Question

The solubility product of nickel(II) hydroxide, Ni (OH)₂, at 25°C is K_sp = 1.6x10^-16.

(a) Calculate the molar solubility ofNi (OH)₂ in pure water at 25°C.

(b) Calculate the molar solubility ofNi (OH)₂ in 0.100 M NaOH.

Short answer

1. Solubility in pure water is $3.42\times {10}^{-6}mol/L$
2. Solubility is$1.6\times {10}^{-14}mol/L$

Step-by-step solution

Molar solubility

The molar solubility of a sparingly soluble salt can be determined by using its solubility product value.

When a solution with a common ion is added, the solubility decreases further.

Subpart (a)

The solubility of Ni (OH)₂ in pure water is as shown below:

$$\begin{gathered} Ni{\left(OH\right)}_2\left(s\right)\square N{i}^{2+\left(aq\right)}+2O{H}^{-}\left(aq\right) \\ s2s \end{gathered}$$

$\begin{array}{rcl}{K}_{sp}& =& s\times {\left(2s\right)}^2\\ 1.6\times {10}^{-16}& =& 4s^3\\ s& =& \sqrt[3]{\frac{1.6\times {10}^{-16}}{4}}\\ s& =& 3.42\times {10}^{-6}mol/L\end{array}$

Subpart (b)

The compound NaOH undergoes complete ionization in water.

$$\begin{gathered} NaOH\left(aq\right)\to N{a}^{+}\left(aq\right)+O{H}^{-}\left(aq\right) \\ I:0.100M00 \\ F:00.100M0.100M \end{gathered}$$

$$\begin{gathered} Ni{\left(oh\right)}_2\left(s\right)\square N{i}^{2+}\left(aq\right)+2O{H}^{-}\left(aq\right) \\ s2s+0.100 \end{gathered}$$

$\begin{array}{rcl}{K}_{sp}& =& s\times {\left(2s+0.100\right)}^2\\ K_{sp}& =& s\times {\left(2s+0.100\right)}^2\\ 1.6\times {10}^{-16}& =& s\times {\left(0.100\right)}^2\\ s& =& 1.6\times {10}^{-14}mol/L\end{array}$