Problems and Solutions
Chapter 8
Solid-Liquid Equilibria

Textbook Examples:

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08.01           Solubility of Anthracene and Phenanthrene in Benzene

Mathcad (2001) - Solution (zip)
Mathcad (2001) - Solution as XPS

08.02           SLE of Different Xylenes in Benzene

Mathcad (2001) - Solution (zip)
Mathcad (2001) - Solution as XPS

08.03           SLE of Benzene - Ethanol Using UNIQUAC

Mathcad (2001) - Solution (zip)
Mathcad (2001) - Solution as XPS

08.04           SLE in the Ternary Mixture of o-, m- and p-Xylene

Mathcad (2001) - Solution (zip)
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08.05           SLE of the Eutectic System CCl4 - n-Octane With Solid Phase Transition

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08.06           Ideal and Real Solubility of Naphthalene in the Mixture Ethanol - Isooctane

Mathcad (2001) - Solution (zip)
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08.07           Cryoscopic Constant of Water and Naphthalene

no Mathcad solution required

08.08           SLE of the Non-Eutectic System Anthracene – Phenanthrene

Mathcad (2001) - Solution (zip)
Mathcad (2001) - Solution as XPS

08.09           SLE of the System D-Carvoxime - L-Carvoxime With a Congruent Melting Point

Mathcad (2001) - Solution (zip)
Mathcad (2001) - Solution as XPS

08.10           SLE of the Non-Eutectic Mixture Diphenylacetylene - N,N-Diphenylhydrazine

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08.11           SLE of the System CCl4 - p-Xylene With a 1:1 Adduct

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08.12           Ideal and Real Solubility of NaCl, KCl und NH4Cl in Water (LIQUAC)

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Additional Problems:

P08.01        Solubility of Anthracene and Phenanthrene in Benzene and Ethanol (Ideal and Modified UNIFAC)

Calculate the solubility of the isomeric compounds anthracene and phenanthrene in benzene and ethanol at 25 °C assuming ideal behavior and using the group contribution method modified UNIFAC.
       
Pure component properties:
       
 Compare the calculated results with the solubilities measured at 25°C:
       

Mathcad (2001) - Solution (zip)
Mathcad (2001) - Solution as XPS

P08.02        Cryoscopic Constants of Benzene and Camphor 

Calculate the cryoscopic constants of benzene and camphor using the following pure component data:
         

Mathcad (2001) - Solution (zip)
Mathcad (2001) - Solution as XPS

P08.03        Freezing Point Depression of Naphthalene Using the Cryoscopic Constant

Calculate the freezing point depression of naphthalene for the case that 0.2 g of benzene is added to 50 g naphthalene. (Kcry,naphthalene = 6.96 K kg/mol, M = 128.173 g/mol)

Mathcad (2001) - Solution (zip)
Mathcad (2001) - Solution as XPS

P08.04        Molar Mass from Freezing Point Depression 

Calculate the molar mass of an unknown component which leads to a freezing point depression of 0.223 K of naphthalene, when 0.25 g of the unknown compound is added to 100 g naphthalene. (Kcry,naphthalene = 6.96 K kg/mol)

Mathcad (2001) - Solution (zip)
Mathcad (2001) - Solution as XPS

P08.05       Mutual Solubility of Two Isomeric Xylenes
 
Calculate the solubility of m-xylene (1) in p-xylene (2) and p-xylene (1) in m-xylene (2) at a temperature of 225 K.

Pure component properties:
         

Mathcad (2001) - Solution (zip)
Mathcad (2001) - Solution as XPS

P08.06        SLE of Eutectic Mixtures Using Ideal Behavior and Modified UNIFAC  

Calculate the SLE diagram for the following binary eutectic systems 1,2,3-trichlorobenzene  – n-decane and 1,2,4-trichlorobenzene  – n-tetradecane assuming
        a) ideal behavior
        b) taking into account the real behavior using modified UNIFAC
Compare the results with the published data that can be downloaded from the textbook page on www.ddbst.com.

