Summary

We began this chapter by introducing the need for Gibbs energy to calculate phase equilibria in pure fluids because it is a natural function of temperature and pressure. We also introduced fugacity, which is a convenient property to use instead of Gibbs energy because it resembles the vapor pressure more closely. We also showed that the fugacity coefficient is directly related to the deviation of a fluid from ideal gas behavior, much like a departure function (Eqns. 9.23 and 9.24). This principle of characterization of non-ideality extends into the next chapter where we consider non-idealities of mixtures. In fact, much of the pedagogy presented in this chapter finds its significance in the following chapters, where the phase equilibria of mixtures become much more complex.

Methods for calculating fugacities were introduced using charts, equations of state, and derivative manipulations. (In the homework problems, we offer illustration of how tables may also be used.) Liquids and solids were considered in addition to gases, and the Poynting correction was introduced for calculating the effect of pressure on condensed phases. These pure component methods are summarized in Table 9.1, and they are applied often in the analysis of mixtures. Skills in their application must be kept ready throughout the following chapters.

Table 9.1. Techniques for Calculation Pure Component Fugacities

A critical concept in this chapter is that when multiple EOS roots exist from a process calculation, the stable root has a lower Gibbs energy or lower fugacity. We also provided methods to find saturation conditions for pure fluids.

Important Equations

Eqns. 9.3 and 9.27 basically state that equilibrium occurs when fugacity in each phase is equal. This is a general principle that can be applied to components in mixtures and forms the basis for phase equilibrium computations in mixtures. Eqn. 9.11 is a special form of Eqn. 9.6 that is particularly convenient for estimating the vapor pressure over wide ranges of temperature. It may not be as precise as the Antoine equation over a narrow temperature range, but it is less likely to lead to a drastic error when extrapolation is necessary. Nevertheless, Eqn. 9.11 is not a panacea. When you are faced with phase equilibrium problems other than vapor pressure, like solid-liquid (e.g., melting ice) or solid-vapor (e.g., dry ice), you must start with Eqn. 9.6 and re-derive the final equations subject to relevant assumptions for the problem of interest.

Fugacity is commonly calculated by Eqns. 9.28(Gases), 9.29(Ideal gases), 9.41(Liquids), and 9.43(Solids), and is dependent on the calculation of the fugacity coefficient. Fugacity is particularly helpful in identifying the stable root.