9
Marine Carbonates: Their Formation and Destruction
320
not equal to zero with sufficient accuracy, the
estimation for the pH in step 2 will have to be
improved until the correct value is found.
Irrespective whether a solution to this system
is found in the iterative manner described, or
whether it is solved by finding an analytical solution of the cubic equation, the pH-value of the
equilibrium is at all times determined by the partial
pressure pCO 2 in the atmosphere. As it remains in
contact with the solution, such a system is
referred to as open to CO 2 . It is characteristic of
such systems that the reactions can cause the release of CO 2 into the atmosphere at any time and
that CO 2 can be drawn from the atmosphere without directly affecting total atmospheric pCO 2 .
9.3.2
Primary Reactions of the CalciteCarbonate-Equilibrium without
Atmospheric Contact
A system which is closed to CO 2 exists wherever
the final calcite-carbonate-equilibrium is reached
without any concurrent uptake or release of atmospheric CO 2 in its process. This implies that the
Equations 9.1 and 9.2 are no longer valid. In their
stead, a balance of various C-species is related to
calcium. This balance maintains that the sum of Cspecies must equal the calcium concentration in
solution, since both can enter the solution only
by dissolution of calcite or aragonite:
(Ca 2+ ) = (H 2 CO 3
0 ) + (HCO 3
- ) + (CO 3
2- )
(9.13)
Analogous to Equations 9.11 and 9.12, Equation 9.13 is only valid if the initial solution consists of pure water. In the normal case, in which
the solution will already contain dissolved carbonate- and/or calcium ions, the difference between equilibrium concentrations (...) f and the initial concentrations (...) i needs to be regarded:
(Ca 2+ ) f – (Ca 2+ ) i =
(H 2 CO 3
0 ) f – (H 2 CO 3
0 ) i + (HCO 3
- ) f –
(HCO 3
- ) i + (CO 3
2- ) f – (CO 3
2- ) i
(9.14)
The six Equations 9.4, 9.6, 9.8, 9.10, 9.12, and
9.14 must now be solved for the six variables
(Ca
2+
), (H
+
), (OH
-
), (H 2 CO 3
0
), (HCO 3
-
), (CO 3
2).
There is no analytical solution for this non-linear
equation system. If there were one, it would be irrelevant because an iterative solution, similar to
the one described in the previous section, would
always be easier to handle and besides be more
reliable. However, still independent of the method
of mathematical solution is the fact that the equilibrium is exclusively determined by the carbonate
concentration which the system previously contained and which is defined by the concentrations
(...) i . At this particular point, the amount of CO 2
would also have to be considered which is liberated into such a system, e.g. from the oxidation of
organic matter. This amount would be simply
added to the 'initial' concentrations and would
influence the equilibrium in the same way as the
pre-existing carbonate.
9.3.3
Secondary Reactions of the CalciteCarbonate-Equilibrium in Seawater
In seawater, the differences between activities and
concentrations must always be considered (cf.
Sect. 15.1.1). The activity coefficients for monovalent ions in seawater assume a value around 0.75,
for divalent ions this value usually lies around 0.2.
In most cases of practical importance, the activity
coefficients can be regarded with sufficient
exactness as constants, since they are, over the
whole range of ionic strengths in solution,
predominately bound to the concentrations of
sodium, chloride, and sulfate which are not directly involved in the calcite-carbonate-equilibrium. The proportion of ionic complexes in the
overall calcium or carbonate content can mostly
be considered with sufficient exactness as constant in the free water column of the ocean. Yet,
this cannot be applied to pore water which frequently contains totally different concentrations
and distributions of complex species due to diagenetic reactions.
Figure 9.4 shows the distribution of carbonate
and calcium species in ocean water and in an anoxic pore water, calculated with the program
PHREEQC (Parkhurst 1995). It is evident that
about 10 % of total calcium is prevalent in the
form of ionic complexes and 25 – 30 % of the total
dissolved carbonate in different ionic complexes
other than bicarbonate. These ionic complexes are
not included in the equations of Sections 9.3.1
and 9.3.2. Accordingly, the omission of these
complexes would lead to an erraneous calculation
of the equilibrium. The inclusion of each complex
shown in Figure 9.4 implies further additions to
the system of equations, consisting in another
concentration variable (the concentration of the
complex) and a further equation (equilibrium of the
complex concentration relative to the non-
Marine Carbonates: Their Formation and Destruction
320
not equal to zero with sufficient accuracy, the
estimation for the pH in step 2 will have to be
improved until the correct value is found.
