AP Chemistry · Unit 7 · Topic 7.11
Introduction to Solubility Equilibria
A little solid at the bottom of a beaker can be evidence of equilibrium, not failed mixing. Dissolution and crystallization may be exchanging ions continuously at the solid surface.
Write the dissolution reaction
For the model salt \(MX_2(s)\rightleftharpoons M^{2+}(aq)+2X^-(aq)\), the solubility product is \(K_{sp}=[M^{2+}][X^-]^2\) in the dilute concentration approximation. The solid does not appear explicitly because its activity is treated as one. A saturated solution in contact with that solid satisfies Qsp = Ksp.
Solubility and Ksp are not synonyms
Molar solubility s is the moles of solid formula units that dissolve per liter to reach saturation under stated conditions. It has units of molarity. Ksp is an equilibrium ratio determined by the dissolution equation and temperature. Their numerical relationship depends on stoichiometry and on any ions already present.
Connect formula units to ions
| Salt model | Ion concentrations | Ksp relation |
|---|---|---|
| MX | s and s | \(s^2\) |
| MX₂ | s and 2s | \(4s^3\) |
| M₂X₃ | 2s and 3s | \(108s^5\) |
These different powers explain why comparing raw Ksp values across different salt stoichiometries can mislead you about molar solubility.
A fully worked saturation calculation
Let the hypothetical MX₂ salt have \(K_{sp}=3.20\times10^{-11}\). In pure water, [M²⁺] = s and [X⁻] = 2s, so
Thus [X⁻] = 4.00 × 10⁻⁴ M. If the formula mass is 150 g/mol, a 0.250 L sample holds \(sV(150)=0.00750\) g dissolved at saturation, assuming no competing chemistry.
Decide whether a precipitate can form
Calculate ion concentrations after mixing, including dilution, then calculate Qsp. If Qsp exceeds Ksp, precipitation is thermodynamically favored. If Qsp is smaller, the solution is unsaturated with respect to that solid. It can dissolve additional solid if some is added; “shift toward dissolution” does not create nonexistent solid reactants.
Interpret cloudy and clear samples
Cloudiness suggests suspended particles but does not identify their composition. A clear sample may be unsaturated, saturated without visible excess solid, or temporarily supersaturated. Filter an equilibrated suspension before measuring dissolved ions, control temperature, and avoid counting suspended particles as dissolved material.
State what the model leaves out
Ion pairing, complex formation, acid–base reactions, and nonideal activities can change the relation between total dissolved material and free-ion concentrations. Ksp refers to the free species in its expression. The simple s calculation is appropriate only when those additional processes are negligible or explicitly accounted for.
Practice with answers
- For MX₂, is [X⁻] equal to s in pure water? No; it is 2s.
- If Qsp = 10Ksp, which process is favored? Precipitation, provided nucleation can occur.
- Does adding excess solid change Ksp at fixed temperature? No.
Factual reference: OpenStax Chemistry 2e, 15.1. The hypothetical salt values, table, worked example, and questions are original.
Official curriculum reference: College Board AP Chemistry course page. The explanation and worked example are independently written for this study site.