A sparingly soluble salt of the type XY₂ has a molar solubility of 2 10⁻³ mol L ⁻¹ in its saturated aqueous solution. What is the solubility product ( K_ sp ) of this salt?

Step-by-step solution

For a sparingly soluble salt of type XY₂ , the dissociation equilibrium is: XY₂(s) X²⁺(aq) + 2Y^-(aq) If the molar solubility is s , then at equilibrium: [X²⁺] = s [Y^-] = 2s The solubility product K_ sp is given by: K_ sp = [X²⁺][Y^-]^2 = (s)(2s)^2 = 4s^3 Given s = 2 10⁻³ mol L ⁻¹ : K_ sp = 4 (2 10⁻³)^3 K_ sp = 4 (8 10⁻⁹) = 32 10⁻⁹ = 3.2 10⁻⁸ Answer: 3.2 10⁻⁸