Mixing excess entropy, nonideal mixed

Perhaps the most important term in Eq. (5.2-3) is the liquid-phase activity coefficient, and mathods for its prediction have been developed in many forms and by many workers. For binery systems die Van Laar [Eq. (1.4-18)]. Wilson [Eq. (1.4-23)]. NRTL (Eq. (1.4-27)], and UNIQUAC [Eq. (1.4-3 )] relationships are useful for predicting liquid-phase nonidealities, but they require some experimental data. When no data are available, and an approximate nonideality correction will suffice, the UNiFAC approach Eq-(1.4-31)], which utilizes functional group contributions, may be used. For special cases Involving regular solutions (no excess entropy of mixing), the Scatchard-Hiidebmod mathod provides liquid-phase activity coefficients based on easily obtained pane-component properties. 

The other limiting case of nonideal solutions is when AGe —TASe, in which case the deviation from ideality is mostly due to the excess entropy of mixing AHe 0. In this case, using (8.4.17) in... 

SOLUTION In this example, we assume that all the nonideality is associated with a difference in energetics between the species in the mixture and the pure species that is, the excess entropy is zero. This assumption is valid for species of roughly the same size. Let s consider the difference in energetics between a andfc in a mixture vs. a andb as pure species. Figure E7.9A illustrates the possible interactions in the mixture and of pure a and pure b. Pure a and b exhibit only a-a interactions and h-h interactions, respectively. The mixture contains not only these like a-a and h-h interactions but also unlike a-h interactions. In fact, when species a and h are mixed, we can view the process in terms of intermolecular interactions. Some a-a interactions of pure a are replaced by a-h interactions, while some h-h interactions of pure h are also replaced by a-h interactions. To quantify the difference in energy of the mixture relative to the pure species and, therefore, the nonideality of the mixture, we compare the magnitude of the interactions in the mixture with those that existed as pure species. 

One of the simplest and most widely used models for the thermodynamic characterization of a nonideal solution is the so-called simple solution model . In this model the excess free energy of mixing, accounting for deviations from the ideal entropy of mixing, is taken as an expression that is proportional to the product of the mole fractions of the constituents. 

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