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Does PO4^3− Dissolve with Ca^2+? Calcium Phosphate and Ksp

In aqueous solution, does PO4^3− remain dissolved when Ca2+ is present, or does calcium phosphate precipitate under typical concentrations?

Subject: General Chemistry Chapter: Solubility and Complex Ion Equilibria Topic: Criteria for Precipitation and Its Completeness Answer included
does po43- dissolve with ca2 calcium phosphate Ca3(PO4)2 solubility product Ksp ionic product Qsp precipitation common ion effect
Accepted answer Answer included

The query “does po43- dissolve with ca2” concerns whether phosphate ions stay in solution when calcium ions are present. In general chemistry, the relevant idea is that many calcium phosphates are sparingly soluble, so mixtures containing appreciable \(\mathrm{Ca^{2+}}\) and \(\mathrm{PO_4^{3-}}\) tend to form a precipitate unless concentrations are extremely low or phosphate is largely protonated at low pH.

Calcium phosphate precipitation is favored in water because the solubility product is very small. The mixture remains clear only when the ionic product \(Q_{sp}=[\mathrm{Ca^{2+}}]^3[\mathrm{PO_4^{3-}}]^2\) is less than \(K_{sp}\); otherwise a solid phase forms until equilibrium is restored.

Relevant equilibrium for phosphate with calcium

A common sparingly soluble solid that represents the “calcium + phosphate” endpoint in introductory solubility problems is tricalcium phosphate:

\[ \mathrm{Ca_3(PO_4)_2(s)\rightleftharpoons 3\,Ca^{2+}(aq)+2\,PO_4^{3-}(aq)} \]

The associated solubility product expression is

\[ K_{sp}=\big[\mathrm{Ca^{2+}}\big]^3\big[\mathrm{PO_4^{3-}}\big]^2 \]

Different references may quote different numerical values for “calcium phosphate” because multiple solid phases exist and conventions differ. The important qualitative fact is that the effective \(K_{sp}\) is extremely small, so precipitation is usually expected when millimolar-to-molar ion concentrations are mixed.

Precipitation criterion using the ionic product

A mixture of ions has an ionic product (reaction quotient for the solubility equilibrium)

\[ Q_{sp}=\big[\mathrm{Ca^{2+}}\big]^3\big[\mathrm{PO_4^{3-}}\big]^2 \]

The comparison between \(Q_{sp}\) and \(K_{sp}\) determines the outcome:

Comparison Interpretation in solution Observable result
\(Q_{sp} < K_{sp}\) Ion product is below the solubility limit; the solution can accommodate more dissolved ions. No precipitate; ions remain dissolved.
\(Q_{sp} = K_{sp}\) Saturation with respect to the solid phase. Equilibrium at the solubility limit; solid may be present without net change.
\(Q_{sp} > K_{sp}\) Ion product exceeds the solubility limit; the dissolved state is not stable. Precipitation occurs until \(Q_{sp}\) decreases to \(K_{sp}\).

Illustrative concentration check for “does po43- dissolve with ca2”

A typical classroom mixing situation uses millimolar concentrations. Consider equal volumes of \(0.010\,\mathrm{M}\) \(\mathrm{CaCl_2}\) and \(0.010\,\mathrm{M}\) \(\mathrm{Na_3PO_4}\). After mixing, the initial (diluted) ion concentrations are

\[ [\mathrm{Ca^{2+}}]_0=0.0050\,\mathrm{M},\qquad [\mathrm{PO_4^{3-}}]_0=0.0050\,\mathrm{M} \]

The ionic product is

\[ Q_{sp}=(0.0050)^3(0.0050)^2=(5.0\times 10^{-3})^5=3.1\times 10^{-12} \]

An extremely small \(K_{sp}\) (many orders of magnitude smaller than \(10^{-12}\)) makes \(Q_{sp}\gg K_{sp}\) under these conditions, so precipitation is expected. The solid formed is commonly represented as \(\mathrm{Ca_3(PO_4)_2(s)}\), and dissolved phosphate and calcium decrease until the saturation condition is met.

Solubility & Precipitation Dashboard A premium scientific visualization comparing Qsp and Ksp for calcium phosphate, indicating the precipitation threshold. 10⁻³³ 10⁻²⁷ 10⁻²¹ 10⁻¹⁵ 10⁻⁹ Ion Product (Log Scale) PRECIPITATION ZONE (Qsp > Ksp) K Solubility Limit (Very Small) Qsp Typical Mixing Solution State: CLEAR CLOUDY
The dashboard displays the logarithmic scale of ion activity. For calcium phosphate, the ionic product \(Q_{sp}\) in typical mixtures resides far beyond the solubility limit (\(K_{sp}\)), resulting in the characteristic cloudy precipitate of \(\mathrm{Ca_3(PO_4)_2}\).

Phosphate speciation and pH effects

The symbol \(\mathrm{PO_4^{3-}}\) is the fully deprotonated form of phosphoric acid and is most significant only at high pH. In many aqueous mixtures near neutral pH, phosphate exists largely as \(\mathrm{H_2PO_4^-}\) and \(\mathrm{HPO_4^{2-}}\). The acid–base equilibria are

\[ \mathrm{H_3PO_4 \rightleftharpoons H^+ + H_2PO_4^-},\qquad \mathrm{H_2PO_4^- \rightleftharpoons H^+ + HPO_4^{2-}},\qquad \mathrm{HPO_4^{2-} \rightleftharpoons H^+ + PO_4^{3-}} \]

Lower pH reduces \([\mathrm{PO_4^{3-}}]\) by protonation, which lowers \(Q_{sp}\) and can increase apparent solubility. Higher pH increases the fraction of \(\mathrm{PO_4^{3-}}\), raising \(Q_{sp}\) and favoring precipitation with \(\mathrm{Ca^{2+}}\).

Practical conclusion for mixtures of Ca2+ and phosphate

Under typical general-chemistry concentrations, \(\mathrm{Ca^{2+}}\) and phosphate do not remain freely dissolved together; a calcium phosphate solid phase forms until the solution satisfies \(\big[\mathrm{Ca^{2+}}\big]^3\big[\mathrm{PO_4^{3-}}\big]^2=K_{sp}\). Clear solutions are most plausible only under strongly acidic conditions (phosphate protonation), extremely dilute ion concentrations, or specialized conditions where the effective free-ion concentrations are suppressed.

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