A-Level Chemistry October/November 2024 Q1(c): Calculate the solubility product, Ksp, of magnesium hydroxide. Include units. Ksp = units

1 answer

• ▲0
  accepted ✓

  The dissolution of magnesium hydroxide is represented by the equilibrium:

  $Mg(OH)₂(s) ⇌ Mg²⁺(aq) + 2OH⁻(aq)$

  The expression for the solubility product, Ksp, is:

  $K_{sp} = [Mg^{2+}][OH⁻]²$

  From the previous part of the question, the solubility of Mg(OH)₂ is $1.4 \times 10^{-4} \, mol \, dm^{-3}$. This means in a saturated solution, $[Mg^{2+}] = 1.4 \times 10^{-4} \, mol \, dm^{-3}$.

  Due to the 1:2 stoichiometry, the concentration of hydroxide ions is double the concentration of magnesium ions:

  $[OH⁻] = 2 \times [Mg^{2+}] = 2 \times 1.4 \times 10^{-4} = 2.8 \times 10^{-4} \, mol \, dm^{-3}$

  Now, substitute these values into the Ksp expression:

  $K_{sp} = (1.4 \times 10^{-4}) \times (2.8 \times 10^{-4})²$

  $K_{sp} = (1.4 \times 10^{-4}) \times (7.84 \times 10^{-8})$

  $K_{sp} = 1.0976 \times 10^{-11}$

  Rounding to 3 significant figures:

  $K_{sp} = 1.10 \times 10^{-11}$

  To find the units:

  Units = $(mol \, dm^{-3}) \times (mol \, dm^{-3})² = mol^3 \, dm^{-9}$

  $K_{sp} = 1.10 \times 10^{-11} \, mol^3 \, dm^{-9}$

  ---

  How the marks are awarded

  • M1 — Correctly writing the Ksp expression as Ksp = [Mg²⁺][OH⁻]² and substituting the concentrations, showing that [OH⁻] is twice [Mg²⁺], as seen in the line: Ksp = (1.4 × 10⁻⁴) × (2.8 × 10⁻⁴)².
  • A1 — Calculating the correct final numerical answer of 1.10 × 10⁻¹¹ (or 1.1 × 10⁻¹¹), which is accurate to at least two significant figures.
  • B1 — Stating the correct units for this Ksp calculation, which are mol³ dm⁻⁹, derived from (mol dm⁻³) × (mol dm⁻³)².

  Common mistakes

  • Forgetting to square the hydroxide ion concentration, calculating Ksp = [Mg²⁺][OH⁻] instead of Ksp = [Mg²⁺][OH⁻]².
  • Forgetting to double the concentration for [OH⁻], incorrectly assuming [OH⁻] = [Mg²⁺] and calculating Ksp = (1.4 × 10⁻⁴)³.
  • Making a calculation error when squaring the [OH⁻] term, for example calculating 2 × (1.4 × 10⁻⁴)² instead of (2 × 1.4 × 10⁻⁴)².
  • Providing incorrect units, such as mol² dm⁻⁶, by failing to account for the stoichiometry in the unit calculation.

  Examiner tip: Always write the dissolution equilibrium equation first to correctly identify the stoichiometric ratio, which dictates both the powers in the Ksp expression and the molar relationship between the ions.

  ---

  AI-generated model answer, grounded in the official Cambridge mark scheme and reviewed by the MarkScheme team. Mark your own answer to this question →

  @markscheme_answers

Your answer

Sign in to answer this question.