Fugacity concept

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... 

Simple models are used to Identify the dominant fate or transport path of a material near the terrestrial-atmospheric Interface. The models are based on partitioning and fugacity concepts as well as first-order transformation kinetics and second-order transport kinetics. Along with a consideration of the chemical and biological transformations, this approach determines if the material is likely to volatilize rapidly, leach downward, or move up and down in the soil profile in response to precipitation and evapotranspiration. This determination can be useful for preliminary risk assessments or for choosing the appropriate more complete terrestrial and atmospheric models for a study of environmental fate. The models are illustrated using a set of pesticides with widely different behavior patterns. 

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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