Geology Reference
In-Depth Information
species distribution within the upper and lower stability limits of water.
In general, the relationships between pe and pH for redox equilibria
involving proton and electron transfer give lines, e.g. pe
¼
apH
þ
b
(where a and b are constants), with slope
¼
a. Redox equilibria
involving only electron transfer give rise to horizontal lines, i.e. pe
¼
b, a
¼
0. Vertical lines arise from equilibria involving only proton
transfer and pH
¼
c (where c is a constant). The relationships between
pe and pH for As-H
2
O and Cr
H
2
O systems at 298 K and 1 atm total
are shown in Examples 3.11 and 3.12, respectively. The importance of
both As and Cr speciation as represented in these pe-pH diagrams is
discussed further in Sections 3.3.2.1 and 3.3.2.5, respectively.
Example 3.11: Construction of a pe-pH graph for Cr-H
2
O. Assume
that no solid phases are formed.
Acid-base behaviour of Cr
VI
:
HCrO
4
CrO
2
4
þ
H
1
K
1
¼
10
6.45
"
Hydrolysis behaviour of Cr
III
:
Cr
3
þ
þ
H
2
O
Ð
Cr
ð
OH
Þ
2
þ
þ
H
þ
K
2
¼
10
4
:
00
Cr
ð
OH
Þ
2
þ
þ
H
2
O
Ð
Cr
ð
OH
Þ
2
þ
H
þ
K
3
¼
10
5
:
62
Cr
ð
OH
Þ
2
þ
H
2
O
Ð
Cr
ð
OH
Þ
3
þ
H
þ
K
4
¼
10
7
:
13
Cr
ð
OH
Þ
3
þ
H
2
O
Ð
Cr
ð
OH
Þ
4
þ
H
þ
K
5
¼
10
11
:
02
Reduction of Cr
VI
to Cr
III
:
HCrO
4
þ
7H
þ
þ
3e
Ð
Cr
3
þ
þ
4H
2
O K
6
¼
10
70
:
55
HCrO
4
þ
6H
þ
þ
3e
Ð
Cr
ð
OH
Þ
2
þ
þ
3H
2
O K
7
¼
10
66
:
55
HCrO
4
þ
5H
þ
þ
3e
Ð
Cr
ð
OH
Þ
2
þ
2H
2
O K
8
¼
10
60
:
93
CrO
2
4
þ
6H
þ
þ
3e
Ð
Cr
ð
OH
Þ
2
þ
2H
2
O
K
9
¼
10
67
:
38
CrO
2
4
þ
5H
þ
þ
3e
Ð
Cr
ð
OH
Þ
3
þ
H
2
O
K
10
¼
10
60
:
25
CrO
2
4
þ
4H
þ
þ
3e
Ð
Cr
ð
OH
Þ
4
K
11
¼
10
49
:
23
Construction of vertical lines:
e.g. K
1
¼
{H
1
}{CrO
2
4
}/{HCrO
4
}
On the line, the concentrations of the Cr
VI
species are equal,
so pH
¼
pK
1
¼
6.45.
Construction of sloped lines:
e.g. K
8
¼
{Cr(OH)
2
}/{HCrO
4
}{H
1
}
5
{e
}
3
On the line, the concentrations of the Cr
III
and Cr
VI
species are equal,
so pe
¼
log K
8
/3 - 5/3 pH
¼
20.31-1.6 pH.
Crossing points:
For the lines defined by K
1
and K
8
, substitute pH
¼
6.45 in pe
¼
20.31-1.6 pH, so pe
¼
9.99.
