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Ksp describes the equilibrium between a sparingly soluble solid and its dissolved ions. Its expression follows the balanced dissolution equation, with stoichiometric coefficients used as exponents. For a given salt, algebraic substitution relates Ksp to molar solubility; comparisons of Ksp are meaningful only for salts with the same ion ratio. The reaction quotient, Qsp, indicates whether a solution is undersaturated, at equilibrium, or prone to precipitation. Adding a common ion shifts dissolution toward the solid and reduces solubility without changing Ksp. Solubility can also change when pH removes an anion, when temperature or ionic strength changes, or when complex ions form. These principles support selective and fractional precipitation for separating ions.