Second pKₐ of Carbonic Acid

At pH 10.33 a water is half bicarbonate and half carbonate; below pH 8.3 the carbonate fraction is negligible, which is exactly why the phenolphthalein endpoint at pH 8.3 is used to split total alkalinity into its carbonate and bicarbonate parts. That two-endpoint titration — phenolphthalein at 8.3, methyl orange at 4.5 — is a piece of practical chemistry built directly on the two pK_a values of a single acid.

The wide separation between pK_a1 = 6.35 and pK_a2 = 10.33 is what makes carbonate chemistry tractable: nearly four units apart means the two equilibria barely overlap and can be treated one at a time. Lime softening exploits the upper one deliberately, raising pH past 10.3 to convert bicarbonate to carbonate and force calcium out of solution as CaCO₃, then recarbonating to bring the treated water back down to a stable pH.