Even 'insoluble' salts dissolve a tiny amount, and the saturated solution is an equilibrium. The solubility product, Ksp, turns that equilibrium into numbers: solubilities, the effect of a common ion, and whether a precipitate will form.
In a saturated solution of a sparingly soluble salt, the solid is in dynamic equilibrium with its ions: AgCl(s) ⇌ Ag+(aq) + Cl−(aq). The solubility product is the product of the ion concentrations, each raised to the power of its coefficient: Ksp = [Ag+][Cl−] (mol2 dm−6), Ksp = [Pb2+][I−]2 (mol3 dm−9). The solid does not appear. From a solubility s: AgCl has s = 1.34 × 10−5 mol dm−3, so Ksp = s2 = 1.80 × 10−10 mol2 dm−6; for PbI2, Ksp = 4s3. Adding a common ion shifts the equilibrium to the left and lowers the solubility. If the ionic product of mixed solutions exceeds Ksp, a precipitate forms.
Compare sparingly soluble salts in the simulator, then add a common ion. Barium sulfate is so sparingly soluble that its saturated solution is best described by a solubility product.
| Salt | Equilibrium | Ksp expression | Units | Link to solubility s |
|---|---|---|---|---|
| AgCl | AgCl(s) ⇌ Ag+ + Cl− | [Ag+][Cl−] | mol2 dm−6 | s2 |
| BaSO4 | BaSO4(s) ⇌ Ba2+ + SO42− | [Ba2+][SO42−] | mol2 dm−6 | s2 |
| PbI2 | PbI2(s) ⇌ Pb2+ + 2I− | [Pb2+][I−]2 | mol3 dm−9 | s × (2s)2 = 4s3 |
| CaF2 | CaF2(s) ⇌ Ca2+ + 2F− | [Ca2+][F−]2 | mol3 dm−9 | 4s3 |
Four quick checks. Each correct answer earns XP and records this skill on your profile.
What is the Ksp expression for lead(II) iodide, PbI2?
What are the units of Ksp for calcium fluoride, CaF2?
The solubility of AgCl is 1.34 × 10−5 mol dm−3. What is Ksp?
How does the solubility of AgCl in 0.100 mol dm−3 NaCl compare with its solubility in water?
Use Ksp the other way round: fix one ion concentration and find the most of the other ion that can stay in solution.
| Situation | Working | Result |
|---|---|---|
| AgCl in pure water | s = √(1.80 × 10−10) | 1.34 × 10−5 mol dm−3 |
| AgCl in 0.100 mol dm−3 NaCl | s = 1.80 × 10−10 ÷ 0.100 | 1.80 × 10−9 mol dm−3 (7450 times less) |
| PbI2 in 0.100 mol dm−3 KI | s = 8.49 × 10−9 ÷ 0.1002 | 8.49 × 10−7 mol dm−3 |
| equal volumes of 2.00 × 10−4 mol dm−3 AgNO3 and NaCl | after mixing each is 1.00 × 10−4; ionic product 1.00 × 10−8 | > Ksp: precipitate |
| equal volumes of 1.00 × 10−5 mol dm−3 AgNO3 and NaCl | each 5.00 × 10−6; ionic product 2.50 × 10−11 | < Ksp: no precipitate |
Square or cube the right terms: for PbI2, [I−] = 2s and Ksp = 4s3, not s3 or s2. When two solutions are mixed, each concentration is diluted (halved for equal volumes) before you work out the ionic product. The common ion lowers the solubility, not Ksp. Units of Ksp depend on the formula: mol2 dm−6 for AB, mol3 dm−9 for AB2.
Unlocks once the four checks above are done. Worth more XP, written to A Level Paper 4 standard.
Ksp for PbI2 is 8.49 × 10−9 mol3 dm−9. What is its solubility?
What is the solubility of AgCl (Ksp = 1.80 × 10−10 mol2 dm−6) in 0.100 mol dm−3 NaCl?
Equal volumes of 2.40 × 10−3 mol dm−3 Pb(NO3)2 and 2.40 × 10−3 mol dm−3 KI are mixed. Ksp(PbI2) = 8.49 × 10−9 mol3 dm−9. What happens?
Ksp for BaSO4 is 1.08 × 10−10 mol2 dm−6. What mass dissolves in 1.00 dm3 of water (Mr 233.4)?
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