Geology Reference
In-Depth Information
The usefulness of Equation (3.72) will be demonstrated further in
Example 3.10.
Although the electron activity is a hypothetical phenomenon, pe is a
useful parameter to describe the redox intensity of natural systems and
hence the species distribution under prevailing redox conditions (Ex-
ample 3.10).
Example 3.10: Calculate the pe values for the following solutions (298
K, I
¼
0) (i) a solution at pH 2 containing
{
Fe
31
} ¼
10
4.5
mol L
1
and
{
Fe
21
} ¼
10
2.7
mol L
1
where log K
¼
13; (ii) a neutral solution
containing
{
Mn
21
} ¼
10
6
mol L
1
in equilibrium with the solid phase,
Mn
IV
O
2
and log K
¼
40.84.
(i) At pH 2, the hydrated metal ion has not undergone hydrolysis
to any significant extent:
Fe
3
þ
þ
e
Ð
Fe
2
þ
K
¼f
Fe
2
þ
g=f
Fe
3
þ
gf
e
g
pe
¼
log K
þ
log
ðf
Fe
3
þ
g=f
Fe
2
þ
gÞ
¼
13
þ
log
ð
10
4
:
5
=
10
2
:
7
Þ
¼
13
1
:
8
¼
11
:
2
(ii)
MnO
2
þ
4H
þ
þ
2e
Ð
Mn
2
þ
þ
2H
2
O
K
¼f
Mn
2
þ
g=f
H
þ
g
4
f
e
g
2
pe
¼
0
:
5 log K
þ
0
:
5 log
ðf
H
þ
g
4
=f
Mn
2
þ
gÞ
¼
20
:
42
þ
0
:
5 log
ð
10
28
=
10
6
Þ
¼
20
:
42
11
¼
9
:
42
For a fixed pH value (e.g. pH
¼
2), the species distribution (e.g. where
{Fe
T
}
¼
1
10
3
mol L
1
) at different pe values can be illustrated by
plotting log{}against pe. This is analogous to the treatment of pH as
a master variable. The pe range is split into two parts, pe
o
pe
0
and
pe4pe
0
. Using pe
0
¼
(1/n) log K, this becomes {e
}4K
1
and
{e
}
o
K
1
(because n
¼
1 in this Example). Thereafter, construction
of the graph is achieved by the same method used in Example 3.5.
