Primary Reactions of the Calcite-Carbonate-Equilibrium without Atmospheric Contact

2 Primary Reactions of the Calcite-Carbonate-Equilibrium without Atmospheric Contact 

A system which is closed to CO exists wherever the final calcite-carbonate-equilibrium is reached without any concurrent uptake or release of atmospheric CO 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 This implies that the Equations 9.1 and 9.2 are no longer valid.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 C-species must equal the calcium concentration in solution, since both can enter the solution only by dissolution of calcite or aragonite  

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 (...)j,and the initial concentrations (...) needs to be regarded  

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 ), (H ), (OH-), (H CO, ), (HCO ), (CO, )-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 

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