A-Level Chemistry May/June 2024 Q1(c)(ii): Calculate the value of Ksp of Fe(OH)2. Include its units.

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  The dissolution of iron(II) hydroxide is represented by the equilibrium:

  $Fe(OH)_2(s) \rightleftharpoons Fe^{2+}(aq) + 2OH^-(aq)$

  The solubility product constant expression is:

  $K_{sp} = [Fe^{2+}][OH^-]^2$

  Let the solubility of $Fe(OH)_2$ be $s$ mol dm⁻³. From the stoichiometry of the equation:

  $[Fe^{2+}] = s = 5.85 \times 10^{-6}$ mol dm⁻³

  $[OH^-] = 2s = 2 \times (5.85 \times 10^{-6})$ mol dm⁻³

  Substitute these into the $K_{sp}$ expression:

  $K_{sp} = (s) \times (2s)^2 = 4s^3$

  $K_{sp} = 4 \times (5.85 \times 10^{-6})^3$

  $K_{sp} = 4 \times (2.0026 \times 10^{-16})$

  $K_{sp} = 8.0104 \times 10^{-16}$

  $K_{sp} = 8.01 \times 10^{-16}$ (to 3 s.f.)

  For the units:

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

  Answer: $K_{sp} = 8.01 \times 10^{-16}\ mol^3\ dm^{-9}$

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  How the marks are awarded

  • M1 — Correctly calculating the numerical value of Ksp. This involves substituting the solubility (s) into the correct expression, 4s³, to get 8.01 × 10⁻¹⁶.
  • M2 — Stating the correct units for Ksp, which are mol³ dm⁻⁹, derived from the expression [concentration] × [concentration]².

  Common mistakes

  • Forgetting to square the hydroxide ion concentration in the Ksp expression, leading to an incorrect formula like Ksp = [Fe²⁺][OH⁻].
  • Incorrectly relating the hydroxide concentration to solubility, using [OH⁻] = s instead of [OH⁻] = 2s. This leads to an incorrect calculation of Ksp = s³.
  • Making an algebraic error when simplifying (s)(2s)², often calculating it as 2s³ instead of the correct 4s³.
  • Providing incorrect or missing units. A common error is stating mol² dm⁻⁶, which would be correct for a 1:1 salt.

  Examiner tip: Always write the full Ksp expression first, paying close attention to the stoichiometric coefficients which become the powers in the expression.

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