The solubility product, Ksp, applies in situations where salts do not fully dissolve in a solvent. The solvent is generally water. A substance's solubility product is the mathematical product of its dissolved ion concentrations raised to the power of their stoichiometric coefficients. This definition can be a little hard to understand on first reading. It's easier to see how things work with examples, as you'll see below.
Significance
The smaller the solubility product of a substance, the lower is its solubility.
The solubility product is a heterogeneous equilibrium constant, a specific form of the equilibrium constant. It is relevant in saturated solutions in which an ionic compound has not fully dissolved.
Solubility products change with temperature, so the temperature at which a solubility product was measured must always be quoted.
Example 1
Consider an ionic compound A3B that partly dissolves in water. Most of the compound does not dissolve.
As usual, we write the concentrations of the ions as [A] and [B].
The solubility product, Ksp is given by:
Ksp = [A]3[B]
Example 2
The salt A2B5 partly dissolves in solution.
The solubility product, Ksp is given by:
Ksp = [A]2[B]5
Explanation
Many ionic compounds do not fully dissolve in water. When added to water, some of the salt continues to exist as an ionic solid, while some ions are released into the water to form a very dilute solution. Even salts we would describe as insoluble often dissolve to a slight extent.
In a saturated solution there is an equilibrium between the solid and its dissolved ions.
In simple cases, where there are no common ions or competing equilibria, the ion concentrations depend only on the equilibrium constant of the particular salt. When we talk about solubility equilibria we always write the equilibrium with the solid on the left. For example, barium iodate:
Ba(IO3)2 (s) 
Ba2+(aq) + 2 IO3-(aq)
We could write the equilibrium constant for this reaction as:
The equilibrium constant expression for an insoluble salt is written following the same rules as for any other equilibrium.
Since [Ba(IO3)2 ] by convention is assigned a value of 1, because Ba(IO3)2 is an undissolved solid, this value has no effect on the equilibrium, and can be incorporated into the equilibrium constant for the reaction. The equilibrium constant is called the solubility product, Ksp.
Ksp = [Ba2+ ] [IO3- ]2
Uses of Ksp
The smaller the solubility product of a substance, the lower is its solubility.
The solubility product can be used to predict whether a precipitate will form when two solutions are mixed.
Consider the equilibrium: PbCl2 Pb2+ + 2Cl-.
If the concentration of Cl- was increased by adding HCl, the solubility product would be exceeded and PbCl2 would be precipitated from solution until equilibrium was restored.
Units of Solubility Product
Solubility products have units of concentration raised to the power of the stoichiometric coefficients of the ions in the equilibrium. So the solubility product of PbCl2 has units of M3 or mol3 dm-9.
For AgCl units would be M2 or mol2 dm-6, and for Gd2(SO4)3 M5 or mol5 dm-10.
| Ionic Compound | Formula | Ksp at 298 K |
|---|---|---|
| aluminum hydroxide | Al(OH)3 | 2 x 10-32 |
| barium carbonate | BaCO3 | 5 x 10-9 |
| barium sulfate | BaSO4 | 1.1 x 10-10 |
| calcium hydroxide | Ca(OH)2 | 5 x 10-6 |
| iron(III) hydroxide | Fe(OH)3 | 3 x 10-39 |
| lead chromate | PbCrO4 | 2 x 10-14 |
| lead sulfide | PbS | 2 x 10-28 |
| magnesium carbonate | MgCO3 | 1 x 10-5 |
| silver(I) chloride | AgCl | 2 x 10-10 |