Antoine equation. Remove
outliers that are not in agreement with the majority of the authors.
Check the manual to clarify the exact formulation of the
Antoine-equation. Convert the parameters so that the Antoine equation
employs the natural logarithm and yields the vapor pressure in the unit
kPa.

P03.09
**Liquid Thermal Conductivity Data For Glycol and 1-Butanol from
the DDB**

Compare the liquid thermal conductivity data for glycol (1,2
ethanediol) and 1-butanol using the free DDBSP Explorer Edition.
Interpret the difference in the absolute value and the temperature
dependence on a molecular basis.

P03.10
**Vapor Pressure Estimation Using Clausius-Clapeyron**

The boiling temperature of water at
J_{1
}= 90°C is P_{1}^{s} = 0.702 bar. At this
temperature, the enthalpy of vaporization is 2282.5 J/g. Estimate the
vapor pressure at
J_{2
}= 95°C using the Clausius-Clapeyron equation.

Mathcad (2001) -
Collected (zip)

Mathcad (2001) -

P03.11
**Standard Enthalpy and Gibbs Energy of Formation of Ethylene Glycol
Using the Joback Method**

Estimate the standard enthalpy of formation and the standard
Gibbs energy of formation of ethylene glycol (CH_{2}OH-CH_{2}OH)
using the Joback method. Can a similarly good result be expected as in
case of ethyl acetate (Example 3.6)?

Mathcad (2001) -
Collected (zip)

Mathcad (2001) -

P03.12
**Heat Capacity of a Gas From Heat Duty of Heating **

An ideal gas is heated up from T_{1} = 300 K to T_{2}
= 350 K. The specific duty is evaluated to be q_{12} =
1040 J/mol. Describe the chemical nature of the gas.

Mathcad (2001) -
Collected (zip)

Mathcad (2001) -

P03.13 **Speed
of Sound in Water Vapor (Ideal Gas) **

Calculate the speed of sound in water vapor at
J
= 100°C, P = 1 bar. The vapor can be regarded as an ideal gas.

Mathcad (2001) -
Collected (zip)

Mathcad (2001) -

P03.14 **Enthalpy
of Vaporization of R134a Using Clausius-Clapeyron **

For the refrigerant R134a, the following data are given:

P^{s} (0°C) = 2.006 bar
r^{V}
(0°C) = 14.428 kg/m^{3}
r^{L}
(0°C) = 1294.78 kg/m^{3}

P^{s} (10°C) =
4.146 bar
r^{V}
(10°C) = 20.226 kg/m^{3}
r^{L}
(10°C) = 1260.96 kg/m^{3}

Mathcad (2001) -
Collected (zip)

Mathcad (2001) -

P03.15 **Pressure
Dependence of the Melting Point of Water Using Clausius-Clapeyron **

At P = 1.01325 bar, the melting point of water is
J_{m}
= 0°C. How is the melting temperature affected, if the pressure rises by
20 bar? Use the Clausius-Clapeyron equation for the solid-liquid
equilibrium. The following values are given:

Dh_{m}
= 333 J/g
r^{L}
= 1000 kg/m^{3}
r^{S}
= 917 kg/m^{3}

Mathcad (2001) -
Collected (zip)

Mathcad (2001) -

P03.16
**Complete Property Estimation for R134a**

Estimate the whole set of physical properties (critical temperature,
pressure, volume and compressibility, acentric factor, boiling and
melting temperature, heat of fusion and heat of vaporization, standard
enthalpy and standard Gibbs energy of formation, vapor pressure, liquid
density, ideal gas heat capacity, liquid and vapor viscosity, liquid and
vapor thermal

conductivity, and surface tension(temperature-dependent properties at ϑ
= 20 °C) of R134a (1,1,1,2-tetraﬂuoroethane, CH2F–CF3) without using any
given information except its molar mass (102.03 g/mol) and its chemical
structure. Compare the results with the values obtained with the data
and equations given in Appendix A.

planned for June 2012

P03.17
**Ideal Gas Heat Capacity of Methane from Spectroscopic Data **

Estimate the ideal gas heat capacity of methane at T = 600 K
using the following information about its basic frequencies from
spectroscopic data:

Q_{1}
=
Q_{2}
=
Q_{3}
= 1876.6 K

Q_{4}
=
Q_{5}
= 2186 K

Q_{6}
= 4190 K

Q_{7}
=
Q_{8}
=
Q_{9}
= 4343 K

The characteristic temperature
Q
is an abbreviation for
Q
= hn_{o}/k.
Verify that the molecule has nine basic frequencies for the vibration.

Mathcad (2001) -
Collected (zip)

Mathcad (2001) -
Collected as XPS

P03.18 **Small
Droplet Vapor Pressure ****of Water and n-Hexane at
the Bankroft Point**

At approximately T = 380 K, the vapor pressure curves of water
and n-hexane intersect. Calculate the difference in the vapor pressures,
if both substances form drops with diameters of d = 2 nm.

Mathcad (2001) - Solution (zip)

Mathcad (2001) - Solution as XPS

P03.19 **Liquid
Viscosity Estimation for 1,1,2-Trichloroethane Using
Rarey/Nannoolal**

Estimate the liquid dynamic viscosity of 1,1,2-trichloroethane at
T = 330 K using the Rarey/Nannoolal method.

P03.20
**Vapor Pressure of p-Tolualdehyde Using Rarey/Moller**

Estimate the vapor pressure of p-tolualdehyde at
J
= 150°C using the Rarey/Moller method. The normal boiling point is
J_{b}
= 206.3°C. Use the Clausius-Clapeyron equation to determine the
corresponding enthalpy of vaporization.

P03.21 **
Isobaric Ideal Gas Heat Capacity of Ammonia From Speed of Sound**

The speed of sound of ammonia at T = 303.15 K, P = 0.01 bar is w*
= 439.11 m/s. Calculate the corresponding isobaric ideal gas heat
capacity.

Mathcad (2001) - Solution (zip)

Mathcad (2001) - Solution as XPS

P03.22
**Enthalpy of Vaporization of Benzene at the Normal Boiling Point
Using Clausius-Clapeyron**

Estimate the enthalpy of vaporization of benzene at the normal
boiling point using the vapor pressure coefficients and the critical
constants from App. A. For the vapor phase, use

a) the ideal gas law

b) the Soave-Redlich-Kwong equation of state

Compare the results with the correlation given in App. A.

Mathcad (2001) - Solution (zip)

Mathcad (2001) - Solution as XPS

P03.23
**Enthalpy of Vaporization of Ethanol at Different Temperatures
Using the Watson Equation**

Estimate the enthalpy of vaporization of ethanol at
¶_{1}=25°C
and
¶_{2}=200°C.
Use eq. 3.62 using B = 0.38 and C=D=E=0. Determine the parameter A from
the reference value
Dh_{vo}=38,470
J/mol at T_{0}= 351.5 K.

Mathcad (2001) - Solution (zip)

Mathcad (2001) - Solution as XPS