Randy Holmes-Farley
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Hi Randy,
Is this calculation a simple mathematical formula?
It is at a single temperature and salinity. In the discussion below the K1 and K2 and KH values are a function of temp and salinity:
Chemistry And The Aquarium: The Relationship Between Alkalinity And pH ? Advanced Aquarist | Aquarist Magazine and Blog
from it:
Carbonate alkalinity (Ac) is mathematically defined as:
1. Ac = [HCO3-] + 2[CO3--]
Where [X] means the concentration of species X. Carbonate (CO3--) is counted twice because it contributes two units of alkalinity for each unit of concentration. The relationship between the amount of bicarbonate and carbonate to pH is well defined if the system is at equilibrium with the atmosphere. Substituting these known relationships into equation 1, we get:
2. Ac = (K1KHPCO2 / [H+]) + 2(K1K2KHPCO2 / [H+]2)
where pCO2 is the concentration CO2 in the air. Current carbon dioxide concentrations are around 350 ppm and have been rising with time, from less than 300 ppm in preindustrial times. KH is the Henry's law constant for CO2(which describes the solubility of CO2 in water from the air to form carbonic acid, H2CO3), K1 is the first dissociation constant for H2CO3 (describing the dissociation of H2CO3 to HCO3-), and K2 is the second dissociation constant for H2CO3 (describing the dissociation of HCO3- to CO3--).

