Question

The pH of aqueous solution of magnesium hydroxide is 9.0. If $K_{sp}$ of magnesium hydroxide is $1.0\times 10^{-11}{\text{M}}^3$ , then the concentration of magnesium ions in the solution is

• A. $10^{-7}\text{M}$
• B. $10^{-2}\text{M}$
• C. $0.1\text{M}$
• D. $10^{-6}\text{M}$

Answer 1

Answer: (C)

$pH=9$

So $[H^{+}]=10^{-9}mol{L}^{-1}$

or $[O{H}^{-}]=10^{-5}mol{L}^{-1}$

$K_{sp}[Mg(OH{)}_2]=[M{g}^{2+}][O{H}^{-}{]}^2$

So $\left[{\mathrm{Mg}}^{2+}\right]=\frac{1\times 10^{-11}}{{\left(10^{-5}\right)}^2}=10^{-1}=0.1\mathrm{M}$