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Solubility Equilibria: Ksp, Common-Ion Effect, and Precipitation

INTOCHEMISTRY · ORIGINAL LESSON

Solve molar-solubility calculations and decide whether a precipitate forms using balanced dissolution equations and Qsp.

Learning goals: Write correct Ksp expressions; convert between Ksp and molar solubility; explain the common-ion effect; compare Qsp with Ksp.

Solubility-product dissolution of calcium fluorideOriginal schematic showing one formula unit of solid calcium fluoride producing one aqueous calcium 2 plus ion and two aqueous fluoride minus ions.One CaF₂ formula unit → three dissolved ionsCaF₂(s)Ca²⁺F⁻F⁻Ksp = [Ca²⁺][F⁻]²
Schematic stoichiometry, not a literal lattice model or complete picture of ion hydration. For idealized dissolution, [Ca²⁺] = s and [F⁻] = 2s, so Ksp = 4s³. Original IntoChemistry diagram.

1. What Ksp measures

For a slightly soluble ionic solid, an equilibrium is established between the solid and dissolved ions. The solubility-product constant, Ksp, expresses the product of equilibrium ion activities; in introductory dilute-solution problems, ion molarities are used as an approximation.

Example: AgCl(s) ⇌ Ag⁺(aq) + Cl⁻(aq), so Ksp ≈ [Ag⁺][Cl⁻]. The pure solid does not appear in the equilibrium expression.

Always balance the dissolution equation first. Coefficients become powers in Ksp and determine the ion-to-solid concentration relationships.

2. Convert molar solubility into ion concentrations

Let s represent the number of moles of formula units dissolving per liter. For CaF₂(s) ⇌ Ca²⁺(aq) + 2 F⁻(aq), dissolving s mol/L produces [Ca²⁺] = s and [F⁻] = 2s in pure water, if no other significant reactions occur.

Expression: Ksp ≈ [Ca²⁺][F⁻]² = s(2s)² = 4s³.

Common pitfall: the squared fluoride concentration is (2s)² = 4s², not simply 2s². Then multiply by the s from calcium.

3. Worked example: molar solubility of CaF₂

Given: For this practice problem, assume Ksp(CaF₂) = 4.0 × 10−11 at the stated temperature and ideal dilute-solution behavior. Find its molar solubility in pure water, ignoring hydrolysis and ion pairing.

  1. Write the balanced dissolution: CaF₂(s) ⇌ Ca²⁺ + 2 F⁻.
  2. Let [Ca²⁺] = s and [F⁻] = 2s.
  3. Substitute: 4.0 × 10−11 = s(2s)² = 4s³.
  4. Divide by 4: s³ = 1.0 × 10−11.
  5. Take the cube root: s ≈ 2.2 × 10−4 M (two significant figures).

This value is the molar solubility of CaF₂ formula units, not the fluoride-ion concentration; [F⁻] ≈ 4.3 × 10−4 M under the stated approximations.

4. Common-ion effect: same solid, less dissolution

Adding a solution containing one of the ions that appear in the dissolution equilibrium shifts the equilibrium toward the solid when a separate solid phase remains. For CaF₂, added F⁻ makes the fluoride ion concentration larger and reduces the additional CaF₂ that can dissolve.

Worked comparison: Suppose the fluoride concentration is initially 0.010 M from a soluble fluoride salt and Ksp = 4.0 × 10−11. If the small additional 2s from CaF₂ is negligible, then:

Ksp ≈ s(0.010)² → s ≈ (4.0 × 10−11)/(1.0 × 10−4) = 4.0 × 10−7 M.

Check the approximation: 2s ≈ 8.0 × 10−7 M, far smaller than 0.010 M. This is appropriate for the simplified problem.

5. Qsp predicts precipitation

The ion product Qsp has the same algebraic form as Ksp but uses the ion concentrations at the moment being assessed.

  • Qsp < Ksp: solution is unsaturated relative to the solid; precipitation is not favored.
  • Qsp = Ksp: equilibrium saturation.
  • Qsp > Ksp: supersaturation; precipitation is thermodynamically favored, though nucleation can take time.

For mixing problems, find the diluted concentrations after mixing and before precipitation, compute Qsp, then compare it with Ksp.

6. A repeatable exam strategy

  1. Balance the dissolution equation and write Ksp.
  2. Identify whether the ions come only from the dissolving solid or include a common ion.
  3. Let s be molar solubility and express each ion concentration correctly.
  4. Solve the equation; evaluate whether approximations are justified.
  5. For precipitation decisions, calculate concentrations after any dilution and compare Qsp with Ksp.
  6. State assumptions, units and the meaning of the result.

Common mistakes to avoid

  • Writing the concentration of a pure solid in the Ksp expression.
  • Forgetting the 2 in CaF₂ and its squared effect.
  • Assuming Ksp is numerically the same as molar solubility for every ionic solid.
  • Calculating Qsp with unmixed stock concentrations after two solutions are combined.
  • Assuming an equilibrium prediction guarantees instantaneous visible crystals.
  • Ignoring other ionic equilibria in situations where pH, complexes, or ion pairing matter.

Check your understanding

Work each problem before opening the solution. This self-check does not store grades or require a student account.

1. Write Ksp for Mg(OH)₂(s) ⇌ Mg²⁺ + 2OH⁻.

Answer and reasoning: Ksp ≈ [Mg²⁺][OH⁻]². Pure solid is omitted.

2. If s is the molar solubility of CaF₂ in pure water, express Ksp in terms of s.

Answer and reasoning: Ksp = s(2s)² = 4s³ under the simple idealized assumptions.

3. Does adding a common chloride ion increase or decrease the solubility of AgCl?

Answer and reasoning: It decreases the amount of AgCl that dissolves at equilibrium, other factors equal.

4. What does Qsp greater than Ksp predict?

Answer and reasoning: The mixture is supersaturated relative to that solid; precipitation is thermodynamically favored.

Interactive practice · automatically checked

Select one response per question, then choose Check my answers. The quiz calculates your score on this page, explains every response, and does not require a student account.

1. For CaF₂(s) ⇌ Ca²⁺ + 2 F⁻, Ksp is…
2. If CaF₂ molar solubility is s in pure water, [F⁻] is…
3. Which concentration expression follows from idealized CaF₂ dissolution?
4. Adding a soluble source of chloride usually does what to AgCl solubility?
5. Qsp > Ksp for a mixed ion solution predicts…
6. When two ionic solutions are mixed, Qsp uses…

Download the printable practice set

Eight original questions: six concept/application problems and two written or structure-drawing tasks. The separate worked key explains the reasoning.

Student worksheet (PDF)   |   Worked answer key (PDF)

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References and further reading

This original IntoChemistry lesson is an independent companion resource. Consult your course syllabus for chapter numbering and required material.