Irrespective whether a solution to this system
is found in the iterative manner described, or
whether it is solved by finding an analytical solution of the cubic equation, the pH-value of the
equilibrium is at all times determined by the partial
pressure pCO 2 in the atmosphere. As it remains in
contact with the solution, such a system is
referred to as open to CO 2 . It is characteristic of
such systems that the reactions can cause the release of CO 2 into the atmosphere at any time and
that CO 2 can be drawn from the atmosphere without directly affecting total atmospheric pCO 2 .
9.3.2
Primary Reactions of the CalciteCarbonate-Equilibrium without
Atmospheric Contact
A system which is closed to CO 2 exists wherever
the final calcite-carbonate-equilibrium is reached
without any concurrent uptake or release of atmospheric CO 2 in its process. This implies that the
Equations 9.1 and 9.2 are no longer valid. In their
stead, a balance of various C-species is related to
calcium. This balance maintains that the sum of Cspecies must equal the calcium concentration in
solution, since both can enter the solution only
by dissolution of calcite or aragonite:
(Ca 2+ ) = (H 2 CO 3
0 ) + (HCO 3
- ) + (CO 3
2- )
(9.13)
Analogous to Equations 9.11 and 9.12, Equation 9.13 is only valid if the initial solution consists of pure water. In the normal case, in which
the solution will already contain dissolved carbonate- and/or calcium ions, the difference between equilibrium concentrations (...) f and the initial concentrations (...) i needs to be regarded:
(Ca 2+ ) f – (Ca 2+ ) i =
(H 2 CO 3
0 ) f – (H 2 CO 3
0 ) i + (HCO 3
- ) f –
(HCO 3
- ) i + (CO 3
2- ) f – (CO 3
2- ) i
(9.14)
The six Equations 9.4, 9.6, 9.8, 9.10, 9.12, and
9.14 must now be solved for the six variables
(Ca
2+
), (H
+
), (OH
-
), (H 2 CO 3
0
), (HCO 3
-
), (CO 3
2).
There is no analytical solution for this non-linear
equation system. If there were one, it would be irrelevant because an iterative solution, similar to
the one described in the previous section, would
always be easier to handle and besides be more
reliable. However, still independent of the method
of mathematical solution is the fact that the equilibrium is exclusively determined by the carbonate
concentration which the system previously contained and which is defined by the concentrations
(...) i . At this particular point, the amount of CO 2
would also have to be considered which is liberated into such a system, e.g. from the oxidation of
organic matter. This amount would be simply
added to the 'initial' concentrations and would
influence the equilibrium in the same way as the
pre-existing carbonate.
9.3.3
Secondary Reactions of the CalciteCarbonate-Equilibrium in Seawater
In seawater, the differences between activities and
concentrations must always be considered (cf.
Sect. 15.1.1). The activity coefficients for monovalent ions in seawater assume a value around 0.75,
for divalent ions this value usually lies around 0.2.
In most cases of practical importance, the activity
coefficients can be regarded with sufficient
exactness as constants, since they are, over the
whole range of ionic strengths in solution,
predominately bound to the concentrations of
sodium, chloride, and sulfate which are not directly involved in the calcite-carbonate-equilibrium. The proportion of ionic complexes in the
overall calcium or carbonate content can mostly
be considered with sufficient exactness as constant in the free water column of the ocean. Yet,
this cannot be applied to pore water which frequently contains totally different concentrations
and distributions of complex species due to diagenetic reactions.
Figure 9.4 shows the distribution of carbonate
and calcium species in ocean water and in an anoxic pore water, calculated with the program
PHREEQC (Parkhurst 1995). It is evident that
about 10 % of total calcium is prevalent in the
form of ionic complexes and 25 – 30 % of the total
dissolved carbonate in different ionic complexes
other than bicarbonate. These ionic complexes are
not included in the equations of Sections 9.3.1
and 9.3.2. Accordingly, the omission of these
complexes would lead to an erraneous calculation
of the equilibrium. The inclusion of each complex
shown in Figure 9.4 implies further additions to
the system of equations, consisting in another
concentration variable (the concentration of the
complex) and a further equation (equilibrium of the
complex concentration relative to the non-