Environmental Engineering Reference
In-Depth Information
Sidebar 8.3: Activities and Activity Coefficients
a i denotes the activity of the i th species in a multi-species system. It is the
product of concentration c i and activity coefficient
g i that is species-dependent,
i.e. for the i th chemical species holds:
a i ¼ g i c i
The activity depends on ionic strength
m
in the solution, defined by
2 X c i z 2
1
m ¼
i
where the sum has to be extended over all charged components. z i denotes the
electrical charge of species i . The logarithm of the activity coefficient can be
computed explicitly by a formula like:
g i ¼A z i 2 m
p
log
This is the simplest formulation that can be derived theoretically. For very
low values of
10 2.3 ; Sigg and Stumm 1989 ), the formula is valid with
m
(
<
0.51 (in water of 25 C, see: Krauskopf and Bird 1995 ).
An extended formula was proposed by Davies:
a value of A ¼
p
m
g i ¼A z i 2
log
þ p
0
:
3
m
1
The Davies equation is usually assumed to be valid for ionic strengths up to
m ¼
0.5. The coefficient A depends on temperature only. Values for A are
given in Table 8.1 . The activity coefficient thus depends on temperature, on
ionic strength and the electric charge of the species.
Another extended formulation for the relation between activity coefficients
and ionic strength is found with reference to Debye 4 -H
uckel 5 :
A z i 2
p
log
g i ¼
þBa i p þb i m
1
with coefficients B , a i 0 and b i
uckel 1923 ). The coefficient
B depends on temperature only. The ion-size parameter a i 0 as well as b i are
species-dependent. The latter formulation is used in the speciation code
(continued)
(Debye and H
4 Peter Debye (1884-1966), Dutch chemist and physicist.
5 Erich Armand Arthur Joseph H
uckel (1896-1980), German chemist and physicist.
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