What is the mathematical expression for Ksp of a compound MX2?

To derive the expression for the solubility product constant (Ksp) of the compound MX2, we must consider the dissociation of that compound in solution. When MX2 dissolves, it separates into one neutral M cation and two X anions:

[ \text{MX}_2 (s) \leftrightarrow \text{M}^{2+} (aq) + 2 \text{X}^- (aq) ]

Letting the solubility of MX2 be represented by ( x ), we can see the following stoichiometric relationships after dissociation:

• The concentration of the M cation will be ( x ) because one formula unit of MX2 produces one M^2+ ion.
• The concentration of each X anion will be ( 2x ) because one formula unit produces two X^- ions.

Now, the expression for Ksp is derived from the product of the concentrations of the ions, each raised to the power of its stoichiometric coefficient from the balanced equation:

[ Ksp = [\text{M}^{2+}][\text{X}^-]^2 ]

Substituting the expressions for the concentrations into this equation, we get