Direct answer
The query does co32-- precipitate with ca2 corresponds to the solubility equilibrium of calcium carbonate. In water, Ca2+ and CO32− commonly form the sparingly soluble solid CaCO3(s), so precipitation is expected whenever their dissolved concentrations make the ion product exceed the solubility product constant.
\[ Q_{sp} = [\mathrm{Ca^{2+}}]\,[\mathrm{CO_3^{2-}}] \]
\[ \text{precipitation of CaCO}_3(s)\ \text{is favored when}\ Q_{sp} > K_{sp} \]
\[ \text{no precipitation when}\ Q_{sp} < K_{sp},\quad \text{equilibrium saturation when}\ Q_{sp} = K_{sp} \]
Equilibrium that controls precipitation
The relevant dissolution equilibrium is CaCO3(s) ⇌ Ca2+(aq) + CO32−(aq). At a fixed temperature, \(K_{sp}\) is constant for pure CaCO3(s), and the solution’s status depends on \(Q_{sp}\). For CaCO3, \(K_{sp}\) is very small (commonly on the order of \(10^{-9}\) at room temperature in dilute solutions), so moderate millimolar concentrations of the ions readily exceed the precipitation threshold.
Concentration mixing example
A common laboratory situation is mixing equal volumes of two solutions: one containing Ca2+ and the other containing CO32−. For equal-volume mixing, each concentration halves immediately after mixing (before any precipitation changes them).
\[ [\mathrm{Ca^{2+}}]_{\text{mix}} = \frac{[\mathrm{Ca^{2+}}]_0}{2},\qquad [\mathrm{CO_3^{2-}}]_{\text{mix}} = \frac{[\mathrm{CO_3^{2-}}]_0}{2} \]
\[ Q_{sp,\text{mix}} = \left(\frac{[\mathrm{Ca^{2+}}]_0}{2}\right)\left(\frac{[\mathrm{CO_3^{2-}}]_0}{2}\right) = \frac{[\mathrm{Ca^{2+}}]_0[\mathrm{CO_3^{2-}}]_0}{4} \]
For example, if both starting solutions are \(0.010\ \mathrm{mol\cdot L^{-1}}\), then
\[ Q_{sp,\text{mix}} = \frac{(0.010)(0.010)}{4} = 2.5\times 10^{-5} \]
A value like \(2.5\times 10^{-5}\) is far larger than a \(K_{sp}\) on the order of \(10^{-9}\), so CaCO3(s) formation is strongly favored under these conditions.
Threshold relationship between ions
The precipitation boundary can be written as a concentration relationship:
\[ Q_{sp} = K_{sp}\ \Longleftrightarrow\ [\mathrm{CO_3^{2-}}] = \frac{K_{sp}}{[\mathrm{Ca^{2+}}]} \]
Small \(K_{sp}\) means the required carbonate concentration for precipitation can be very small when calcium is present at typical analytical concentrations. The same relationship shows the common-ion effect: raising one ion lowers the equilibrium concentration of the other in solution once CaCO3(s) is present.
Carbonate speciation and pH effects
The carbonate ion concentration in water is not fixed solely by “added carbonate,” because carbonate participates in acid–base equilibria. Lower pH converts CO32− into bicarbonate (and ultimately carbonic acid/CO2), decreasing \([\mathrm{CO_3^{2-}}]\) and therefore decreasing \(Q_{sp}\).
\[ \mathrm{CO_3^{2-}} + \mathrm{H^+} \rightleftharpoons \mathrm{HCO_3^-} \qquad \mathrm{HCO_3^-} + \mathrm{H^+} \rightleftharpoons \mathrm{H_2CO_3} \rightleftharpoons \mathrm{CO_2} + \mathrm{H_2O} \]
Under acidic conditions, CaCO3(s) can dissolve because carbonate is removed from solution as bicarbonate/CO2, shifting the dissolution equilibrium to the right. Under basic conditions (higher CO32− fraction), precipitation becomes more likely.
Visualization: precipitation region in concentration space
Summary table of controlling factors
| Factor | Effect on \(Q_{sp} = [\mathrm{Ca^{2+}}][\mathrm{CO_3^{2-}}]\) | Typical outcome for CaCO3(s) |
|---|---|---|
| Higher dissolved Ca2+ | Raises \(Q_{sp}\) | Precipitation more likely |
| Higher dissolved CO32− | Raises \(Q_{sp}\) | Precipitation more likely |
| Lower pH (more H+) | Lowers \([\mathrm{CO_3^{2-}}]\) by conversion to HCO3−/CO2 | Precipitation suppressed; existing solid tends to dissolve |
| Higher pH (more basic) | Raises the fraction present as CO32− | Precipitation promoted |
| Dissolved CO2 (carbonation) | Shifts carbonate to bicarbonate/carbonic acid, reducing CO32− | Precipitation less likely; solid more soluble |
Solubility-rule heuristic and its limits
A standard aqueous solubility rule states that most carbonates are insoluble except those of alkali metals and ammonium. Calcium carbonate fits the “sparingly soluble” category, consistent with precipitation under many mixing conditions. The equilibrium criterion \(Q_{sp}\) versus \(K_{sp}\) remains the rigorous statement, especially when pH and dissolved CO2 alter the free CO32− concentration.