### Textbook Examples:

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**05.01 Poynting factor for Ethanol and Water at Various Pressure**

**Differences (p. 188)**

**05.02 Fugacity coefficients and Real Gas Factor for the System**

**Ethanol-Water Using the Virial Equation (p. 188)**

**05.03 Activity Coefficients from Experimental xyPT-Data (p. 192)
**Mathcad (2001) – Solution (zip)

Mathcad (2001) – Solution as XPS

**05.04 Construct a Diagram with g ^{E}, h^{E} and –Ts^{E} (p. 197)**Mathcad (2001) – Solution (zip)

Mathcad (2001) – Solution as XPS

**05.05 Temperature Dependence of the Activity Coefficients (p. 199)
**Mathcad (2001) – Solution (zip)

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**05.06 Activity Coefficients at Infinite Dilution at Different Temperatures Using the Partial Molar Excess Enthalpy at Infinite Dilution (p. 200)**

**05.07 Excess Volume of the Liquid Mixture Ethanol – Water (p. 201)**

**05.08 Activity Coefficient of the Monomer in a Polymer Using the Athermal Flory-Huggins Equation (p. 205)
**Mathcad (2001) – Solution (zip)

Mathcad (2001) – Solution as XPS

**05.09 Compare Experimental VLE to Wilson Equation Results (p. 207)**

Mathcad (2001) – Solution (zip)

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**05.10 Thermodynamic Consistency Using the Area Test (p. 219)**

Mathcad (2001) – Solution (zip)

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**05.11 VLE of N2 – CH4 Using SRK (p. 238)**

Mathcad (2001) – Solution (zip)

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**05.12 Azeotropic Points of the System Acetone – Methanol (p. 245)**

Mathcad (2001) – Solution (zip)

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**05.13 Estimate the Temperature Dependence of the Azeotropic Composition**

**Using the Heat of Vaporization (p. 247)**

**05.14 Henry Constant for CO2 from Phase Equilibrium Data (p. 260)**

Mathcad (2001) – Solution (zip)

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**05.16 Henry Constant for Methane in Benzene at 60 °C with the Help of the Soave-Redlich-Kwong Equation of State (p. 262)**

Mathcad (2001) – Solution (zip)

Mathcad (2001) – Solution as XPS

**05.17 Henry Constant for Methane in Benzene at 60 °C Using the Method**

**of Prausnitz and Shair (p. 264)
**Mathcad (2001) – Solution (zip)

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**05.18 VLLE of n-Butanol – Water at 50°C Using UNIQUAC (p. 271)
**Mathcad (2001) – Solution (zip)

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**05.19 Liquid-Liquid Equilibrium for the System Water – Ethanol – Benzene – K-Factor Method UNIQUAC (p. 275)**

Mathcad (2001) – Solution (zip)

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**05.21 VLE of Hexane-Butanone-2 Via UNIFAC (p. 286)
**Mathcad (2001) – Solution (zip) – step by step

Mathcad (2001) – Solution as XPS- step by step

Mathcad (2001) – Solution (zip) – as function

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**05.22 Liquid-Liquid Solubility for Alkane-Water from Empirical Correlation (p. 302)**

### 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.

Mathcad (2001) – Solution (zip) (Wilson)

Mathcad (2001) – Solution as XPS

Mathcad (2001) – Solution (zip) (NRTL)

Mathcad (2001) – Solution as XPS

Mathcad (2001) – Solution (zip) (UNIQUAC)

Mathcad (2001) – Solution as XPS

**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

Mathcad (2001) – Solution (zip)

Mathcad (2001) – Solution as XPS

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:

Mathcad (2001) – Solution (zip)

Mathcad (2001) – Solution as XPS

VTPR:

Mathcad (2001) – Solution (zip)

Mathcad (2001) – Solution as XPS

**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: (see solution file)

Mathcad (2001) – Solution (zip)

Mathcad (2001) – Solution as XPS

**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.

Mathcad (2001) – Solution (zip)

Mathcad (2001) – Solution as XPS

**P05.06**** 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.

Mathcad (2001) – Solution (zip)

Mathcad (2001) – Solution as XPS

**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 http://www.ddbst.com. For the calculation by modified UNIFAC ideal vapor phase behavior should be assumed.

Mathcad (2001) – Solution (zip)

Mathcad (2001) – Solution as XPS

**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)

Mathcad (2001) – Solution as XPS

**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 http://www.ddbst.com. For the calculation, ideal vapor phase behavior should be assumed.

auxiliary data download (xlsx)

Mathcad (2001) – Solution (zip)

Mathcad (2001) – Solution as XPS

**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.

auxiliary data download

Mathcad (2001) – Solution (zip)

Mathcad (2001) – Solution as XPS

**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.

Mathcad (2001) – Solution (zip)

Mathcad (2001) – Solution as XPS

**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.

Mathcad (2001) – Solution (zip)

Mathcad (2001) – Solution as XPS