Solubility and other equilibria
Equilibrium ideas explain why some salts barely dissolve, how kidney stones form, and how complex ions colour solutions.
Solubility equilibria
A sparingly soluble salt sets up an equilibrium with its ions: \(\text{AgCl}(s) \rightleftharpoons \text{Ag}^+(aq) + \text{Cl}^-(aq)\). The solubility product is \(K_{sp} = [\text{Ag}^+][\text{Cl}^-] = 1.8 \times 10^{-10}\). Small \(K_{sp}\) values mean low solubility.
K_{sp} = [\text{Ag}^+][\text{Cl}^-]Calculating solubility
If \(s\) mol/L of AgCl dissolves, \([\text{Ag}^+] = [\text{Cl}^-] = s\), so \(s^2 = 1.8 \times 10^{-10}\) and \(s \approx 1.3 \times 10^{-5}\) M. For salts like \(\text{CaF}_2\), \(K_{sp} = s(2s)^2 = 4s^3\): the coefficients change the algebra.
Predicting precipitation
Compare the ion product \(Q\) with \(K_{sp}\). If \(Q > K_{sp}\), the solution is supersaturated and a precipitate forms until \(Q = K_{sp}\). If \(Q < K_{sp}\), more solid can dissolve. Chemists use this to separate ions selectively.
The common ion effect
Adding an ion already in the equilibrium reduces a salt's solubility, by Le Chatelier's principle. AgCl is much less soluble in salt water than in pure water, because the added chloride pushes the equilibrium toward the solid. This principle is used to precipitate metals from wastewater.
Kidney stones and teeth
Kidney stones often form when calcium oxalate's ion product in urine exceeds its \(K_{sp}\). Tooth enamel, hydroxyapatite, dissolves in acid because \(\text{H}^+\) removes its phosphate and hydroxide ions; fluoride converts it to the less soluble fluorapatite, which is why fluoride protects teeth.
Complex ions
Metal ions can bind molecules or ions (ligands) to form complex ions, such as deep blue \(\text{Cu(NH}_3)_4^{2+}\). Formation constants are often very large. Complex formation can dissolve otherwise insoluble salts: AgCl dissolves in ammonia because \(\text{Ag(NH}_3)_2^+\) forms.
Coupled equilibria in nature
Ocean chemistry links several equilibria: \(\text{CO}_2\) dissolving, carbonic acid ionising, and calcium carbonate dissolving. Adding \(\text{CO}_2\) shifts this whole chain, lowering carbonate concentration and making shell formation harder, which connects equilibrium chemistry to climate science.
Common mistakes
Forgetting coefficients when setting up \(K_{sp}\) expressions. Including the solid in \(K_{sp}\). Comparing solubilities of salts with different formulas by \(K_{sp}\) alone; compute \(s\) instead.
Key takeaways
\(K_{sp}\) describes sparingly soluble salts; solve for molar solubility using the formula's coefficients. Compare \(Q\) with \(K_{sp}\) to predict precipitation. Common ions reduce solubility. Complex ions and coupled equilibria explain dissolving, teeth protection, and ocean chemistry.
Flashcard
K_{sp}
Check your understanding
Why is AgCl less soluble in a NaCl solution than in pure water?