Test of the Regular Solution Model

Compare the regular solution theory predictions for the activity coefficients of the benzene–2,2,4-trimethyl pentane mixture with the experimental data given in Illustration 9.5-1.

Question

Test of the Regular Solution Model

Compare the regular solution theory predictions for the activity coefficients of the benzene–2,2,4-trimethyl pentane mixture with the experimental data given in Illustration 9.5-1.

Accepted Answer

From Table 9.6-1 we have [latex]\underline{V}^{ L }=89 cc / mol ext { and } \delta=9.2( cal / cc )^{1 / 2}[/latex] for benzene. The parameters for 2,2,4-trimethyl pentane are not given. However, the molar volume of this compound is approximately 165 cc/mol, and the solubility parameter can be estimated from

[latex]\delta=\left(\frac{\Delta_{ vap } \underline{U}}{\underline{V}^{ L }} ight)^{1 / 2}=\left(\frac{\Delta_{ vap } \underline{H}-R T}{\underline{V}^{ L }} ight)^{1 / 2}[/latex]

where in the numerator we have neglected the liquid molar volume with respect to that of the vapor, and further assumed ideal vapor-phase behavior. Using the value of [latex]\Delta_{ ext {vap }} \underline{H}[/latex] found in Illustration 7.7-1, we obtain [latex]\delta=6.93( cal / cc )^{1 / 2}[/latex].

Our predictions for the activity coefficients, together with the experimental data, are plotted in Fig. 9.6-1. It is evident that although the regular solution theory prediction leads to activity coefficient behavior that is qualitatively correct, the quantitative agreement in this case is, in fact, poor. This example should serve as a warning that theoretical predictions may not always be accurate and that experimental data are to be preferred.

Table 9.6-1 Molar Liquid Volumes and Solubility Parameters of Some Nonpolar Liquids
	[latex]\underline{V}^{ L }( cc / mol )[/latex]	[latex]\delta( cal / cc )^{1 / 2}[/latex]
Liquefied gases at 90 K
Nitrogen	38.1	5.3
Carbon monoxide	37.1	5.7
Argon	29.0	6.8
Oxygen	28.0	7.2
Methane	35.3	7.4
Carbon tetrafluoride	46.0	8.3
Ethane	45.7	9.5
Liquid solvents at 25°C
Perfluoro-n-heptane	226	6.0
Neopentane	122	6.2
Isopentane	117	6.8
n-Pentane	116	7.1
n-Hexane	132	7.3
1-Hexene	126	7.3
n-Octane	164	7.5
n-Hexadecane	294	8.0
Cyclohexane	109	8.2
Carbon tetrachloride	97	8.6
Ethyl benzene	123	8.8
Toluene	107	8.9
Benzene	89	9.2
Styrene	116	9.3
Tetrachloroethylene	103	9.3
Carbon disulfide	61	10.0
Bromine	51	11.5
Source: J. M. Prausnitz, Molecular Thermodynamics of Fluid-Phase Equilibria. 1969. Reprinted with permission from Prentice-Hall, Englewood Cliffs, N.J. Note: In regular solution theory the solubility parameter has traditionally been given in the units shown. For this reason the traditional units, rather than SI units, appear in this table.

Question 9.6.1: Test of the Regular Solution Model Compare the regular solut...

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