Fugacity capacity

Equilibrium. Equilibrium between compartments can be expressed either as partition coefficients K.. (i.e. concentration ratio at equilibrium) or in the fugacity models as fugacity capacities and Z. such that K.. is Z./Z., the relationships being depicted in Figur 1. Z is dellned as tfte ratio of concentration C (mol/m3) to fugacity f (Pa), definitions being given in Table I. 

An advantage of the fugacity capacity approach is that for N compartments N values of Z are defined while there may be N(N-l)/2 partition coefficients. Using Z values the partitioning properties between two phases are attributed independently to each phase. It is possible to assign (accidentally) three inconsistent partition coefficients between air, soil and water but the three Z values are inherently consistent. 

Figure 1. Relationships between fugacity capacities and partition coefficients. See Table 1 for symbol definitions.

The Level I calculation proceeds by deducing the fugacity capacities or Z values for each medium (see Table 1.5.3), following the procedures described by Mackay (2001). These working equations show the necessity of having data on molecular mass, water solubility, vapor pressure, and octanol-water partition coefficient. The fugacity f (Pa) common to all media is deduced as... 

Equation (34) allows us to redefine the fugacity capacity as Zij0W=Kii0W/Hj. 

Instead of a solid-water equilibrium relationship, a solid-air equilibrium relationship could be used in the same manner to define the fugacity capacity and the fugacity. 

The advantage of using fugacity to calculate the equilibrium distribution coefficients becomes apparent when one compares the fugacity capacities of a HOP for several different phases. For example, consider a region of the unsaturated zone just below the ground surface where naphthalene is distributed between air, water, pure phase octanol, and soil at equilibrium. The fugacity capacities for these phases are repeated below in Eqs. (46)-(49) ... 

Naphthalene at 25 °C has Kow=2239 and Hj=4.9xl0 1 atm l/mol [18]. Chiou et al. [19] measured Kd=6.211/kg for naphthalene on Anoka soil. This yields Zair=4.09xl0 2 mol/(l- atm), Zwater=2.04 mol/(l atm), Zoct=4,569 mol/(l- atm), and Z] so id= 12.7 mol/(kg atm). It is obvious from these values that most of the naphthalene will reside in the octanol at equilibrium. If octanol is not present, most of the naphthalene will reside on the soil. However, note that the units of the fugacity capacity for soil are different than those for the other phases. Hence, if octanol is not present we can only say that more naphthalene will reside on one kg of soil than one liter of the other phases. An alternative approach would be to convert the units of Z solid by multiplying by the soil bulk density (this allows us to normalize the fugacity capacity by a REV containing soil). If... 

The fugacity was defined above in terms of a concentration and a fugacity capacity. At constant pressure and temperature, fugacity capacities were constant (except when isotherms were nonlinear). Hence, Eq. (55) can be simplified to the following ... 

Fugacity has units of pressure, and can be related to the concentration of a chemical in a system through a fugacity capacity constant, commonly with units of (mol/atm m3). Thus the chemical concentration in a given... 

In the air phase, under pressures normally found in the environment, fugacity equals the pressure exerted by the chemical s vapor. (At higher pressures, vapors do not exactly obey the ideal gas law, and a correction must be applied this is small enough to ignore for practical purposes of fate and transport modeling in the environment.) By combining the ideal gas law (Eq. [1-29]) and Eq. [1-34], it is evident that the fugacity capacity for air is 1/RT, for all chemicals ... 

The fugacity capacity for other phases is a function of both the chemical s partition coefficient between that phase and water and the chemical s Henry s law constant. For water, the fugacity capacity is... 

Once the fugacity capacity for each phase has been calculated, the moles of chemical in each phase are given by... 

Fugacity modeling does not allow any new calculations to be made that cannot already be made with the partition coefficients described in the previous three sections. However, a comparison of the fugacity capacity of a chemical in different phases permits a direct assessment of which phase will have the highest chemical concentration at equilibrium. For further details, the reader is referred to Mackay and Paterson (1981) and Schwarzenbach et al. (1993). 

Next, calculate the fugacity capacity for each phase. For the air phase, use Eq. [1-36] ... 

Therefore, at equilibrium, the mass of methylene chloride will be overwhelmingly in the air as compared with the other two phases. However, the highest concentration of methylene chloride is in the water (1 X ICE7 mol/m3), the phase with the highest fugacity capacity. 

The equilibrium constant is then the ratio of the fugacity capacities. The magnitude of Z will depend on temperature and the properties of the compound as they relate to the characteristics of a given phase. Compounds will accumulate in compartments with a high value of Z. The next step is to define Z for environmental compartments air, water, soil, sediments, and biota. 

---