Solubility Product (Ksp) & Common Ion Effect

The solubility product, Ksp, is the equilibrium constant for the dissolution of a sparingly soluble salt: for AgCl(s) ⇌ Ag+ + Cl−, Ksp = [Ag+][Cl−] = 1.8 × 10^−10 at 25 °C. It tells you exactly how much solid can dissolve before the solution is saturated.

The common ion effect is Le Chatelier's principle applied to this equilibrium: if the solution already contains one of the ions (say Cl− from NaCl), the dissolution is pushed left and the salt becomes far less soluble. This effect is exploited in qualitative analysis, water treatment, and even kidney-stone chemistry.

Key Concepts

• For AxBy(s) ⇌ xA + yB: Ksp = [A]^x[B]^y; the solid itself is omitted, as with all heterogeneous equilibria.
• Molar solubility s (mol/L) is derived from Ksp: for a 1:1 salt s = √Ksp; for CaF2 (1:2), Ksp = 4s³.
• Compare the ion product Q with Ksp: Q < Ksp → unsaturated, more dissolves; Q = Ksp → saturated; Q > Ksp → precipitation occurs.
• Common ion effect: adding NaCl lowers AgCl's solubility because [Cl−] is already high, so less Ag+ is needed to hit Ksp.
• Ksp changes only with temperature.

Formulas

• General: Ksp = x^x · y^y · s^(x+y) for AxBy, where s is the molar solubility.
• 1:1 salt: s = √Ksp. 1:2 salt: s = ∛(Ksp/4). 2:3 salt: s = ∛∛(Ksp/108) — i.e. the 5th root of Ksp/108.
• With a common ion of concentration C (C ≫ s): s ≈ Ksp / C^x for the ion appearing x times.

Worked Example

Silver chloride, Ksp = 1.8 × 10^−10. Compare its solubility in pure water versus 0.10 M NaCl:

1. Pure water: s = √(1.8 × 10^−10) = 1.34 × 10^−5 mol/L.
2. In 0.10 M NaCl: Ksp = s(0.10 + s) ≈ 0.10s, since s ≪ 0.10.
3. s = 1.8 × 10^−10 / 0.10 = 1.8 × 10^−9 mol/L.
4. Ratio: 1.34 × 10^−5 / 1.8 × 10^−9 ≈ 7,400 — the common ion makes AgCl about 7,400 times less soluble.

Common Misconceptions

• "Ksp is the solubility." Ksp is a product of concentrations. Two salts' Ksp values can only be compared directly when their stoichiometries match — convert to s first.
• "A common ion increases solubility." It decreases it, by pushing the dissolution equilibrium left.
• "Ksp changes when you add more solid." Adding solid changes Q, not K. Ksp moves only with temperature.

Real-World Applications

• Qualitative analysis: selective precipitation separates metal cations group by group using controlled common-ion concentrations.
• Water treatment: lime softening precipitates CaCO3 by exceeding its Ksp.
• Teeth and bones: fluoride converts hydroxyapatite to less-soluble fluorapatite (smaller Ksp), resisting acid attack.

Ksp turns "how much dissolves" into a number, and the common ion effect turns that number into a tool: control one ion's concentration and you control exactly when a solid appears or disappears.