Applications of Equilibrium Thermodynamics - Elements of Environmental Engineering: Thermodynamics and Kinetics - page 166

or

f i
f i

1
V j γ ij

C i B = η j . (4.91)

j

For the aqueous phase we have

f i x i w γ i w f i C i w V w γ i w f i = = (4.92)

or

f i
f i

1
V w γ i w

.

C i w = (4.93)

f i , we obtain

Now since f i =

V w γ i w
j

η j
V j γ ij

C i B
C i w =

K Bw = . (4.94)

Since the dominant accumulation of hydrophobic solutes in an organism occurs in its
lipid content, we can write

V w
V L

γ i w
γ i L

K BW = · · η L , (4.95)

where L refers to the lipid phase. Organisms with high lipid content ( η L ) should have

high K BW values.
Since γ i w is directly proportional to the octanol-water partition coefficient, K ow ,

we can expect an LFER relationship between K BW and K ow . Using the definition of
K ow given previously along with Equation 4.95, we obtain

K ow = η L γ i o

V o
V L

.

K BW

(4.96)

γ i L

For compounds that have similar volume fraction of lipids ( η L ) and similar ratios

of activity coefficients ( γ i w ) , the ratio K BW / K ow should be fairly constant. This

suggests that a linear one-constant correlation should suffice:

γ i o /

log K BW = a log K ow + b . (4.97)

Such a correlation was tested and confirmed by Mackay (1982). The correlation
developed was for a restricted set of compounds, namely, those with log K ow < 6,
nonionizable, and those with small K B values. The overall fit to the experimental
data was

1.32, r 2 log K BW = log K ow − = 0.95. (4.98)