Five Famous Fugacity Formulae

4 we showed the similarities that occur in the fugacity ratios that define the fugacity coefficient, the activity, and the activity coefficient, and in 6.3 those quantities were given physical interpretations. In this section we summarize certain generalized expressions that relate the fugacity to measurables. Many such relations can be written, but only five forms are in common use. 

Fugacity Formula 1. If along an isotherm T, we have a complete Pvx equation of state for our mixture, then we can compute from the definition of the fugacity coefficient (4.3.18). Here we write that definition in the form 

Fugacity Formula 2. If we have, from experiment or correlation, the value of a standard-state fugacity f° at the mixture temperature and pressure, so we can use the Lewis-Randall rule (5.1.5), then we recast FFF 1 into an alternative form. First multiply and divide (6.4.1) by the known standard-state fugacity f°, 

This activity coefficient is simply related to the excess chemical potential (5.4.10). 

Professor M. M. Abbott originated this name for the following useful forms for fugacity [5]. 

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Values for fugacities are nearly always calculated using one of the five famous fugacity formulae dted in 6.4. Again, these five formulae represent options that we can exploit in solving all kinds of phase separation and chemical reaction problems. The commonly used procedxues for attacking such problems will be developed in Chapter 10, the solution techniques will be described in Chapter 11, and particular examples will be offered in Chapter 12. 

Here Vjy is the stoichiometric coefficient for species i in reaction j and G,- is the chemical potential for component i. To translate (10.3.7) into a computational form, we choose to use fugacities rather than chemical potentials, for then we can exploit the five famous fugacity formulae presented in 6.4. Recall the fugacity is defined in terms of the chemical potential by... 

All phase and reaction equilibrium computations require expressions for the fugaci-ties of all components. The possible expressions are presented in 6.4 as the five famous fugacity formulae (FFF). Here are some general guidelines for choosing from those possibilities. 

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