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The theories developed in this chapter are based on the local composition concept. Similar to models developed in the previous chapter, accurate representation of highly nonideal solutions requires the introduction of at least two adjustable parameters. These adjustable parameters permit us to compensate for our ignorance in a systematic fashion. By determining reasonable values for…

As discussed during the development of quadratic mixing rules, there comes a point at which the assumption of random mixing cannot completely explain the nonidealities of the solution. Local compositions are examples of nonrandomness. The popularity of local composition models like Wilson’s equation or UNIFAC means that we need to develop some appreciation of the…

In principle, all electronic and molecular interactions are described by quantum mechanics, so you may wonder why we have not considered computing mixture properties from this fundamental approach. In practice, two considerations limit the feasibility of this approach. First, quantum mechanical computations tend to be time consuming. Precise computations can require days for a single…

UNIFAC13 (short for UNIversal Functional Activity Coefficient model) is an extension of UNIQUAC with no user-adjustable parameters to fit to experimental data. Instead, all of the adjustable parameters have been characterized by the developers of the model based on group contributions that correlate the data in a very large database. The assumptions regarding coordination numbers, and…

UNIQUAC5 (short for UNIversal QUAsi Chemical model) builds on the work of Wilson by making three primary refinements. First, the temperature dependence of Ωij is modified to depend on surface areas rather than volumes, based on the hypothesis that the interaction energies that determine local compositions are dependent on the relative surface areas of the molecules. If…

The NRTL model4 (short for Non-Random Two Liquid) equates UE from Eqn. 13.16 directly to GE, ignoring the proper thermodynamic integration. At the same time, it introduces a third binary parameter that generates an extremely flexible functional form for fitting activity coefficients.  See Actcoeff.xlsx, worksheet NRTL MATLAB: nrtl.m For a binary mixture, the activity equations become For a binary mixture, the…

Wilson2 made a bold assumption regarding the temperature dependence of Ωij. Wilson’s original parameter used in the literature is Λji, but it is related to Ωij in a very direct way. Wilson assumes3 (note: Λii = Λjj = 1, and Aij ≠ Aji even though εij = εji), and integration with respect to T becomes very simple. Assuming Nc,j = 2 for all j at all ρ, A convenient simplifying assumption…

Now that we see the capabilities of the predictions, we have motivation to understand the model. One of the major assumptions of van der Waals mixing was that the mixture interactions were independent of each other such that quadratic mixing rules would provide reasonable approximations as shown in Eqn. 12.3 on page 467. But in some cases, like…