A-Level Chemistry May/June 2025 Q3(a)(i): Chromium(III) hydroxide, Cr(OH)3, is only slightly soluble in water. The value of the s…

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  First, write the dissolution equilibrium for chromium(III) hydroxide:

  $Cr(OH)_3(s) \rightleftharpoons Cr^{3+}(aq) + 3OH^-(aq)$

  The expression for the solubility product, $K_{sp}$, is the product of the concentrations of the aqueous ions, each raised to the power of its stoichiometric coefficient.

  $K_{sp} = [Cr^{3+}][OH^{-}]^3$

  To find the units, substitute the units for concentration (mol dm⁻³) into the expression:

  Units = (mol dm⁻³) × (mol dm⁻³)³ Units = (mol dm⁻³) × (mol³ dm⁻⁹) Units = mol⁴ dm⁻¹²

  Expression: $K_{sp} = [Cr^{3+}][OH^{-}]^3$ Units: mol⁴ dm⁻¹²

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  How the marks are awarded

  • M1 — The correct Ksp expression is written, showing the concentration of chromium(III) ions multiplied by the concentration of hydroxide ions raised to the power of 3, i.e., $[Cr^{3+}][OH^{-}]^3$.
  • M2 — The correct units for Ksp, mol⁴ dm⁻¹², are stated. This is derived by combining the units from the expression: (mol dm⁻³)¹ × (mol dm⁻³)³.

  Common mistakes

  • Forgetting to raise the hydroxide ion concentration to the power of 3, writing $K_{sp} = [Cr^{3+}][OH^{-}]$. The stoichiometric coefficient from the balanced equation must be used as the power.
  • Incorrectly multiplying the concentration term by the stoichiometric coefficient instead of raising it to the power, for example writing $[Cr^{3+}][3OH^{-}]$.
  • Making an error when calculating the units, such as adding the indices instead of multiplying the unit terms, leading to an incorrect final power (e.g., mol² dm⁻⁶).
  • Including the concentration of the solid reactant, $[Cr(OH)_3]$, in the denominator of the expression. The concentration of a pure solid is constant and is excluded from equilibrium constant expressions.

  Examiner tip: Always write the balanced dissolution equation for the sparingly soluble salt first, as the stoichiometric coefficients directly give you the powers for each ion's concentration in the Ksp expression.

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