Definition of Solubility Product, Ksp

A substance's solubility product, Ksp, is the mathematical product of its dissolved ion concentrations raised to the power of their stoichiometric coefficients. Solubility products are relevant when a sparingly soluble ionic compound releases ions into solution. A solubility product is a specific form of an equilibrium constant. Solubility products change with temperature, so the temperature at which a solubility product was measured must always be quoted.

Significance

The smaller the solubility product of a substance, the lower is its solubility.

Examples

The definition above can be a little hard to understand on first reading. It's easier to see how things work with examples.

Example 1

Consider a sparingly soluble ionic compound, A3B, which releases ions into a solution.

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 sparingly soluble ionic compound, A2B5, releases ions into a solution.

The solubility product, Ksp is given by:

Ksp = [A]2[B]5

Explanation

Many ionic compounds are sparingly soluble in water. When added to water, most of the compound remains as an insoluble salt, but some ions are released into the water to form a dilute solution. Even compounds we would describe as insoluble often dissolve to a slight 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, barium iodate:

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

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 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 insoluble (i.e. sparingly soluble) salts at 298 K:

Silver chloride, AgCl, 1.8 x 10-10
Aluminum hydroxide, Al(OH)3, 2 x1 0-32
Barium carbonate, BaCO3, 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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