Calculate the pH of a saturated solution of a sparingly soluble metal hydroxide, M(OH) ₂ , at 298 K . (Given: K_ sp of M(OH) ₂ = 3.2 10⁻¹¹ , 2 = 0.3 )

Step-by-step solution

The dissociation of the metal hydroxide is given by: M(OH) ₂ (s) M ²⁺ (aq) + 2 OH ⁻ (aq) Let the solubility of M(OH) ₂ be s . Then, [ M ²⁺] = s and [ OH ⁻] = 2s . The solubility product expression is: K_ sp = [ M ²⁺][ OH ⁻]^2 = (s)(2s)^2 = 4s^3 Substituting the given K_ sp : 3.2 10⁻¹¹ = 4s^3 s^3 = 0.8 10⁻¹¹ = 8 10⁻¹² s = 2 10⁻⁴ M The concentration of hydroxide ions is: [ OH ⁻] = 2s = 2(2 10⁻⁴) = 4 10⁻⁴ M Calculating the pOH: pOH = - [ OH ⁻] = - (4 10⁻⁴) = 4 - 4 pOH = 4 - 2 2 = 4 - 2(0.3) = 3.4 The pH of the solutio