Author: admin
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Excess Properties
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…
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Deriving Modified Raoult’s Law
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…
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Calculations Using Activity Coefficients
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…
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Modified Raoult’s Law and Excess Gibbs Energy
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…
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Homework Problems
10.1. For a separations process it is necessary to determine the VLE compositions of a mixture of ethyl bromide and n-heptane at 30°C. At this temperature the vapor pressure of pure ethyl bromide is 0.7569 bar, and the vapor pressure of pure n-heptane is 0.0773 bar. Calculate the bubble pressure and the composition of the vapor in equilibrium…
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Practice Problems
P10.1. The stream from a gas well consists of 90 mol% methane, 5 mol% ethane, 3 mol% propane, and 2 mol% n-butane. This stream is flashed isothermally at 233 K and 70 bar. Use the shortcut K-ratio method to estimate the L/F fraction and liquid and vapor compositions. (ANS. L/F = 0.181) P10.2. An equimolar mixture of n-butane and n-hexane at pressure P is isothermally flashed at…
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Summary
The concepts in this chapter are relatively simple but far-reaching. A simple extension of the chain rule to multicomponent systems led to the equilibrium constraint for multicomponent multiphase equilibria. A simple application of the entropy of mixing derived in Chapter 4 led to the ideal solution model, Gibbs energy for a component in a mixture, and fugacity…
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Activity Coefficient and Fugacity Coefficient Approaches
The discussion in Sections 10.8–10.11 sets the stage for the next few chapters. The principles discussed here form the basis for these chapters and a thorough understanding facilitates rapid understanding of the extensions. There are two main approaches to modeling nonideal fluids. They differ in the way that they treat the fugacities in the vapor and liquid…
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The Ideal Solution Approximation and Raoult’s Law
By our equilibrium constraint, By our ideal solution approximation in both phases, the equilibrium criteria becomes Now we need to substitute the expressions for fiV and fiL that we developed in Chapter 9. The fugacity of the pure vapor comes from Eqn. 9.25: The fugacity of the liquid comes from Eqn. 9.39: Combining Eqns. 10.70–10.72, Writing in terms of the Ki ratio, Note: at reasonably low…
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Mixture Properties for Ideal Solutions
Ideal solutions are similar to ideal-gas mixtures, but they to not follow the ideal-gas law. The internal energy and enthalpy for ideal solutions were introduced in Section 3.5. Since these properties are additive, the partial molar properties are equal to the pure component properties, As for the entropy change of mixing, the loss of order due…