Solubility & Complex-Ion Equilibria Cheat Sheet
Ksp, molar solubility, the common-ion effect, Q vs Ksp, selective precipitation, and coupled equilibria.
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Solubility & Complex-Ion Equilibria
Ksp, molar solubility, the common-ion effect, Q vs Ksp, selective precipitation, and coupled equilibria.
Ksp expression
CORE RULEKsp = product of ion concentrations, each to its coefficient, in a saturated solution. The pure solid is excluded. AgCl ⇌ Ag⁺ + Cl⁻: Ksp = [Ag⁺][Cl⁻].
Ksp in terms of solubility s
REFERENCE| Salt type | Ksp |
|---|---|
| MX | s² |
| MX₂ or M₂X | 4s³ |
| MX₃ or M₃X | 27s⁴ |
| M₂X₃ | 108s⁵ |
Molar solubility from Ksp
METHODICE with x for the reference ion, write the Ksp polynomial, solve for x. If solubility is given in g/L, convert to mol/L (÷ molar mass) before using Ksp.
Insoluble hydroxides & pH
CORE RULEFor M(OH)ₙ, [OH⁻] = n·s, so pOH = −log[OH⁻], pH = 14 − pOH. Given pH instead: [OH⁻] = 10^(−(14−pH)), then solve Ksp for the metal-ion concentration.
Common-ion effect
CORE RULEA shared ion already in solution goes into the ICE initial row, lowering molar solubility vs pure water. The x-small approximation (x ≪ common-ion concentration) is usually valid; check x < 5%.
Q vs Ksp (will it precipitate?)
CORE RULECompute Q from initial ion concentrations (apply dilution when mixing: [ion] × V_part/V_total). Q < Ksp → no precipitate; Q > Ksp → precipitates until Q = Ksp; Q = Ksp → just saturated.
Selective precipitation
CORE RULEFind the counter-ion concentration each salt needs to hit Q = Ksp; the lowest threshold precipitates first. Comparing Ksp values directly is valid only for the same salt stoichiometry.
Complex-ion / coupled equilibria
CORE RULECoupling dissolution to complex formation raises solubility: K_overall = Ksp × Kf. E.g. Al(OH)₃(s) + OH⁻ ⇌ Al(OH)₄⁻. With excess ligand ([L] ≈ [L]₀), a 1:1 salt gives s = √(K_overall·[L]ʲ). Acid-coupled M(OH)ₙ: K = Ksp/Kwⁿ.