Question

What is the maximum concentration of equimolar solutions of ferrous sulphate and sodium sulphide so that when mixed in equal volumes, there is no precipitation of iron sulphide? (For iron sulphide, Ksp = 6.3 × 10^–18).

Answer 1

Equimolar solutions of FeSO₄ and Na₂S, each of concentration C, are mixed in equal volumes. The resulting concentrations are [Fe²⁺] = [S²⁻] = C/2. For no precipitation of FeS, the ionic product must not exceed K_sp = 6.3 × 10⁻¹⁸, so (C/2)² ≤ K_sp.<>

Derivation

\[\left[ \ce{Fe^{2+}} \right] = \frac{C}{2}, \quad \left[ \ce{S^{2-}} \right] = \frac{C}{2}\]

\[\left( \frac{C}{2} \right)^2 \leq 6.3 \times 10^{-18}\]

\[\frac{C^2}{4} \leq 6.3 \times 10^{-18}\]

\[C^2 \leq 4 \times 6.3 \times 10^{-18} = 2.52 \times 10^{-17}\]

\[C \leq \sqrt{2.52 \times 10^{-17}} = 5.02 \times 10^{-9} \, \ce{M}\]

The maximum concentration is 5.02 × 10⁻⁹ M.<>