The solubility product ( K_ sp ) of a sparingly soluble salt of the type M₂X is 3.2 10⁻¹¹ . What is the molar concentration of M^+ ions in its saturated aqueous solution?

Step-by-step solution

For a sparingly soluble salt of type M₂X , the dissociation equilibrium is: M₂X(s) 2M^+(aq) + X²⁻(aq) If the molar solubility of the salt is s , then at equilibrium: [M^+] = 2s [X²⁻] = s The solubility product K_ sp is given by: K_ sp = [M^+]^2[X²⁻] = (2s)^2(s) = 4s^3 Given K_ sp = 3.2 10⁻¹¹ = 32 10⁻¹² : 4s^3 = 32 10⁻¹² s^3 = 8 10⁻¹² s = (8 10⁻¹²)^ 1/3 = 2 10⁻⁴ mol L ⁻¹ The concentration of M^+ ions is: [M^+] = 2s = 2 (2 10⁻⁴) = 4.0 10⁻⁴ mol L ⁻¹ Answer: 4.0 10⁻⁴ mol L ⁻¹