Fugacity approach

The heart of the question of non-ideality deals with the determination of the distribution of the respective system components between the liquid and gaseous phases. The concepts of fugacity and activity are fundamental to the interpretation of the non-ideal systems. For a pure ideal gas the fugacity is equal to the pressure, and for a component, i, in a mixture of ideal gases it is equal to its partial pressure yjP, where P is the system pressure. As the system pressure approaches zero, the fugacity approaches ideal. For many systems the deviations from unity are minor at system pressures less than 25 psig. 

Whereas the fugacity approach was used by Mackay for the computation of mass flows and the concentration levels, the SimpleBox adopt the concentration-based piston velocity type mass transfer coefficients (ms-1). This is, mainly, because most scientific papers express the mass transfer in these terms, rather than in terms of the fugacity-based conductivity type coefficients (mol h 1 Pa-1). Furthermore, the transfer and transformation phenomena are treated as simple pseudo first-order processes, similar to Mackay models. 

Mainly, the available models have been developed based on the fugacity approach, which use the fugacity as surrogate of concentration, for the compilation and solution of mass-balance equations involved in the description of chemicals fate. However, a new... 

Mackay D (1991) Multimedia environmental models the fugacity approach. Lewis Publishers, Chelsea... 

Mackay D (2001) Multimedia environmental models - the fugacity approach, 2nd edn. CRC Press/Taylor Francis Group, Boca Raton... 

Lohmann U, Roeckner E (1996) Design and performance of a new cloud microphysics scheme developed for the ECHAM4 general circulation model. Clim Dyn 12 557-572 Mackay D (1991) Multimedia Environmental Models The Fugacity Approach. Lewis Publishers, Chelsea, MI, USA... 

Paterson and Mackay (1985), Mackay and Paterson (1990, 1991), and a recent text (Mackay 2001). Only the salient features are presented here. Three evaluations are completed for each chemical, namely the Level I, II and III fugacity calculations. These calculations can also be done in concentration format instead of fugacity, but for this type of evaluation the fugacity approach is simpler and more instructive. The mass balance models of the types described below can be downloaded for the web site www.trentu.ca/cemc... 

Mackay, D. (2001) Multimedia Environmental Models The Fugacity Approach. 2nd edition, Lewis Publishers, CRC Press, Boca Raton, FL. 

Mackay, D., Shiu, W.Y. (1990) Physical-chemical properties and fate of volatile organic compounds an application of the fugacity approach. In Significance and Treatment of Volatile Organic Compounds in Water Supplies. Ram, N.M., Christman, R.F., Cantor, K.P., Eds., pp. 183-203, Lewis Publishers, Chelsea, Michigan. 

That is, as the pressure approaches zero, the fugacity approaches the pressure. Figure 10.5 indicates the relationship between P and/for ideal and real gases. The standard state for a real gas is chosen as the state at which the fugacity is equal to 0.1 MPa, 1 bar, along a line extrapolated from values off at low pressure, as indicated in Figure 10.5. The standard state for a real gas is then a hypothetical 0.1 MPa standard state. 

The integration constant I is chosen so that the fugacity approaches the pressure as the pressure approaches zero. It is clear that for an ideal gas the fugacity is numerically equal to the pressure at all pressures. 

Water solubility and vapor pressures of PFOS and PFOA are given in Table 2. These data were obtained from products that were not refined and as a result may contain more than one PFA such that these data may not be representative of the pure compounds, especially in environmental media. Due to the lack of accurate information on the physico-chemical properties, accurate prediction of the environmental fate and transport of most perfluoroalkyl substances has not yet been possible. The prediction of the distribution and ultimate fates of perfluoroalkyl substances is further complicated by their hydrophobic and lipophobic properties, such that the fugacity approach that has been useful in describing the environmental fates of organochlorines is less useful for describing the environmental fate of PFAs and their precursors. The bulk of the available physical and chemical information is for PFOS... 

D. Mackay, Multimedia Environmental Models-The Fugacity Approach, Lewis, 1991. 

Mackay, D. (1991) Multimedia Environmental Models the Fugacity Approach, Ujwis, Chelsea, MI. 

More simple models, requiring only an approximate description of the main driving forces as input data, produce less precise results but their versatility allows their application to relatively non-homogeneous areas and, therefore, on a larger scale. Simple runoff models derived from the original fugacity approach , were developed at the University of Toronto by Mackay and co-workers, but too technical to be described here. (Mackay,... 

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