## Problems and Solutions

Chapter 5

Phase Equilibria in Fluid Systems

### Textbook Examples:

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05.03
Activity Coefficients
from Experimental xyPT-Data (p. 188)

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05.04
Construct a Diagram with
g^{E}, h^{E} and –Ts^{E} (p. 193)

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05.05
Temperature Dependence
of the Activity Coefficients (p. 195)

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05.06
Activity Coefficients at Infinite Dilution at Different
Temperatures Using the Partial Molar Excess Enthalpy at Infinite
Dilution (p. 196)

05.07
Excess Volume of the
Liquid Mixture Ethanol - Water (p. 198)

05.08
Activity Coefficient of
the Monomer in a Polymer Using the Athermal Flory-Huggins Equation
(p. 202)

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05.09
Compare Experimental VLE to Wilson Equation Results (p. 204)

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05.10
Thermodynamic
Consistency Using the Area Test (p. 217)

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05.11
Liquid Density Using the Peng-Robinson EOS (p. 231)

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05.12
VLE of N2 - CH4 Using SRK
(p. 237)

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05.13
Azeotropic Points of the
System Acetone – Methanol (p. 246)

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05.14
Estimate the Temperature Dependence of the Azeotropic Composition
Using the Heat of Vaporization
(p. 248)

05.15
Henry Constant for CO2
from Phase Equilibrium Data (p. 259)

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05.17
Henry Constant for
Methane in Benzene at 60 °C with the Help of the Soave-Redlich-Kwong
Equation of State (p. 264)

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05.18
Henry Constant for Methane in Benzene at 60 °C Using the Method
of Prausnitz and Shair
(p. 266)

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05.19
VLLE of n-Butanol -
Water at 50°C Using UNIQUAC (p. 272)

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05.20
Liquid-Liquid
Equilibrium for the System Water - Ethanol - Benzene - K-Factor Method
UNIQUAC (p. 277)

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05.22
VLE of Hexane-Butanone-2
Via UNIFAC (p. 289)

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05.23
Liquid-Liquid Solubility for Alkane-Water from Empirical
Correlation (p. 305)

### Additional Problems:

P05.01 **VLE
Calculation For the System Ethanol - Water Using Wilson, NRTL and
UNIQUAC**

Calculate the pressure and the vapor phase mole fraction for the
system ethanol (1)- water (2) at 70°C with the help of the different g^{E}-models
(Wilson, NRTL, UNIQUAC) for an ethanol mole fraction of 0.2152 using the
interaction parameters, auxiliary parameters and Antoine constants given
in Fig. 5.30 and assuming ideal vapor phase behavior. Besides total and
partial pressures and vapor phase composition, calculate also K-factors
and separation factors. Repeat the calculation using the real gas
factors φ_{1}=0.9955 and φ_{2}=1.0068.

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(Wilson)

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(NRTL)

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(UNIQUAC)

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P05.02 ** Regression of UNIQUAC
Parameters to Binary VLE Data For the Mixture Ethanol - Water**

Regress the
binary interaction parameters of the UNIQUAC model to the isobaric VLE
data measured by Kojima et al. at 1 atm and listed below. As objective
function, use:

a) relative quadratic deviation in the activity coefficients

b) quadratic deviation in boiling temperatures

c) relative quadratic deviation in vapor phase compositions

d) relative deviation in separation factors

Adjust the vapor pressure curves using a constant factor to exactly
match the author's pure component vapor pressures.

Reference: Kojima K., Tochigi K., Seki H., Watase K., Kagaku Kogaku, 32,
p149-153, 1968

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P05.03 **Experimental VLE Data and
Modified UNIFAC and VTPR Predictions for the Mixture Ethanol - Water**

Compare the
experimental data for the system ethanol – water measured at 70°C (see
Fig. 5.30 and below) with the results of the group contribution method
modified UNIFAC and the group contribution equation of state VTPR.

Reference: Mertl I., Collect.Czech.Chem.Commun., 37(2), 366-374, 1972

Modified UNIFAC:

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P05.04 **VLE
Calculation For the System Ethanol - Benzene Using the Wilson Model**

Calculate the Pxy-diagram at 70°C for the system ethanol (1) –
benzene (2) assuming ideal vapor phase behavior using the Wilson
equation. The binary Wilson parameters
Λ_{12} and
Λ_{21 }should be derived from the activity coefficients
at infinite dilution (see Table 5.6). Experimentally the following
activity coefficients at infinite dilution were determined at this
temperature:

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P05.05
**Azeotropic Composition of Homogeneous Binary Mixtures Using
Modified UNIFAC**

Determine the azeotropic composition of the following homogeneous
binary systems

a) acetone - water

b) ethanol -
1,4-dioxane

c) acetone - methanol

at 50, 100, and 150°C using the group contribution method modified
UNIFAC.

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**Discontinuous
Distillation of Ethanol - Water Contaminated with Methanol**

In the manual of a home glass distillery (s. Fig. 1) the
following recommendation is given: “After some time liquid will drip out
of the cooler. You are kindly requested to collect the first small
quantity and not to use it, as first a methanol enrichment takes place.”
Does this recommendation make sense? The purpose of the glass distillery
is to enrich ethanol. Consider the wine to be distilled as a mixture of
ethanol (10 wt.-%), methanol (200 wt.-ppm) and water. The one stage
distillation takes place at atmospheric pressure.

Calculate the percentages of methanol and ethanol removed from 200 g
feed, when 10 g of the distillate is withdrawn. For the calculation the
modified UNIFAC method should be applied. The constants for the Antoine
equation for ethanol and water can directly be taken from Fig. 5.30. For
methanol the vapor pressure constants and molar mass are given in
Appendix A. For the calculation ideal vapor phase should be assumed.

