Ksp

Meaning: Ksp describes the equilibrium between an undissolved ionic solid and its ions in a saturated solution. The solid is left out of the expression because its concentration is constant. Ksp changes only with temperature. Adding a common ion shifts the ion concentrations and lowers solubility, but Ksp stays the same.

Equation: Ksp = [cation]^a [anion]^b for the dissolution AaBb(s) ⇌ a cation + b anion, where brackets mean equilibrium molar concentration (mol/L) and a and b are the coefficients. Ksp is usually given without units. Example: PbCl₂(s) ⇌ Pb²⁺ + 2Cl⁻, so Ksp = [Pb²⁺][Cl⁻]² = s(2s)² = 4s³, where s is the molar solubility (mol/L).

On the MCAT: Expect to convert between Ksp and molar solubility, or to mix two solutions and compare Q with Ksp. If Q < Ksp, the solution is unsaturated. If Q = Ksp, it is saturated. If Q > Ksp, a precipitate forms until Q equals Ksp. Other common questions: the common ion effect (solubility falls), adding acid (solubility rises for salts with basic anions such as hydroxides, carbonates and fluorides), and complex-ion formation (solubility rises).

Common confusion: Students rank solubility by Ksp alone. This works only for salts that give the same number of ions, such as AgCl and AgBr. A salt like Ag₂CrO₄ has a different ion ratio, so its solubility depends on a different power of s. Solve for s before you compare. Also, a common ion changes solubility, not Ksp.