The correct order of solubility of the given salts in water at 298 K is Salt K_ sp at 298 K AgBr 5.0 10⁻¹³ Zn(OH)₂ 1.0 10⁻¹⁵ H g₂ Cl₂ 1.3 10⁻¹⁸

Step-by-step solution

Let s be the solubility of the salt in water. For AgBr : AgBr Ag ^+ + Br ^- K_ sp = s^2 s = 5.0 10⁻¹³ = 50 10⁻¹⁴ 7.07 10⁻⁷ M For Zn(OH) ₂ : Zn(OH) ₂ Zn ²⁺ + 2 OH ^- K_ sp = s(2s)^2 = 4s^3 s = ( 1.0 10⁻¹⁵ 4 )^ 1/3 = (250 10⁻¹⁸ )^ 1/3 6.3 10⁻⁶ M For Hg ₂ Cl ₂ : Hg ₂ Cl ₂ Hg ₂²⁺ + 2 Cl ^- K_ sp = s(2s)^2 = 4s^3 s = ( 1.3 10⁻¹⁸ 4 )^ 1/3 = (0.325 10⁻¹⁸ )^ 1/3 6.87 10⁻⁷ M Comparing the solubilities: 6.3 10⁻⁶ > 7.07 10⁻⁷ > 6.87 10⁻⁷ Thus, the correct order of solubility is Zn(OH) ₂ > AgBr > Hg ₂ Cl ₂ . Answer: Zn(OH) ₂> A