Page 40 - Soil and water contamination, 2nd edition

Basic environmental chemistry 27

where M = the total number of moles of compound i in the system and V = the volume of
i j
3
phase j [L ]. By combining the ideal gas law (Equation 2.15) and Equation (2.24) with m =
i,j
n /V, it can be shown that:
i
1
Z (2.26)
air
R T
where Z = the fugacity capacity constant for air. The fugacity capacity constant for other
air
phases depends on the compound’s partition coefficient between that phase and water and
the compound’s Henry’s law constant . The fugacity capacity constant for water is:
1
Z
water (2.27)
K
H
2
-2
where Z = the fugacity capacity constant for water, K = the Henry’s law constant [L T ].
water H
For sediment , the fugacity capacity constant is:
K
Z s d
sed (2.28)
K
H
where Z = the fugacity capacity constant for sediment , ρ = the bulk density of sediment [M
s
sed
-3
3
-1
L ] and K = the distribution coefficient [L M ] (see Equation 2.12). The number of moles
d
of the compound in each phase can then be calculated by:
M Z f V (2.29)
i, j i, j i j
For further details about the fugacity concept, see Mackay (1991) or Schwarzenbach et al.
(1993).
Example 2.5 Fugacity
3
3
Consider a pond ecosystem comprising 10 000 000 m of air, 50 000 m of water, and
400 m of bottom sediment . Ten litres of the organic liquid benzene is spilled into it.
3
Calculate the equilibrium partitioning among air, water, and sediment using the fugacity
approach. Relevant data is given in the table below.
Benzene properties
Vapour pressure 0.125 atm
3
Henry’s law constant 5.55·10 -3 atm · m mol -1
Molecular weight 78.11 g mol -1
Specific density 873.81 kg m -3
Sediment properties
Bulk density 1100 kg m -3
Distribution coefficient for benzene 0.6 l kg -1
Solution
First, calculate the total amount of benzene released expressed in moles:
-1
-1
10 l × 873.81 g l /78.11 g mol = 112 mol

Second, calculate the fugacity capacity for the three phases considered. For the air phase ,
use Equation (2.26):
1 1 -1 -3
Z 40 9 . mol atm m
air 4
RT . 8 21 10 298 . 15

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Soil and Water.indd 39 10/1/2013 6:44:12 PM