Derive equilibrium expressions for saturated solutions in terms of Ksp and calculate the solubility of an ionic substance from its Ksp value

Ksp is the solubility product constant or simply the solubility product. It is the product of the molar concentrations of the constituent ions, each raised to the power of its stoichiometric coefficient in the equilibrium equation. Consider a saturated solution of silver chloride that is in contact with a solid silver chloride. The solubility equilibrium can be represented as

Because salts such as AgCl are treated as strong electrolytes, all the AgCl that dissolve in water is assumed to dissociate completely into  and   ions. Thus, we can write the equilibrium constant for the dissociation of AgCl as

Sample Problem:

Calculate the solubility product constant for lead(II) chloride, if 50.0 mL of a saturated solution of lead(II) chloride was found to contain 0.2207 g of lead(II) chloride dissolved in it.

First, write the equation for the dissolving of lead(II) chloride and the equilibrium expression for the dissolving process.

Second, convert the amount of dissolved lead(II) chloride into moles per liter.

Third, create an “ICE” table.

Fourth, substitute the equilibrium concentrations into the equilibrium expression and solve for Ksp.