# Mg(OH)2 has a solubility of 9.0x10^-5 M. What is the value of Ksp for Mg(OH)2?

## Mg(OH)2 has a solubility of 9.0x10^-5 M. What is the value of Ksp for Mg(OH)2?

Jun 2, 2016

${K}_{\text{sp" = 2.9 × 10^"-12}}$

#### Explanation:

The chemical equation for the equilibrium is

$\textcolor{w h i t e}{m m m m m m} \text{Mg(OH)"_2"(s)" ⇌ "Mg"^(2+)"(aq)" + 2"OH"^"-""(aq)}$
$\text{E:/mol·L"^"-1} \textcolor{w h i t e}{m m m m m m m m l l m} x \textcolor{w h i t e}{m m m m m l l} 2 x$

K_"sp" = ["Mg"^(2+)]["OH"^"-"]^2 = x(2x)^2 = 4x^3

x = 9.0 × 10^"-5"

${K}_{\text{sp" = = 4(9.0 × 10^"-5")^3 = 2.9 × 10^"-12}}$