Chapter 15 · Chemical Equilibrium
15.11The Solubility-Product Constant
11 min · two checks
Predict
What is K_sp for PbCl₂(s) ⇌ Pb²⁺ + 2 Cl⁻?
The idea
- Write K_sp.
- Estimate molar solubility for a simple 1:1 salt.
K_sp is the equilibrium constant for dissolving an ionic solid. AgCl(s) ⇌ Ag⁺ + Cl⁻ has K_sp = [Ag⁺][Cl⁻]. If no other source of those ions is present, each equals the molar solubility s, so K_sp = s² and s = √K_sp. For PbCl₂, K_sp = [Pb²⁺][Cl⁻]² = (s)(2s)² = 4s³. The algebra follows the stoichiometry. You cannot compare a 1:1 salt’s K_sp with a 1:2 salt’s K_sp by eye and declare a winner; the powers differ.
A solution is unsaturated if Q < K_sp, saturated at equilibrium if Q = K_sp, and ready to precipitate if Q > K_sp. Adding a common ion, such as extra Cl⁻ from NaCl into a solution of AgCl, lowers the solubility of AgCl. That is Le Châtelier applied to K_sp, and it is why some precipitates wash better in a solution that already contains one of their ions — carefully, so you do not redissolve them another way.
Keep these
- K_sp includes dissolved ions only, with coefficients as exponents.
- For AgCl, s = √K_sp. For PbCl₂, K_sp = 4s³.
- Q > K_sp means a precipitate can form.
Worked path
K_sp of BaSO₄ is 1.1 × 10⁻¹⁰. Estimate the molar solubility.
Observe
BaSO₄(s) ⇌ Ba²⁺ + SO₄²⁻. K_sp = s².