The correct order of solubility of the given salts in water at 298 K (Ksp: AgBr =5.0×10⁻¹³; Zn(OH)₂=1.0×10⁻¹⁵; Hg₂Cl₂=1.3×10⁻¹⁸) is:

Solution & Explanation

Concept — Molar solubility must be derived FROM Ksp using each salt's dissolution stoichiometry; comparing the bare Ksp values directly is wrong because the salts dissolve into different numbers of ions. AgBr (1:1): AgBr ⇌ Ag⁺ + Br⁻, Ksp = S². So S = √(5.0×10⁻¹³) ≈ 7.1×10⁻⁷ mol/L. Zn(OH)₂ (1:2): Zn(OH)₂ ⇌ Zn²⁺ + 2 OH⁻, Ksp = 4S³. So S = (1.0×10⁻¹⁵ / 4)^(1/3) ≈ 6.3×10⁻⁶ mol/L. Hg₂Cl₂ (Hg₂²⁺ + 2 Cl⁻, type 1:2): Ksp = 4S³. So S = (1.3×10⁻¹⁸ / 4)^(1/3) ≈ 6.9×10⁻⁷ mol/L. Compare: Zn(OH)₂ (6.3×10⁻⁶) > AgBr (7.1×10⁻⁷) > Hg₂Cl₂ (6.9×10⁻⁷). Note how Zn(OH)₂, despite a smaller Ksp than AgBr, is the most soluble — its cube-root (4S³) law gives a much larger S. Hence the order of solubility is Zn(OH)₂ > AgBr > Hg₂Cl₂ — option D.