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Fitting of the Margules equations to limited data has been discussed in Examples 11.2 and 11.5. Fits to multiple points are preferred, which requires regression of the parameters to optimize the fit. In a few cases, the Gibbs excess function can be rearranged to form the basis for a linear regression. In general, a non-linear regression may be…

Recall from Section 10.7 that azeotropes occur at x=y, where a maximum or minimum appears in all the plots. Also note that the bubble and dew lines do not cross, but they touch at the azeotrope composition. Occasionally when a P-x-y or T-x-y diagram is generated in a Stage III calculation, the diagram can look very odd. The two-parameter fit in Fig. 11.5 was…

Two parameter models provide sufficient flexibility with a balance of relative simplicity to provide successful VLE modeling. Determination of activity for each component permits two parameters to be fitted, and special compositions can be used. Azeotropes The location of an azeotrope is very important for distillation design because it represents a point at which further…

We noted in Example 11.1 a shortcoming in the one-parameter model’s representation of the skewness of experimental excess Gibbs energy. In principle, adjusting both the magnitude and skewness of GE is possible with a two-parameter model equation. The mathematical relations in Sections 11.3–11.5 liberate us to conjecture freely about forms of GE that may fit any given set of VLE data. Based on…

The excess Gibbs energy is  Excess Gibbs energy. where we have added and subtracted the sum of the component Gibbs energies in the second line, and used Eqns. 10.65 and 10.66 in the last line. Let us further examine . Recall that , (Eqn. 10.42). Previously in Eqn. 10.48 we expressed μi relative to a pure component value using a ratio of fugacities. Generalization…

The deviation of a property from its ideal-solution value is called the excess property. For a generic property M, the excess property is given the symbol ME, and ME is the value of the property for the mixture relative to the property for an ideal mixture, ME = M – Mis. Ideal solutions were discussed in Section 10.10. The molar volume of an ideal…

In Chapter 10 we demonstrated that Raoult’s law requires an ideal solution model for the vapor and liquid phases as well as conditions where the fugacity coefficients can be ignored. In Section 11.1 we have shown that a relatively simple function is able to capture a major correction to Raoult’s law, but we have superficially made the connections to…

Once the activity coefficient model’s parameters are known for a given system, the K-ratio can be calculated as a function of composition using Eqn. 11.1. For the one-parameter Margules equation, the activity coefficients are given by Eqn. 11.6. Then the bubble, dew, and flash routines can be executed from Table 10.1 on page 373. Because the activity coefficients depend on xi, the…

In Section 10.7 we demonstrated that deviations from Raoult’s law were manifested by changes in the bubble line and thus characterized positive and negative deviations. With a purely mathematical perspective for modeling the behavior, we could develop a “correction” to Raoult’s law as illustrated in Fig 11.1. Figure 11.1. P-x-y diagram for isopropanol water at 30°C illustrating the…