Geoscience Reference
In-Depth Information
Using these notations, the equilibrium conditions are formulated:
K
0
p
c
¼ CO
2
½
;
ð
4
:
3
Þ
¼ K
1
CO
2
HCO
3
H
þ
½
=
½
;
ð
4
:
4
Þ
¼ K
2
HCO
3
H
þ
CO
2
3
½
;
ð
4
:
5
Þ
2
.
K
1
K
2
CO
2
¼ L
p
H
þ
Ca
2
þ
½
ð
½
Þ ;
ð
4
:
6
Þ
'
°
where K
0
is the indicator of CO
2
solubility (=250 mmol/
atm at 30
C and
640 mmol/
'
atm at
°
C), L
p
is the solubility indicator for CaCO
3
,
К
1
and
К
2
are the
first and second apparent coef
cients of dissociation of carbonic acid (depend on
temperature and pressure).
From Eqs. (
4.1
)
(
4.6
) we obtain:
-
X
C ¼ CO
2
K
1
=
H
þ
2
2
1
þ
K
1
=
H
þ
þ
K
1
K
2
=
H
þ
;
A ¼ CO
2
3
þ
2K
1
K
2
=
H
þ
½
½
½
½
½
and calculated the relative
changes of [CO
2
], [Ca
2+
], p
c
, and A. Any of these components are denoted as U and
taking
Eriksson (1963) used a differentiation operator
ʴ
ʔ
U =
ʴ
U/U, we obtain:
D
p
c
¼
D
½
CO
2
D
K
0
ð
4
:
7
Þ
¼
D
Ca
2
þ
H
þ
D
L
p
þ
2
D
½
D
K
1
D
K
2
D
½
CO
2
ð
4
:
8
Þ
þ
F
1
D
K
1
=
F
0
þ
a
2
D
K
2
=
F
0
F
2
D
H
þ
DR
C ¼
D
CO
2
½
½
=
F
0
ð
4
:
9
Þ
H
þ
D
A ¼
D
½
CO
2
þD
K
1
þ
2a
2
D
K
2
=
F
2
F
3
D
½
=
F
2
ð
4
:
10
Þ
where
F
0
¼ 1
þ
a
1
þ
a
2
;
F
1
¼ a
1
þ
a
2
;
F
2
¼ a
1
þ
2a
2
;
F
3
¼ a
1
þ
4a
2
;
2
H
þ
H
þ
a
1
¼ K
1
=
½
;
a
2
¼ K
1
K
2
=
½
:
Based on (
4.7
) through (
4.10
), and considering the experimental data, Eriksson
(1963) showed that a 1
C increase of the temperature of the upper layer of the
marine medium causes an increase of the partial pressure of CO
2
in the atmosphere
by 4.2
°
5.8 %, a 1 % decrease of the water volume implies an increase of the partial
pressure of CO
2
in the atmosphere by 3 %, with 1 % of carbon dioxide in the water
medium precipitating as CaCO
3
. With variations of the equilibrium state in deep
layers of the hydrosphere a 1 % output of CO
2
in the form of gas is followed by a
1 % sediment of CO
2
in the form of CaCO
3
. Moreover, variations in the CO
2
partial
pressure correlate with changes of the concentration of phosphorus P, so that a
decrease of P in deep layers by 1 % leads to an increase of p
c
by 5.6 %.
-
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