# Physics:Multimedia fugacity model

Short description: Model for calculating equilibrium partitioning between different phases

Multimedia fugacity model is a model in environmental chemistry that summarizes the processes controlling chemical behavior in environmental media by developing and applying of mathematical statements or "models" of chemical fate.[1]

Most chemicals have the potential to migrate from the medium to medium. Multimedia fugacity models are utilized to study and predict the behavior of chemicals in different environmental compartments.[1][2]

The models are formulated using the concept of fugacity, which was introduced by Gilbert N. Lewis in 1901 as a criterion of equilibrium and convenient method of calculating multimedia equilibrium partitioning. The fugacity of chemicals is a mathematical expression that describes the rates at which chemicals diffuse, or are transported between phases. The transfer rate is proportional to the fugacity difference that exists between the source and destination phases. For building the model, the initial step is to set up a mass balance equation for each phase in question that includes fugacities, concentrations, fluxes and amounts. The important values are the proportionality constant, called fugacity capacity expressed as Z-values (SI unit: mol/m3 Pa) for a variety of media, and transport parameters expressed as D-values (SI unit: mol/Pa h) for processes such as advection, reaction and intermedia transport. The Z-values are calculated using the equilibrium partitioning coefficients of the chemicals, Henry's law constant and other related physical-chemical properties.[1][3]

## Application of models

There are four levels of multimedia fugacity Models applied for prediction of fate and transport of organic chemicals in the multicompartmental environment:[1][4][5][6]

 Level I Closed system in equilibrium Equilibrium between compartments according to thermodynamics assumed (partition coefficients such as KOW, KAW or KS); transformation and active transport not taken into account Level II Open system in equilibrium In addition to level I: continuous emissions and transformation (e.g. biodegradation, photolysis) taken into account Level III Open system in steady state In addition to level II: active transport and compartment-specific emissions taken into account Level IV Open system, non steady state In addition to level III: dynamics of emissions and resulting temporal concentration course taken into account

Depending on the number of phases and complexity of processes different level models are applied. Many of the models apply to steady-state conditions and can be reformulated to describe time-varying conditions by using differential equations. The concept has been used to assess the relative propensity for chemicals to transform from temperate zones and “condense out” at the polar regions. The multicompartmental approach has been applied to the “quantitative water air sediment interaction" or "QWASI" model designed to assist in understanding chemical fate in lakes.[7] Another application found in POPCYCLING-BALTIC model, which is describing fate of persistent organic pollutants in Baltic region.[8]

## References

1. Mackay, Donald (2001). Multimedia Environmental Models. Lewis Publishers. ISBN 1-56670-542-8. Retrieved 2 June 2011.
2. Mackay, D; Wania, Frank (1999). The evolution of mass balance models of persistent organic pollutant fate in the environment. Environmental Pollution. 100. pp. 223–240.
3. Mackay, Donald; Shiu, Wan Ying Shiu; Ma, Kuo Ching (2000). Physical-Chemical Properties and Environmental Fate and Degradation Handbook. Boca Raton, Florida: CRC Press. ISBN 1-56670-255-0. Retrieved 2 June 2011.
4. Donald Mackay, Sally Paterson (1991). "Evaluating the multimedia fate of organic chemicals: a level III fugacity model". Environmental Science & Technology 25 (3): 427–436. doi:10.1021/es00015a008. Bibcode1991EnST...25..427M.
5. D. Mackay; S. Paterson; W.Y. Shiu (1992). "Generic models for evaluating the regional fate of chemicals". Chemosphere 24 (6): 695–717. doi:10.1016/0045-6535(92)90531-U. Bibcode1992Chmsp..24..695M.
6. Donald Mackay; Antonio Di Guardo; Sally Paterson; Gabriel Kicsi; Christina E. Cowan; David M. Kane (1996). "Assessment of chemical fate in the environment using evaluative, regional and local-scale models: Illustrative application to chlorobenzene and linear alkylbenzene sulfonates". Environmental Toxicology and Chemistry 15 (9): 1638–1648. doi:10.1002/etc.5620150930.