Page 47 - Soil and water contamination, 2nd edition

34 Soil and Water Contamination

2-
2-
The molar mass of SO = 32.07 + 4 × 16.00 = 96.07, so the SO concentration is
4
4
-1
-3
-1/
-1/
90 mg l 1000 mg g 96.07 g mol = 1.56 · 10 mol l -1
-1
2+
2-
Second, calculate the activities of Ba and SO in mol l :
4
Use Equation (2.4) to calculate the log activity coefficient s. The values for A (= 0.5085)
and B (= 0.3281) at 25 °C are read from table 2.3, as well as the ion-specific values for
a Ba 2+ (= 5.0), and a 2- (= 4.0). Filling in Equation (2.4) we obtain logγ Ba 2+ = -0.355 and
SO 4
logγ 2- = -0.377. So, the activity coefficients are γ 2+ = 0.44 and γ 2- = 0.42. The Ba
2+
SO 4 Ba SO 4
-1
-7
-1
-7
2-
activity is 0.44 × 4.37 · 10 mol l = 1.92 · 10 mol l and the SO activity is 0.42 ×
4
-3
-1
-4
-1
1.56 · 10 mol l = 6.55 10 mol l .
Third, calculate the reaction coefficient Q, also referred to as the ion activity product
(IAP):
2+
2-
IAP = Q = [Ba ][SO ] = 1.26 10 -10
4

Finally, calculate the saturation index SI (Equation 2.41)
Q
-10
SI log log Q log K = log(1.26 · 10 ) – (-9.97) =
s
K s
–9.90 + 9.97 = 0.07.
This implies that the solution is lightly oversaturated with barite . Barite is likely to
precipitate until equilibrium has been reached (SI = 0).
2.8 COMPLEXATION
Not only the solubility product but also the total concentration of an ion in an aqueous
solution is controlled by the formation of inorganic and organic complexes. Such complexes
may considerably reduce the activity of ions, thereby enhancing the total concentration of
substances in solution. This section focuses on inorganic complexes ; the formation of organic
complexes is further elaborated upon in Section 4.3.2.
+
0
+
+
Examples of aqueous complexes are CaSO , CaOH , CdCl , PbHCO . The formation
4 3
of aqueous complexes can be described by equilibria of the type:
xM m yA a M x A m a (2.46)
y
The accompanying mass action law yields:
[ M A m a ]
K x y (2.47)
a
[ M m ] x [ A ] y

The equilibrium constant K for complexation reactions is also termed the stability constant.
Stability constants can be obtained from extensive databases, such as the WATEQ /
PHREEQE database (Nordstrom et al., 1990) or hydrochemical textbooks (e.g. Appelo and
Postma, 1996). The total concentration of the element M is equal to the sum of the molal
concentrations of all species of M:
M m m m m .... (2.48)
M m M x y A m a M p q B m b
-1
where m refers to the molal concentrations [mol M ]. Even in normal fresh water, a
-
2-
significant part (up to tens of percents) of some dissolved ions, such as SO and HCO ,
4 3
may be present in the form of aqueous complexes.
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