The mathematical product of ion concentrations raised to the power of their stoichiometric coefficients where the ions are released into solution by a sparingly soluble ionic compound.
Explanation
Many metal ionic compounds are sparingly soluble in water. When added to water, most of the compound remains an insoluble solid, but some ions are released into the water to form a dilute solution. Even compounds we would often describe as insoluble do often in fact dissolve to a small extent.
A sparingly soluble salt in contact with water maintains an equilibrium between the solid and its ions.
In simple cases where there are no common ions or competing equilibria, the ion concentrations depend only on the equilibrium constant for the particular salt. When we talk about solubility equilibria we always write the equilibrium with the solid on the left. For example:
Ba(IO3)2 (s) 
Ba2+(aq) + 2 IO3-(aq)
We could write the equilibrium constant for this reaction as:
Keq = [Ba2+ ] [IO3-]2 / [Ba(IO3)2 ]
The equilibrium constant expression for an insoluble salt is written following the same rules as for any other equilibrium. Because so very little of it dissolves, the number of moles of solid barium iodate per liter of water is the same at the start of the reaction as at equilibrium. Since [Ba(IO3)2 ] is a constant, it 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
Use 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 l-3. For AgCl units would be M2 or mol2 l-2 and for Gd2(SO4)3 M5 or mol5 l-5
Ksp Values for Some Precipitates
Silver chloride, AgCl, 1.8 x 10-10Aluminum hydroxide, Al(OH)3, 2 x1 0-32
Barium carbonate, BaCO<>3, 5 x 10-9
Barium iodate, Ba(IO3)2, 1.6x10-9
Barium sulfate, BaSO4, 1.3 x 10-10
Iron (II) hydroxide, Fe(OH)2, 8 x 10-16
Iron (III) hydroxide, Fe(OH)3, 4 x 10-38
Iron sulfide, FeSi, 6 x 10-18
Lead chromate, PbCrO4, 1.8 x 10-14
Lead hydroxide, Pb(OH)2, 2.5 x 10-16
Lead sulfide, PbS, 7 x 10-28
Lead sulfate, PbSO4, 1.6 x 10-8
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