The pH of a saturated solution of a sparingly soluble metal hydroxide, M(OH) ₃ , at 298 K is 10.477 . What is the solubility product ( K_ sp ) of M(OH) ₃ at this temperature? (Given: 3 = 0.477 )

Step-by-step solution

First, find the pOH of the solution at 298 K : pOH = 14 - pH = 14 - 10.477 = 3.523 Using the given value 3 = 0.477 , we can rewrite the pOH as: pOH = 4 - 0.477 = 4 - 3 This corresponds to a hydroxide ion concentration of: [ OH ⁻] = 3 10⁻⁴ M The dissociation of the metal hydroxide is: M(OH) ₃ (s) M ³⁺ (aq) + 3 OH ⁻ (aq) If the solubility of M(OH) ₃ is s , then [ OH ⁻] = 3s . 3s = 3 10⁻⁴ M s = 10⁻⁴ M The solubility product expression is: K_ sp = [ M ³⁺][ OH ⁻]^3 = (s)(3s)^3 = 27s^4 Substituting the value of s : K_ sp