Solubility Product Ksp Defined
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The solubility product Ksp is the equilibrium constant for a sparingly soluble solid dissolving into ions, the product of ion concentrations raised to coefficients, the solid omitted.
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For AgCl(s) ⇌ Ag+(aq) + Cl−(aq), Ksp = [Ag+][Cl−].
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Ksp describes a solid at its solubility limit — it says nothing about an unsaturated solution.