Solubility Product Relation

\[K_{sp}=[M^{m+}]^a[X^{x-}]^b\]

Variables

Kspsolubility product constant

Mcation concentration at equilibrium (mol/L)

Xanion concentration at equilibrium (mol/L)

astoichiometric coefficient of the cation

bstoichiometric coefficient of the anion

Description

What is this formula?

The solubility product relation defines the equilibrium constant for a slightly soluble ionic compound dissolving into its ions.

When to use it

Use this formula to calculate Ksp, estimate ion concentrations at equilibrium, or evaluate whether a sparingly soluble salt can remain dissolved under given conditions.

Example

For a salt MX2:

Ksp = [M][X]^2

Given:

[M] = 1.0×10^-4 mol/L

[X] = 2.0×10^-4 mol/L

Formula:

Ksp = M × X^2

Substitution:

Ksp = 1.0×10^-4 × (2.0×10^-4)^2

Result:

Ksp = 4.0×10^-12

Applications

Solubility equilibrium

Precipitation analysis

Analytical chemistry

Water chemistry

Inorganic chemistry education

Note

The solubility product expression is written using equilibrium ion activities. In many basic calculations, concentrations are used as an approximation. This approximation works best in dilute solutions where activity coefficients are close to unity. At higher ionic strength, activity corrections may be necessary.