Applications of Equilibrium Thermodynamics - Elements of Environmental Engineering: Thermodynamics and Kinetics - page 165

contaminants then make their way into the food chain of higher animals, including
humans. This is the process of bioaccumulation .
The uptake of organic chemicals by aquatic species can be modeled at different
levels of complexity. The uptake depends on factors such as exposure route (dermal,
ingestion by mouth, and inhalation), and loss through digestion and defecation. An
animal can also imbibe chemicals through its prey that has been exposed to the chem-
ical. Although rate-based models may be better suited to describe these phenomena,
thermodynamic models have been traditionally used to obtain first-order estimates
of the extent of bioaccumulation (Mackay, 1982). It has been suggested that abiotic
species are in near-equilibrium conditions in most circumstances. Hence, it is appro-
priate to discuss briefly the thermodynamic basis for modeling the bioaccumulation
phenomena.
In its simplest form, a partition coefficient (also called a bioconcentration factor ,
K bw ) is used to define the concentration level of a pollutant in an aquatic species
relative to that in water. Since the major accumulation of a pollutant in an animal
occurs in its lipid fraction, it is customary to express the concentration on a lipid
weight basis.
The general equation for partitioning between the organism and water is given by

C i B
C i w

K bw = , (4.85)

where C i B is the animal concentration (mg/kg) and C i w is the aqueous concentration
(mg/L)atequilibrium.Ifweassumethattheorganismiscomprisedof j compartments,
each of concentration I given by C ij , and with a volume fraction η j , then we can write

the total moles of solute i in the organism as

m ij = C ij η j V ,

(4.86)

j j

where V is the total organism volume. Thus, we have

j m ij
V

C i B = = C ij η j . (4.87)

j

For the aqueous phase we have

x i w
V w

C i w = . (4.88)

Atequilibrium,thefugacityinall j compartmentswouldbeequaltothatintheaqueous
phase, f i f i . For any compartment j ,

f i =

=

x ij γ ij f i C ij V j γ ij f i ,

=

(4.89)

where f i is the reference fugacity on the Raoult's law basis, V j = η j V . Thus,

f i
f i

1
V j γ ij

C ij = (4.90)