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9476 / 2027
Chemistry of Aqueous Solutions

Lesson 5 of 6

Solubility and precipitation

Use Ksp and the ionic product with the correct dissolved-ion concentrations.

A-Level 9476 (2026-2027)

  • I can understand and apply the solubility-product concept.Syllabus

    Syllabus 9476, 10.2(a). Understand and apply the solubility-product concept.

  • I can calculate Ksp from concentrations and vice versa.Syllabus

    Syllabus 9476, 10.2(b). Calculate Ksp from concentrations and vice versa.

A saturated solution has a fixed product of free-ion concentrations

Ksp describes an equilibrium with an undissolved solid at a specified temperature.

For AgCl(s) ⇌ Ag+(aq) + Cl-(aq), Ksp = [Ag+][Cl-]. The pure solid is omitted. For CaF2(s) ⇌ Ca2+(aq) + 2F-(aq), Ksp = [Ca2+][F-]2. The exponent follows the dissolution coefficient. Units follow from the expression: Ksp(AgCl) has units of mol2 dm-6, and Ksp(CaF2) has units of mol3 dm-9.

Worked exampleConvert Ksp into molar solubility

Find the molar solubility of AgCl with Ksp = 1.80 × 10-10 mol2 dm-6, and CaF2 with Ksp = 3.20 × 10-11 mol3 dm-9, in pure water under the simple dissolution model.

Try it first. Then show the worked stepsHide the worked steps
  1. For AgCl, let solubility be s. Both ion concentrations are s, so s2 = 1.80 × 10-10 mol2 dm-6 and s = 1.34 × 10-5 mol dm-3.
  2. For CaF2, [Ca2+] = s and [F-] = 2s, so Ksp = s(2s)2 = 4s3. Square the 2s as a whole: (2s)2 = 4s2, not 2s2.
  3. s = cube root(3.20 × 10-11 / 4) = 2.00 × 10-4 mol dm-3.
Answer

AgCl: 1.34 × 10-5 mol dm-3; CaF2: 2.00 × 10-4 mol dm-3. Comparing raw Ksp values alone is not a valid solubility ranking for different stoichiometries.

Try it step by step

Work it out in steps: Ksp in terms of s, then Molar solubility, s, then Solubility in g dm-3.

  1. Problem 1. CaSO4 has Ksp = 4.90 x 10-5 mol2 dm-6 and M = 136.1 g mol-1. Find its solubility in pure water in mol dm-3 and in g dm-3, to 3 significant figures.
  2. Problem 2. PbCl2 has Ksp = 1.60 x 10-5 mol3 dm-9 and M = 278.2 g mol-1. Find its solubility in pure water in g dm-3, to 3 significant figures.
  3. Problem 3. Ag2SO4 has Ksp = 1.20 x 10-5 mol3 dm-9 and M = 311.9 g mol-1. Find its solubility in pure water. Give s and the mass solubility to 3 significant figures.
Show the answer

Problem 1.

Ksp in terms of s: CaSO4 gives s of Ca2+ and s of sulfate, so Ksp = s2.

Molar solubility, s: s = sqrt(4.90 x 10-5) = 7.00 x 10-3 mol dm-3.

Solubility in g dm-3: Solubility = 7.00 x 10-3 x 136.1 = 0.953 g dm-3.

Problem 2.

Ksp in terms of s: PbCl2 gives s of Pb2+ and 2s of Cl-, so Ksp = s(2s)2 = 4s3.

Molar solubility, s: s = cube root(1.60 x 10-5 / 4) = 0.0159 mol dm-3.

Solubility in g dm-3: Solubility = 0.0159 x 278.2 = 4.42 g dm-3.

Problem 3.

Ksp in terms of s: Ksp = [Ag+]2[SO4 2-] = (2s)2 x s = 4s3.

Molar solubility, s: s = cube root(1.20 x 10-5 / 4) = 0.0144 mol dm-3.

Solubility in g dm-3: Solubility = 0.01442 x 311.9 = 4.50 g dm-3. Keep the unrounded s in the calculator: 0.0144 x 311.9 would give 4.49.

The ionic product, Q, has the same form as Ksp but uses the free-ion concentrations at that moment. If Q < Ksp, the solution is unsaturated. If Q = Ksp, it is saturated and at equilibrium. If Q > Ksp, a precipitate forms. When you mix solutions, first work out each concentration in the total volume.

Worked examplePredict precipitation after mixing

Mix 10.0 cm3 of 0.00200 mol dm-3 AgNO3 with 10.0 cm3 of 0.00100 mol dm-3 NaCl. Does AgCl precipitate if Ksp = 1.80 × 10-10 mol2 dm-6?

Try it first. Then show the worked stepsHide the worked steps
  1. Before precipitation, dilution gives [Ag+] = 0.00100 and [Cl-] = 0.000500 mol dm-3.
  2. Q = 0.00100 × 0.000500 = 5.00 × 10-7 mol2 dm-6.
  3. This exceeds Ksp by a large factor; ions are removed into the solid until the equilibrium condition is approached.
Answer

AgCl precipitates. These diluted concentrations test the initial tendency; they are not the final dissolved concentrations after precipitation.

Check your understanding

Silver chromate dissolves as Ag2CrO4(s) <=> 2Ag+(aq) + CrO42-(aq). What are the units of its Ksp?

  1. mol dm-3
  2. mol2 dm-6
  3. mol3 dm-9
  4. no units
Show the answer

mol3 dm-9

Ksp = [Ag+]2[CrO42-]. Three concentration terms multiply: (mol dm-3)2 x (mol dm-3) = mol3 dm-9.

Check your understanding

A saturated solution of PbI2 contains 1.30 x 10-3 mol dm-3 of dissolved Pb2+. What is Ksp for PbI2?

  1. 8.79 x 10-9 mol3 dm-9
  2. 3.38 x 10-6 mol2 dm-6
  3. 2.20 x 10-9 mol3 dm-9
Show the answer

8.79 x 10-9 mol3 dm-9

[I-] = 2 x 1.30 x 10-3 = 2.60 x 10-3 mol dm-3. Ksp = [Pb2+][I-]2 = (1.30 x 10-3)(2.60 x 10-3)2 = 8.79 x 10-9 mol3 dm-9.