Definition of Fugacity

The definition of fugacity is completed by setting the ideal gas state fugacity of pure species / equal to its pressure ... 

The definition of fugacity of a species in solution is parallel to the definition of pure species fugacity. Equation 154 is analogous to the ideal gas expression ... 

Equation (10.34) takes cognizance of only one part of the definition of fugacity. The second part of the definition states that although / approaches zero as P approaches zero, the ratio//P approaches one. Hence, this ratio might be integrable to zero pressure. 

As the mixture approaches ideality as the total pressure approaches zero, Equation (10.81) should approach Equation (10.17). The second part of the definition of fugacity for a gaseous component, which is analogous to Equation (10.24), is... 

It also follows from Equation 1.20 and the definition of fugacity and fugacity coefficient that for ideal solutions 0 = (J) and... 

In the general case, the definitions of fugacity coefficient and activity coefficient... 

Since the system pressure is not, in general, equal to the vapor pressure, the effect of pressure on the fugacity of the liquid must be taken into account in calculating yjT. Using the basic definition of fugacity, is calculated by carrying out the integration over two pressure steps from zero pressure to the vapor pressure and from the vapor pressure to the system pressure ... 

Equation (11.9) is also useful in providing a one-equation definition of fugacity, rather than the two-equation one we gave above. Substituting (RT/P — 1 ) for a and rearranging, we have... 

This is the equation given by Tunell in his classic paper on fugacity (1931), in which he points out some difficulties with the definition as we have presented it, and shows that equation (11.10) is preferable as a definition of fugacity from a mathematical point of view. Our presentation, which follov s the original one by Lewis and Randell (1923), seems preferable from a pedagogical point of view. 

It is important to see that this is a simple generalization of (11.16), and hence a direct result of the definition of fugacity. We novk define the activity of constituent i as... 

For any component i of a multicomponent, multiphase system, derive (4-12), the equality of fugacity, from (4-8), the equality of chemical potential, and (4-11), the definition of fugacity. 

Equilibrium Composition of Nonideal Gases. In order to provide equations which would be useful for all substances, Lpwis and RandalP defined a term, fugacity. This is an arbitrarily defined term that may be substituted for pressure in the preceding equation and which will make it applicable for all substwces. The mathematical definition of fugacity / is... 

The fugacity is a property, created by G. N. Lewis, to provide an alternative to the chemical potential [8]. Conceptually, fugacity offers no advantage over the chemical potential, but it does offer computational advantages, particularly for mixtures. The definition of fugacity is motivated by the response of the chemical potential in an ideal gas when the state is changed isothermally. For an ideal-gas mixture, that response is derived from (4.1.44) and found to be... 

In this subsection we introduce a ratio measure that indicates how the fugacity of a real substance deviates from that of an ideal gas. As the reference state, we choose the ideal-gas mixture at the same temperature, pressure, and composition as our real mixture. Then, on integrating the definition of fugacity (4.3.8) from the ideal-gas state to the real state, we obtain an algebraic form analogous to (4.3.12) that is, we find... 

To obtain expressions for the partial molar properties of ideal solutions, we first determine the chemical potential. Using the ideal-solution fugacity (5.1.6) in the integrated definition of fugacity (4.3.12) we find... 

Consider the algebraic form (4.3.12) that results from an isothermal integration of the first part of the definition of fugacity. 

Equation (7.2.27) may also be expressed in terms of fugadty to do so, we first integrate the definition of fugacity (4.3.10), at fixed T, from the P-phase to the a-phase. The result is analogous to the algebraic form (4.3.12),... 

The first equality is the definition of Ki, given in eq. fS.g) the second equality follows from the definition of fugacity, eq. (10.ir). Using the Kfactors, the mole fractions in the vapor are... 

Another relationship is needed to complete the definition of fugacity ... 

This equation can be written in terms of activity coefficients using the definition of fugacities as described in Section 1.3.3 ... 

Substituting the definition of fugacity (Eq. 7.1) for gj, three times we find... 

Definitions of Fugacity Capacities and Partition Coefficients Used in the Soil Compartment Model ... 

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