Question

The pH of aqueous solution of magnesium hydroxide is 9.0. If $K_{s p}$ 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 $\left[\right.H^{+}\left]\right.=10^{- 9}molL^{- 1}$

or $\left[\right.OH^{-}\left]\right.=10^{- 5}molL^{- 1}$

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

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