How must the counterions change when the model pH changes?
Choose total inorganic carbon Cₜ and free calcium concentration first. At the defaults these are 2.00 and 1.00 mmol/L. Each pH selection represents adding ideal strong acid or base with negligible volume change, before any solid is removed. Sodium and chloride counterions are included to maintain electrical neutrality.
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Carbonate species at 25 °C
α₀ : α₁ : α₂ = [H⁺]² : K₁[H⁺] : K₁K₂
Read sampled numerical values
| pH | CO₂* | HCO₃⁻ | CO₃²⁻ |
|---|---|---|---|
| 5 | 0.957 | 0.043 | 2.000e-7 |
| 5.7 | 0.817 | 0.183 | 4.288e-6 |
| 6.4 | 0.471 | 0.529 | 6.212e-5 |
| 7.1 | 0.151 | 0.849 | 4.997e-4 |
| 7.8 | 0.034 | 0.963 | 0.003 |
| 8.5 | 0.007 | 0.979 | 0.014 |
| 9.2 | 0.001 | 0.93 | 0.069 |
| 9.9 | 2.054e-4 | 0.729 | 0.271 |
| 10.6 | 1.965e-5 | 0.349 | 0.651 |
| 11.3 | 1.086e-6 | 0.097 | 0.903 |
| 12 | 4.686e-8 | 0.021 | 0.979 |
The three carbon forms sum to the prescribed total. A positive saturation index permits a thermodynamic drive toward calcite precipitation; it gives no rate. The authored starting account is CaCl₂ plus NaHCO₃. NaOH or HCl bookkeeping closes the charge balance at the prescribed pH; added volume is neglected. This is not a measured water sample.
What this model can establish
Fixed 25 °C, concentration used as activity, prescribed pH and free calcium. CO₂* groups dissolved CO₂ and carbonic acid. No gas exchange, precipitation kinetics or mineral depletion is calculated.
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Why include sodium or chloride when pH is adjusted?
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HISTORY THROUGH EVIDENCE
When a convenient formula was replaced
A calculation method can have a history of tested limits.
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