By John Brennan | Updated Aug 30, 2022
When carbon dioxide dissolves in water, it forms carbonic acid (H₂CO₃). This acid can dissociate to yield bicarbonate (HCO₃⁻) or carbonate (CO₃²⁻). Calcium ions in the water will react with these species to produce either soluble calcium bicarbonate or insoluble calcium carbonate. For environmental and water‑quality testing, calculating the bicarbonate concentration from total alkalinity and pH is a common requirement.
Total alkalinity is usually expressed in milligrams per liter of CaCO₃. Divide the value by 100 000 g mol⁻¹ to obtain moles per liter (molarity). This step yields the baseline concentration that will be refined in the next stages.
The general alkalinity formula is:
2 × Total Alkalinity = [HCO₃⁻] + 2[CO₃²⁻] + [OH⁻]
With the carbonate concentration expressed as [CO₃²⁻] = (K₂ [HCO₃⁻])/[H⁺], where K₂ = 5.6 × 10⁻¹¹, the equation becomes:
2 × Total Alkalinity = [HCO₃⁻] + 2 × (K₂ [HCO₃⁻]/[H⁺]) + [OH⁻]
Using the relationship [H⁺] = 10^(−pH) and the hydroxide concentration [OH⁻] = 10^(−14 + pH), the algebraic solution is:
[HCO₃⁻] = (2 × Total Alkalinity – 10^(−14 + pH)) / (1 + 2K₂ × 10^(pH))
Insert the molarity of CaCO₃ obtained in Step 1 into the formula above. The result is the bicarbonate concentration in moles per liter.
The derivation assumes that calcium and carbonate species dominate the alkalinity. If other alkaline components—such as ammonia—are present, a more sophisticated model is required. Refer to the first link under the “References” section for additional guidance.
