Author: admin
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Stability and Excess Gibbs Energy
Expressions for activity coefficients are the same for LLE as they are for VLE. The difference is that multiple liquid compositions can give the same activities or total pressure at a given temperature. This behavior is implied in Fig. 11.10, where we commented that the calculated lines indicate LLE. The time has come to analyze why…
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The Onset of Liquid-Liquid Instability
Our common experience tells us that oil and water do not mix completely, even though both are liquids. If we consider equilibria between the two liquid phases, we can label one phase α and the other β. For such a system we can quickly show that the equilibrium compositions are given by Equations for LLE.…
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Homework Problems
13.1. Show that Wilson’s equation reduces to Flory’s equation when Aij = Aji = 0. Further, show that it reduces to an ideal solution if the energy parameters are zero, and the molecules are the same size. 13.2. The actone(1) + chloroform(2) system has an azeotrope at x1 = 0.38, 248 mmHg, and 35.17°C. Fit the Wilson equation, and predict the P-x-y diagram. 13.3. Model the behavior of…
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Practice Problems
P13.1. The following lattice contains x’s, o’s, and void spaces. The coordination number of each cell is 8. Estimate the local composition (Xxo) and the parameter Ωox based on rows and columns away from the edges. (ANS. 0.68,1.47)
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Important Equations
The UNIFAC method receives broad application throughout thermodynamic modeling. In fact, occasional applications of UNIFAC may be too broad in the sense that experimental data specific to a particular binary system are ignored and UNIFAC predictions are not validated with actual measurements. A literature search should be conducted for experimental data pertaining to every molecular interaction in…
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Summary
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…
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The Molecular Basis of Solution Models
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…
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COSMO-RS Methods
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…
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UNIFAC
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…
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UNIQUAC
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…