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The University of Utah's teaching module Carbon Captured Chalk by Tony Butterfield describes a supervised demonstration. Its Materials and Methods uses a balance, weighing boats, spatula, separate centrifuge tubes, a volume-measuring vessel and filter paper. Sodium carbonate and calcium chloride are dissolved separately in water before mixing. The reported readout is an initially opaque mixture followed by a milky dispersion of fine solid particles; filtration retains the chalk-like product, which is then dried. The module also proposes observing drops together on a slide using an optical microscope.^[ref]

The handout does not report blank trials. Useful additional controls would retain each starting chemical solution separately, mix each with water, and pass water alone through the same filter. A new solid only in the combined sample would support a mixing-dependent chemical reaction; these are proposed comparisons, not reported results. Residue from a filter blank would instead flag contamination.

Cloudiness plus a retained solid supports phase separation; appearance alone cannot establish composition, a particular crystal polymorph, quantitative yield or the solubility product. Fine solid particles may pass through a filter, and retained liquid can leave dissolved salts on drying. Identifying calcium carbonate needs additional chemical or structural evidence. The teaching source supplies no measured ion products, instrument-calibrated cloudiness series or equilibration test. Its concentrated demonstration therefore illustrates precipitation without validating the toy model's conditional constant or proving complete removal of dissolved calcium.

The ion product evaluates the same dissolved-ion thermodynamic activity product as the solubility product, but at the current composition rather than necessarily at chemical equilibrium. For AB, $Q_{\mathrm{sp}}=a_{\mathrm{A}}{a}_{\mathrm{B}}$; its concentration counterpart is $Q_c=c_{\mathrm{A}}{c}_{\mathrm{B}}$. Compare $Q_c$ with $K_{\mathrm{sp},c}$ only under compatible activity coefficient assumptions.^[ref]

For other stoichiometries, use the dissolution coefficients as powers: ${\mathrm{AB}}_2(s)\rightleftharpoons {\mathrm{A}}^{2+}(aq)+2{\mathrm{B}}^{-}(aq)$ gives $Q_{\mathrm{sp}}=a_{\mathrm{A}}{a}_{\mathrm{B}}^2$. A solubility product is not itself the molar concentration dissolved; even in the ideal AB model in pure water, that concentration is $\sqrt{K_{\mathrm{sp},c}}$.

Consider an original toy AB salt model with $K_{\mathrm{sp},c}=10^{-8}{\mathrm{M}}^2$ 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 $V$,, each at molar concentration $C$ of its indicated salt. Before any precipitation, the mixed volume is $2V$, soMultiplying the two stock concentrations would overestimate the mixed ion product by a factor of four. The saturation threshold is $C=2\sqrt{K_{\mathrm{sp},c}}=2\times 10^{-4}\mathrm{M}$.

If $C=10^{-4}\mathrm{M}$, mixing gives $Q_{c,0}=2.5\times 10^{-9}{\mathrm{M}}^2<K_{\mathrm{sp},c}$: no AB precipitate is favored. If $C=4\times 10^{-4}\mathrm{M}$, mixing gives $Q_{c,0}=4\times 10^{-8}{\mathrm{M}}^2>K_{\mathrm{sp},c}$. 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 $10\mathrm{mL}$ portions in the second case, each reacting ion starts with $4\mu \mathrm{mol}$; the final $20\mathrm{mL}$ chemical solution retains $2\mu \mathrm{mol}$ of each, and $2\mu \mathrm{mol}$ of AB enters the solid. The respective X and Y inventories stay at $4\mu \mathrm{mol}$. Exactly half of each reacting inventory precipitates in this toy model.

The chemical equilibrium calculation adds a phase constraint to the inventory balance. Write $x=n_{\mathrm{AB},s}/(2V)$ and $c=C/2-x$. In the equilibrated bulk model,When $x>0$, the last condition requires saturation; when $x=0$, the inventory can leave an undersaturated chemical solution. Together these give $x=\max \{0,C/2-\sqrt{K_{\mathrm{sp},c}}\}$. This excludes a persistent supersaturated solution by its explicit chemical equilibrium assumption; it does not model a nucleation delay.

A supersaturated solution has an ion product above the relevant solubility product. It can persist through metastability: nucleation must first create a sufficiently large new solid region. Added surfaces, impurities and mixing history can affect that barrier. Therefore a clear sample during a finite observation does not prove undersaturation, and visible cloudiness does not measure the ion product.