Page 39 - Soil and water contamination, 2nd edition

26 Soil and Water Contamination

0
-1
-2
-2
-1
where f = the fugacity of compound i [M L T ], and f = the standard fugacity [M L T ].
i i
For gases, the fugacity is:
f x P (2.19)
i i i
where θ = fugacity coefficient [-], x = the molar fraction of i in the mixture or solution [-],
i i
-1
-2
and P = the total pressure [M L T ]. The fugacity coefficient corrects for the non-ideality of
the gas, but under normal environmental conditions it is very close to 1, so:
f P (2.20)
i i

The fugacity of a chemical in the liquid or solid phase is related to the vapour pressure by:
f x P 0 (2.21)
i i i i
where γ = the activity coefficient [-]. For a pure liquid or solid, both the molar fraction
i
x and the activity coefficient γ are equal to 1. The activity coefficient in a liquid solution
i i
(e.g. water) may well be different from 1. For solutions of non-polar organic compounds
in polar solvents like water, the activity coefficients are much larger than 1 (Schwarzenbach
et al. 1993). The following equation can be used to convert the mole fraction x to the molar
i
concentration m :
i
x i
m (2.22)
i
V
mix
-1
where V = the molar volume of the mixture or solution (l mol ). Hence:
mix
f i i m i V mix P i 0 (2.23)
For aqueous solutions of organic compounds that are hardly or moderately soluble, the
contribution of the organic solute to the molar volume may be neglected (Schwarzenbach
et al., 1993). This means we may assume the molar volume to be equal to the molar volume
-1
of water, which amounts to 0.018 l mol . Organic liquids usually have molar volumes of the
-1
order of 0.2 l mol .
From Equation (2.23) it can be seen that the fugacity is linearly related to the molar
concentration. In general, the relation between the concentration and fugacity for a given
phase can be written as:
m i, j Z i, j f i (2.24)

-3

where m , = the molar concentration of compound i in phase j [M L ], Z = the fugacity
i j i,j
2
-2
-3
-1
capacity of compound i in phase j [T L ], usually expressed in units of mol atm m . Each
substance tends to accumulate in compartments where the fugacity capacity Z is large. At
equilibrium , the change in free energy is zero, which implies that the chemical potential is
equal in each phase. This, in turn, implies that the fugacities in each phase are the same. The
fugacity for the entire system, which consists of different phases, is (Hemond and Fechner-
Levy, 2000):
M i
f (2.25)
i
Z ( i, j V )
j
i

10/1/2013 6:44:11 PM
Soil and Water.indd 38 10/1/2013 6:44:11 PM
Soil and Water.indd 38