Geology Reference
In-Depth Information
Originally the extended DH term was similar to that in Equation (3.5),
i.e. with an average ion size parameter, a
i
¼
3. Scatchard
28
showed that a
better fit with experimental data was obtained using an average value of
a
i
¼
4.6, i.e. 0.33a
i
¼
1.5, and so the extended DH expression used in the
SIT model is often
p
p
log g
i
¼
0
:
510 z
i
I
=
1
þ
1
:
5 I
ð
3
:
9
Þ
Overall, however, the SIT approach is limited in application to inter-
mediate ionic strength solutions (0.1-3.5 mol L
1
).
The Pitzer model can be used to obtain activity coecients for solutes
in low (
o
0.1 mol L
1
), intermediate (0.1-3.5 mol L
1
) and high (43.5
mol L
1
) ionic strength solutions. The Pitzer equations
29
include terms
for binary and ternary interactions between solute species as well as a
modified DH expression. The general formula is
ln g
i
¼
z
i
f
g
þ
X
j
D
ij
½
j
þ
X
jk
E
ijk
½
j
½
k
þ
...
ð
3
:
10
Þ
where f
g
is the modified DH term
f
g
¼
0.392 (
O
I/(1
þ
1.2
O
I)
þ
(2/1.2) ln(1
þ
1.2
O
I))
(3.11)
and the D
ij
terms describe interactions between pairs of ions, i and j,
while the E
ijk
terms describe interactions among three ions, i, j, and k.
Higher-order terms can also be added to this general formula. A key
difference between the SIT and Pitzer models is that interactions
between ions of like charge are also included. For ionic strength
solutions of up to
B
3.5 mol L
1
, there is good agreement between the
two models but, at 43.5 mol L
1
, the ternary and higher-order terms in
the Pitzer equations become more important and this model gives the
more accurate ion activity coecients.
12
Although naturally occurring brines and some high ionic strength
contaminated waters may require the more complicated expressions
developed in the Davies, SIT, or Pitzer models, the use of Equations
(3.3)-(3.5) is justified for the ionic strengths of many freshwaters.
Finally, this section has focused primarily on ions in aqueous solution
but it should be remembered that aqueous solutions also contain
important dissolved neutral species, e.g. O
2
,CO
2
,H
2
CO
3
, Si(OH)
4
.
For non-ideal solutions, the Setschenow Equation (1899) has tradition-
ally been used to describe the ionic strength dependence of the activity
coecients for dissolved neutral species and can be written as
log g
i
¼
k
i
[i]
(3.12)
