# How do we find the solubility of magnesium hydroxide in water in terms of K_(sp)?

Sep 14, 2015

$M g {\left(O H\right)}_{2} \left(s\right) r i g h t \le f t h a r p \infty n s M {g}^{2 +} + 2 O {H}^{-}$
From the above reaction, clearly, ${K}_{s p} = \left[M {g}^{2 +}\right] {\left[O {H}^{-}\right]}^{2}$. We call the solubility of the magnesium salt, $S$, and plugging this back into the equation, ${K}_{s p} = S \times {\left(2 S\right)}^{2} = 4 {S}^{3}$ (because for magnesium ion in solution there are 2 hydroxide ions!). So now you have a cubic equation and unknown $S$, which you can solve here without approximation.
S=""^3sqrt(1/4xx1.4xx10^-4)=??*mol*L^-1