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P05.07 **VLE
Behavior, h**^{E}** data,
Azeotropic Data and Activity Coefficients at Infinite Dilution for
Pentane - Acetone Using Modified UNIFAC**

Calculate the VLE behavior, h^{E} data, azeotropic data
and activity coefficients at infinite dilution for the system
pentane-acetone at 373K, 398K and 423K using modified UNIFAC. The
results are shown graphically in Fig. 5.103.

The vapor pressure constants are given in Appendix A. Experimental data
can be downloaded from the textbook page on www.ddbst.com. For the
calculation by modified UNIFAC ideal vapor phase behavior should be
assumed.

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P05.08
**Mixture Data For the System Acetone - Hexane Using DDBSP **

Using the free Explorer Version of DDB/DDBSP, search for mixture
data for the system acetone – hexane.

a) Plot the
experimental pressure as function of liquid and vapor phase

composition
together with the predictions from UNIFAC, mod. UNIFAC

and PSRK for the
data sets at 318 K and 338 K.

b) How large are the
differences in the azeotropic composition as shown

in the plot of
separation factor vs. composition?

c)
Plot the experimental heat
of mixing data as function of liquid phase

composition together with the
predictions from UNIFAC, mod. UNIFAC

and PSRK for the data sets at 243
K, 253 K, and 298 K. Interpret the linear

part in some of the calculated
heat of mixing curves.

d) Plot the
experimental LLE data together with the results from UNIFAC and

mod.
UNIFAC. What led to the improved results in case of mod. UNIFAC?

Mathcad (2001) - Solution (zip)

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P05.09 **Experimental and
Predicted VLE Data For the Systems CO**_{2}**
- n-Hexane and CO**_{2}** -
Hexadecane Using DDBSP**

Using the free
Explorer Version of DDB/DDBSP, search for mixture data for the systems
CO_{2} – n-hexane and CO_{2} – hexadecane. Plot the
experimental high pressure VLE data (HPV) together with the predictions
from PSRK. Compare the
results to those of VTPR (Fig. 5.99-d) and examine the results for SLE
in the binary mixture CO2 – n-hexane.

DDB Explorer Version demonstration video

P05.10
**Regression of Isobaric VLE Data for the System Methanol -
Toluene **

Calculate the activity coefficients in the system methanol (1)
–toluene (2) from the data measured by
Ocon J., Tojo G.,
Espada L., Anal.Quim., 65, 641-648, 1969 at atmospheric pressure
assuming ideal vapor phase behavior. Try to fit the untypical behavior
of the activity coefficients of methanol as function of composition
using temperature independent g^{E}-model parameters (Wilson,
NRTL, UNIQUAC). Explain why the activity coefficients of methanol show a
maximum at high toluene concentration.

The vapor pressure constants are given in Appendix A. Experimental data
as well as molar volumes, r and q values can be downloaded from the
textbook page on www.ddbst.com. For the calculation, ideal vapor phase
behavior should be assumed.

auxiliary data download
(xlsx)

Mathcad (2001) - Solution (zip)

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P05.11 **
Prediction of Henry Constants for Different Gases in Methanol Using PSRK
and VTPR **

Predict the Henry constants of methane, carbon dioxide and
hydrogen sulfide in methanol in the temperature range -50 – 200 °C with
the help of the group contribution methods PSRK and VTPR.

Compare the predicted Henry constants with experimental values from the
textbook page on www.ddbst.com.

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P05.12
**Prediction of Solubilities at
Different Partial Pressures and for Different Gases in Methanol Using
PSRK and VTPR
**
Predict the solubility of methane, carbon dioxide and hydrogen
sulfide in methanol at a temperature of
30°C for a partial pressure of 5, 10 and 20 bar using the
PSRK and VTPR group contribution equations of state. Compare the results
with the solubility obtained using Henry’s law and the Henry constants
predicted in problem P05.11.

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P05.13
**Retrieval, Visualization, Prediction and Regression of Data For
Subsystems of the System Methanol – Methane – Carbon Dioxide Using DDBSP
**

In the free DDBSP Explorer Edition, search for data for all
subsystems of the system methanol – methane – carbon dioxide.

a)
Compare the available gas solubility data
with the results of the PSRK

method via the data prediction option in
DDBSP.

b)
Plot the available high pressure VLE data
(HPV) for the system methanol

– carbon dioxide together with the
predicted curve using the PSRK method.

Examine and familiarize yourself
with the different graphical representations.

c)
Regress the dataset 2256 using the
Soave-Redlich-Kwong equation of state

with the quadratic mixing rule and
a g^{E} mixing rule with activity coefficient

calculation via
the UNIQUAC model. Explain the differences.

DDB Explorer Version demonstration video

P05.14
**Solubility of Benzene in Water from LLE Data and **
**Activity Coefficients at Infinite Dilution Using DDBSP**

In the free DDBSP Explorer Edition, search for all mixture data
for the system benzene – water. Calculate the solubility of benzene in
water from the experimental activity coefficients at infinite dilution
and compare the results to the experimental LLE data.

DDB Explorer Version demonstration video

P05.15
**Azeotropic Points in Binary Systems Using the Regular
Solution Theory, UNIFAC and Modified UNIFAC **

Examine with the help of the regular solution theory, UNIFAC and
modified UNIFAC if the binary systems benzene – cyclohexane and benzene
– n-hexane show an azeotropic point at 80 °C. In case of the regular
solution theory, calculate the solubility parameter from the saturated
liquid density and the heat of vaporization using Eq. 5.70. All required
data are given in Appendix A, H and I.

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