# Question #c548d

Sep 18, 2015

Question 1: ${K}_{s p} = 1.1 \times {10}^{- 11}$

Question 2: $s = 4.9 \times {10}^{- 12} M$

#### Explanation:

Quest (1) determine the ksp for magnesium hydroxide $M g {\left(O H\right)}_{2}$ where the molar solubility of $M g {\left(O H\right)}_{2}$ is $1.4 \times {10}^{- 4} M$?

We will use ICE table to solve this question.

The dissolution of $M g {\left(O H\right)}_{2}$ can be written as follows:

$\text{ " " " " " " " " " }$ $M g {\left(O H\right)}_{2} \left(s\right) \to M {g}^{2 +} \left(a q\right) + 2 O {H}^{-} \left(a q\right)$
$\text{ " " " " }$ Initial: $\text{ " " " " " " " " " " " 0 M " " " " " } 0 M$
$\text{ " " " }$ Change: $- s M \text{ " " " " " " " " +sM " " " " } + 2 s M$
$\text{ " }$ Equilibrium: $\text{ " " " " " " " " " " " s M " " " " " " " " } 2 s M$

The expression of ${K}_{s p}$ can be written as follows:

${K}_{s p} = \left[M {g}^{2 +} \left(a q\right)\right] \cdot {\left[O {H}^{-} \left(a q\right)\right]}^{2}$

$\implies {K}_{s p} = s \cdot {\left(2 s\right)}^{2} = 4 {s}^{3} = 4 \times {\left(1.4 \times {10}^{-} 4\right)}^{3}$

$\implies {K}_{s p} = 1.1 \times {10}^{- 11}$

Quest (2) The ${K}_{s p}$ for $Z n {\left(O H\right)}_{2}$ is $5.0 \times {10}^{- 17}$ . Determine the molar solubility of $Z n {\left(O H\right)}_{2}$ in a buffer solution with a $p H \text{ of } 11.5$?

We will use ICE table to solve this question.

$p H = 11.5 \implies \left[{H}^{+}\right] = {10}^{- 11.5}$

$\implies \left[O {H}^{-}\right] = {10}^{- 2.5} = 3.2 \times {10}^{- 3} M$

The dissolution of $Z n {\left(O H\right)}_{2}$ can be written as follows:

$\text{ " " " " " " " " " }$ $Z n {\left(O H\right)}_{2} \left(s\right) \to Z {n}^{2 +} \left(a q\right) + 2 O {H}^{-} \left(a q\right)$
$\text{ " " " " }$ Initial: $\text{ " " " " " " " " " " " 0 M " " " " } 3.2 \times {10}^{- 3} M$
$\text{ " " " }$ Change: $- s M \text{ " " " " " "" +sM " " " " } + 2 s M$
$\text{ " }$ Equilibrium: $\text{ " " " " " " " " " " " s M " " " " } \left(3.2 \times {10}^{- 3} + 2 s\right) M$

The expression of ${K}_{s p}$ can be written as follows:

${K}_{s p} = \left[Z {n}^{2 +} \left(a q\right)\right] \cdot {\left[O {H}^{-} \left(a q\right)\right]}^{2}$

$5.0 \times {10}^{- 17} = s \cdot {\left(3.2 \times {10}^{- 3} + 2 s\right)}^{2}$

Solve for $s = 4.9 \times {10}^{- 12} M$

Here is a video that explains the solving of Q2 (start at minute 5:14):