Pure component properties:
       

Mathcad (2001) - Solution (zip)
Mathcad (2001) - Solution as XPS

P08.07       SLE of a System With 1:1 Compound Formation Assuming Ideal Behavior  

Calculate the SLE behavior of the system p-toluidine-phenol with 1:1 compound formation assuming ideal behavior, where the melting point and enthalpy of fusion of the 1:1 compound should be adjusted to get a reliable description of the SLE behavior. Published data can be downloaded from the textbook page on www.ddbst.com.

Pure component properties: 
       

Mathcad (2001) - Solution (zip)
Mathcad (2001) - Solution as XPS

P08.08        Solid CO2 Solubility in Propane  Using PSRK and VTPR

Calculate the solubility of solid carbon dioxide in propane with the help of the group contribution equations of state PSRK and VTPR assuming simple eutectic behavior. Compare the results with the results assuming ideal behavior and the experimental data that can be downloaded from the textbook page on www.ddbst.com. All required parameters can be found in Appendix A.

Mathcad (2001) - Solution (zip)
Mathcad (2001) - Solution as XPS

P08.09        Enthalpy of Fusion from Solubility Data 

Estimate the enthalpy of fusion of benzene (1) by regressing the following solubility data of benzene in toluene assuming ideal (g1 = 1) and simple eutectic behavior.
        

Mathcad (2001) - Solution (zip)
Mathcad (2001) - Solution as XPS

P08.10        SLE of Eutectic and Ideal Ternary Mixture (Xylenes)
 
Determine the solid-liquid equilibrium temperature of the ideal ternary system m-xylene (1) - o-xylene (2) - p-xylene (3) for a composition of x1 = 0.1 and x2 = 0.1 with the help of the melting temperatures and enthalpies of fusion given in Example 8.4 in the textbook. Which component will crystallize?

Mathcad (2001) - Solution (zip)
Mathcad (2001) - Solution as XPS

P08.11        Eutectic Inside Miscibility Gap Possible?
 
Is it, at least theoretically, possible that a eutectic binary mixture with liquid-liquid immiscibility shows a eutectic composition inside the miscibility gap?
solution solution video(large), (medium), (small)

P08.12        Regression and Prediction of SLE in DDB/DDBSP

In the free DDBSP Explorer Version, search for solid-liquid equilibrium data for the mixture 2-propanol – benzene. Regress both datasets simultaneously using the Wilson, NRTL and UNIQUAC model. Compare the performance of the three models. Compare the data to the results of the predictive methods UNIFAC, mod. UNIFAC and PSRK. Examine the different graphical representations.

solution solution video(large), (medium), (small)

P08.13       SLE of Sucrose-Water Taking Into Account the Difference in Solid and Liquid Heat Capacity  

For the calculation of the solubility of sucrose in water Peres and Macedo (A.M. Peres, E.A. Macedo, Fluid Phase Equilib. 123 (1996), p. 71-95) proposed the following physical property parameters: 
       
The solubility of sucrose in water at 25°C is 2.0741  per g water corresponding to a sucrose mole fraction of 0.09842. Calculate the activity coefficient of sucrose in water at 25°C at this concentration with and without taking into account the heat capacity difference between subcooled liquid and solid sucrose.

Mathcad (2001) - Solution (zip)
Mathcad (2001) - Solution as XPS

P08.14        Vapor Pressures of Liquid and Solid Non-Eutectic Mixtures 

The vapor pressures of liquid anthracene and phenanthrene can be described by the Antoine equation using the Antoine parameters given below. Calculate the vapor-liquid-solid equilibrium (VLSE) along the solid-liquid saturation curve assuming ideal mixture behavior in the liquid phase. Melting points and heats of fusion of both components are given in Example P08.01 above. Compare the vapor-liquid separation factors to those of an isothermal VLE data set at 220°C (calculate assuming ideal liquid mixture behavior).
         

Mathcad (2001) - Solution (zip)
Mathcad (2001) - Solution as XPS