We now address how the alkalinity changes with pH. One may expect that alkalinity decreases with pH since a decreasing pH increases proton concentration.

Again using the model that all proton activity comes from the presence of CaCO₃

[alk] = [HCO₃^-] + 2[CO₃^2-] + [OH^-] – [H⁺]

where [alk] (mole/L) is the effective alkali concentration.

Henry’s Law solubility will "fix" the CO₂ (aq) concentration at

We need to get the relative amounts of the HCO₃^- and CO₃^2- carbonate species. These are obtained using the "alpha" as functions of pH

Also, [OH^-] and [H⁺] are always related through the water equilibrium

with the equilibrium constant

Here is how we do the calculation; convert the alkalinity equation to be a function only of [H⁺], total CO₂ (aq), and the acid equilibrium constants. I will abbreviate by using the "alpha"

The total CO₂ (aq) is obtained using the first "alpha" expression

and [CO₂ (aq)] is obtained from Henry’s Law.

The calculation is complicated, but can be performed on a spreadsheet program. The results are graphed below.

This page edited Thursday, December 21, 2006

This page was last edited Thursday, December 21, 2006