What is the molar solubility of Mg(OH)2 in 0.025 M NaOH? Ksp = 8.9 ✕ 10-12 for Mg(OH)2.?

0.025 M NaOH completely dissociates to give 0.025 M OH⁻ ions.

______ Mg(OH)₂(s) ⇌ Mg²⁺(aq) + 2OH⁻(aq) …. Ksp = 8.9 × 10⁻¹²
Initial ___ ----- _______ 0 M ___ 0.025 M
Change _ ----- _______ +s M ____ +2s M
At eqm _ ----- ________ s M __ (0.025 + 2s) M

Due to the very small Ksp and common ion effect of OH⁻ ions, we can assume that 0.025 ≫ 2s.
Hence, [OH⁻] at eqm = (0.025 + 2s) M ≈ 0.025 M

Ksp = [Mg²⁺] [OH⁻]²
s (0.025)² = 8.9 × 10⁻¹²
s = (8.9 × 10⁻¹²) / (0.025)²
s = 1.4 × 10⁻⁸

Molar solubility of Mg(OH)₂(s) = 1.4 × 10⁻⁸ M