The Fugacity Concept

Let us recall the basic expression (5.53) for the P dependence of AG under isothermal conditions. For certain purposes, it is convenient to choose a standard state pressure, denoted P°, such that the free energy G = G(P) for any other pressure P is given by 

If the standard state is chosen consistently for all species, the arbitrary choice of P° will cancel out of AGrxn, AGf°[compound], and related free energy changes in chemical reactions. 

Note that the argument v of n(x) must always be a dimensionless number, and this requirement is properly satisfied for the dimensionless ratio P/P° in (5.61) for any choice of standard state. This also remains true for the special choice F° = 1 (in the chosen units), where the denominator of the pressure ratio does not appear explicitly in the equation. 

In effect, activity a is a way of encoding Gibbs free energy of real gases in equations that appear to be of ideal gas form  

We can obtain a more informative expression for fugacity / or fugacity coefficient y in terms of the general virial expansion (Section 2.4.3) 

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The origin of the fugacity concept resides in Eq. (4-72), an equation vahd only for pure species i in the ideal gas state. For a real fluid, an analogous equation is written ... 

In a series of recent papers Q - 4), we have advocated the use of the fugacity concept as an aid to compartmental modeling of chemicals which may be deliberately or inadvertantly discharged into the environment. The use of fugacity instead of concentration may facilitate the formulation and interpretation of environmental models it can simplify the mathematics and permit processes which are quite different in character to be compared... 

Summary. In summary, when modeling with the fugacity concept, all equilibria can be treated by Z values (one for each compartment) and all reaction, advection and transport processes can be treated by D values. The only other quantities requiring definition are compartment volumes and emission rates or initial concentrations. A major advantage is that since all D quantities are in equivalent units they can be compared directly and the dominant processes identified. By converting diverse processes such as volatilization, sediment deposition, fish uptake and stream flow into identical units, their relative importance can be established directly and easily. Further, algebraic manipulation... 

Paterson, S., Mackay, D. (1985) The fugacity concept in environmental modelhng. In The Handbook of Environmental Chemistry. Vol. 2/Part C, Hutzinger, O., Ed., pp. 121-140, Springer-Verlag, Heidelberg, Germany. 

Equation 2.63 is valid for any homogeneous or heterogeneous reaction. The only difference is in the definition of activities. For a species in a perfect gas-phase mixture a = pi/p°, where pi is the partial pressure of species i andp° is the standard pressure (1 bar). For a real gas-phase mixture a =f/p°, where is the fugacity of i. The fugacity concept was developed for the same reason as the activity to extend to real gases the formalism used to describe perfect gas mixtures. In the low total pressure limit (p -> 0), fi = pi. 

Consider a simplified ecosystem consisting of 1010 m3 of air, 7 X 106 m3 of water, and 3.5 m3 of fish. Released into the water is 10 kg of methylene chloride. Predict the equilibrium partitioning of methylene chloride into each phase using the fugacity concept. Assume a BCF of 4.4 liter/kg, a fish density of 1 g/cm3, and a temperature of 25°C. 

The development of the fugacity concept in equations (11.1) to (11.7) is directed toward real gases, using the ideal gas as a model. No mention is made of whether the... 

The fugacity concept was introduced initially to account for the non-ideal behaviour of real gases. Later the concept was generalised to phase equilibrium calculation. Let us go back to the equation describing the variation of Gibbs energy with the pressure at... 

A better perception of the fugacity concept can be obtained by relating it to pressure. Thus, by subtracting the equations (5.77) and (5.78) leads to the expression ... 

Hence, ideal -values can be determined as the ratio of fugacity of the pure components in liquid and vapour phase, and these depend only on T and P. The result is similar with ideal mixtures defined by the Raoult-Dalton law, where Kj = PjlP, P, being the vapour pressure and P the total pressure. A notable difference is that equation (6.4) may be used at high pressures, where the fugacity concept is more suitable. 

For an extensive treatment of the fugacity concept, the reader should refer to references 1,2 and 6. 

The fugacity concept pioneered by Mackay to model phase equilibria and transport in the environment is described in the following ... 

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