Lime Dose for Softening (as CaCO₃)

Lime softening is bookkeeping in a single currency. Free carbon dioxide, bicarbonate alkalinity and magnesium all consume lime, they are all restated as milligrams per litre of CaCO₃ so that they can be added at all, and the sum plus an excess is the dose. A groundwater with 22.7 mg/L of CO₂ as CaCO₃, 180 of alkalinity, 50 of magnesium to be removed and the customary 62.5 of excess needs 315 mg/L as CaCO₃ — which is emphatically not what the plant buys. Converted at equivalent weights that is about 177 mg/L as CaO if the plant feeds quicklime or 233 mg/L as Ca(OH)₂ if it feeds hydrated lime, and both figures still have to be divided by the product's purity, typically 90 % for quicklime and 93–95 % for hydrated lime.

Each term is worth understanding separately, because two of them can be argued with. The CO₂ term buys nothing at all: free carbon dioxide eats lime and precipitates no hardness whatever, which makes aerating a groundwater ahead of the softener one of the cheapest chemical savings available in a treatment plant. The magnesium term is there only because Mg(OH)₂ will not precipitate below about pH 10.6, so removing magnesium costs the lime needed to drive the pH that high — leave magnesium in, as selective softening does, and the term is zero. The excess, usually 1.25 meq/L or 62.5 mg/L as CaCO₃, is what gets the reaction to actually finish inside a basin's detention time; it is not stoichiometry and it does not come back. Treat the whole result as the starting point for a jar test rather than a setpoint: stoichiometry says what the water demands and nothing about how readily it gives it up, and the softened water leaves at pH 10 or above, supersaturated and aggressive, so recarbonation is part of the process rather than a refinement of it.