Page 38 - Soil and water contamination, 2nd edition

Basic environmental chemistry 25

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The suspended sediment concentration is 10 g per 10 l, which is 0.001 kg l . So the
distribution coefficient K is:

d
0. 06 0. 02 -1
K = 2000 l kg
d
0. 02 0. 001
2.5.5 Fugacity
Another way to predict the distribution of chemicals among the different phases is the
concept of fugacity . Fugacity means the tendency of a substance to flee from the phase it is
in. The concept of fugacity is similar to that of activity and has been based on the chemical
potential, which is defined as the increase in free energy with each increment of a substance:
G
M (2.13)
i
n
i
-1
2 -2
-1
where μ = the chemical potential expressed in kJ mol [M L T mol ], and n = the amount
i i
of substance i [mol]. At constant temperature, the incremental change in chemical potential
of a gaseous compound is related to a corresponding change in pressure:
V
dM i dP i (2.14)
n i
-1
-2
3
where V = volume of the gas [L ], and P = the partial pressure of i [M L T ]. The partial
i
pressure of a gas is that pressure it would exert if it occupied the entire volume by itself. The
ideal gas law can be used to convert the partial pressure into corresponding moles per unit
volume:
n P
i i (2.15)
V RT
-1
-1
-1
-1
where R = the gas constant (= 8.3144 J mol K = 0.0821 l atm mol K ), and T = the
temperature (K). Equation (2.14) becomes:
RT
dM i dP i (2.16)
P
i
Integration of Equation (2.16) yields:
P
0
M i M i RT ln i (2.17)
P i 0
2 -2
0
-1
0
where μ = standard chemical potential [M L T mol ], and P = standard vapour pressure
i i
(i.e. the partial pressure that the chemical would have in a gas volume in equilibrium with
-2
-1

the pure liquid or solid phase at 1 atmosphere pressure) [M L T ]. Since chemists are
mostly interested in conditions that prevail under normal environmental conditions near the
Earth’s surface, the standard conditions are commonly chosen at 25 °C (= 298.15 K) and 1
atmosphere pressure. It is difficult to quantify the absolute value for the standard chemical
potential, and so for the chemical potential. However, this issue is less relevant, since the
change and the differences in chemical potential are of most interest. Equation (2.17) applies
for ideal gases. Since gases do not fully behave ideally under all circumstances, the fugacity ,
which is closely related to pressure, has been defined, so that Equation (2.17) becomes:
f i
0
M M RT ln (2.18)
i i 0
f i
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