Consider an original toy AB salt model with stipulated at fixed temperature and fixed activity coefficient product. This is a conditional concentration constant, not measured data for calcium carbonate or any identified material. A stock contains A cations and X anions; another contains Y cations and B anions. All four ions have unit electric charge magnitude. Only AB can form a solid; X and Y remain spectator ions. Assume full dissociation, no other chemical reactions, and a mixed volume equal to the sum of the initial volumes.
Mix two stocks, each of volume ,, each at molar concentration of its indicated salt. Before any precipitation, the mixed volume is , soMultiplying the two stock concentrations would overestimate the mixed ion product by a factor of four. The saturation threshold is .
If , mixing gives : no AB precipitate is favored. If , mixing gives . Suppose nucleation occurs and bulk AB solid remains at chemical equilibrium. Equal starting inventories and one-to-one stoichiometry require equal remaining concentrations, henceFor two portions in the second case, each reacting ion starts with ; the final chemical solution retains of each, and of AB enters the solid. The respective X and Y inventories stay at . Exactly half of each reacting inventory precipitates in this toy model.
The chemical equilibrium calculation adds a phase constraint to the inventory balance. Write and . In the equilibrated bulk model,When , the last condition requires saturation; when , the inventory can leave an undersaturated chemical solution. Together these give . This excludes a persistent supersaturated solution by its explicit chemical equilibrium assumption; it does not model a nucleation delay.
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