Author: admin
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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…
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NRTL
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…
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Wilson’s Equation
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…
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Local Composition Theory
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…
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Homework Problems
12.1. The compositions of coexisting phases of ethanol(1) + toluene(2) at 55°C are x1 = 0.7186, and y1 = 0.7431 at P = 307.81 mmHg, as reported by Kretschmer and Wiebe, 1949. J. Amer. Chem. Soc., 71:1793. Estimate the bubble pressure at 55°C and x1 = 0.1, using a. The Scatchard-Hildebrand model with k12 = 0 b. The SSCED model with a default value of k12 c. The SSCED model with k12 matched…
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Practice Problems
P12.1. Acrolein + water exhibits an atmospheric (1 bar) azeotrope at 97.4 wt% acrolein and 52.4°C. a. Determine the values of Aij for the van Laar equation that match this bubble-point pressure at the same liquid and vapor compositions and temperature. (ANS. 2.97, 2.21) (You may use the shortcut vapor pressure equation for acrolein: Tc = 506 K; Pc = 51.6 bar; and…
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Summary
This has been a somewhat theoretical chapter. We have gone through iterations of observation, prediction, testing, and evaluation with several theories (e.g., van Laar, Scatchard-Hildebrand, Flory-Huggins, SSCED, and MOSCED). With each iteration, we have achieved increasing precision and insight. Sulfuric acid and water may react very favorably toward each other (GE << 0), while 2-propanol and…
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Flory-Huggins and van der Waals Theories
We have shown that the contribution to the excess internal energy in the Flory-Huggins theory is identical to that in the Scatchard-Hildebrand theory. We derived the Scatchard-Hildebrand theory from the excess internal energy function of the van der Waals equation on page 468 and 12.3 on page 471. Therefore, any potential difference between the Flory-Huggins theory and the van der…