Solubility product constant

Question

The 𝐾sp of zinc hydroxide, Zn(OH)2, is 3.00×10−17. Calculate the solubility of this compound in grams per liter.

solubility: ? g/L

Answer 1

Zn(OH)2(s) <==> Zn²⁺(aq) + 2OH-(aq)

Ksp = [Zn²⁺][OH-]²

Let x = [Zn²⁺], and then 2x = [OH-]

Ksp = 3x10^-17 = (x)(2x)² = 4x³

x³ = 7.5x10^-18

x = 1.96x10^-6 M = [Zn²⁺] = [Zn(OH)₂]

Molar mass Zn(OH)₂ = 99.4 g / mol

Solubility in grams/liter = 1.96x10^-6 moles / L x 99.4 g / mole = 1.95x10^-4 g / L