Geoscience Reference
In-Depth Information
Denoting
B
ð
OH
Þ
3
;
K
W
¼ H
þ
OH
K
B
¼ H
þ
B
ð
OH
Þ
4
½
½
;
½
þ
B
ð
OH
Þ
4
B
T
¼ B
ð
OH
Þ
3
and using Eq. (
4.2
) we obtain:
1
Þ
1
A ¼ K
W
H
þ
þ
K
B
B
T
K
B
þ
H
þ
þ
C
U
H
þ
Þ
H
þ
½
ð
½
ð
½
K
1
þ
2K
1
K
2
Þ=
ð
aW
U
½
or
!
K
1
½H
þ
þ
2K
1
K
2
½H
þ
B
T
1
þ
½H
þ
=
K
W
½H
þ
½H
þ
A ¼½CO
2
þ
K
B
þ
ð
4
:
11
Þ
2
The solution of this equation relative to [H
+
] enables one to determine p
c
as a
function of C
U
. According to Bjorkstrom (1979), K
B
=2
10
−
9
and K
W
=10
−
14
.
The right-hand part of Eqs. (
4.2
) and (
4.11
) implies an account of all weak acids
in the salt water. Ions of other compounds are taken into account through the
dependence of the equilibrium constants on salinity or chlorine content. The
characteristic parameter of the equilibrium of the carbonate system is a variable:
×
1
=
2
1
=
2
½CO
2
3
½CJ
2
X ¼
ð
K
1
K
2
Þ
¼
½H
þ
In the terms of this parameter we have:
CO
2
C ¼ 1
þ
KX
þ
X
2
R
½
ð
4
:
12
Þ
CO
2
A ¼ KX
þ
2X
2
½
þ
W
ðÞ;
ð
4
:
13
Þ
p
K
1
=
where K ¼
K
2
;
n
o
=
1
=
2
X
1
1
=
2
1
=
2
X
1
W
ðÞ
¼B
T
=
1
þ
K
1
K
2
½
K
B
þ
K
W
XK
1
K
2
½
K
1
K
2
½
Excluding [CO
2
] from the Eqs. (
4.12
) and (
4.13
):
2C
A
0
Þ
X
2
KA
0
C
Þ
X
A
0
¼ 0
ð
ð
;
ð
4
:
14
Þ
where A
0
¼ A
W
ð
X
Þ
.
Since W(X)<<A, the following iterative procedure can be used beginning with
an estimation of X = X
1
(
≅
1) in order to solve the Eq. (
4.14
):
h
i
=
1
=
2
A
i
¼ A
WX
ð ;
5
b
þ
b
2
X
i
¼ 0
:
4ac
ai
2
ð
Þ;
where a ¼ 2C
A
i
1
;
b ¼ K
ð
A
i
1
C
Þ:
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