Question

The copper ion forms a chloride salt that has ${\mathit{K}}_{\mathbf{s}\mathbf{p}}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{2}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{6}}$. Copper also forms a complex ion with $\mathit{C}{\mathit{l}}^{\mathbf{-}}$:

$\mathit{C}{\mathit{u}}^{\mathbf{+}}\mathbf{\left(}\mathbf{aq}\mathbf{\right)}\mathbf{+}\mathbf{2}\mathit{C}{\mathit{l}}^{\mathbf{-}}\mathbf{\left(}\mathbf{aq}\mathbf{\right)}\mathbf{}\boxed{\xcancel{}}\mathbf{}\mathbf{}\mathbf{}\mathit{C}\mathit{u}\mathit{C}{{\mathit{l}}_{\mathbf{2}}}^{\mathbf{-}}\mathbf{\left(}\mathbf{aq}\mathbf{\right)}\mathit{K}\mathbf{=}\mathbf{8}\mathbf{.}\mathbf{7}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{4}}$

1. Calculate the solubility of copper (I) chloride in pure water.

2. Calculate the solubility of copper (I) chloride in 0.10 M NaCl.

Short answer

Answer

1. The solubility of copper (I) chloride in pure water is $\mathit{x}\mathbf{}\xcancel{\boxed{}}\mathbf{}\mathbf{1}\mathbf{.}\mathbf{1}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{3}}$.

2. The solubility of copper (I) chloride in 0.10 M NaCl is $\mathit{x}\mathbf{=}\mathbf{9}\mathbf{.}\mathbf{4}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{3}}$.

Step-by-step solution

Subpart (a) Calculation of solubility of copper (I) chloride in pure water.

The expression for solubility constant of CuCl is

$\mathit{s}{\mathit{p}}_{}\mathbf{=}\left[C{u}^{+}\right]\left[C{l}^{-}\right]$

Substituting the values in expression for solubility constant is

$$\begin{gathered} \mathbf{1}\mathbf{.}\mathbf{2}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{6}}\mathbf{=}\left(x\right)\left(x\right) \\ \mathit{x}\mathbf{=}{\left(1.2\times {10}^{-6}\right)}^{\mathbf{1}\mathbf{/}\mathbf{2}} \\ \mathit{x}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{09}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{3}} \\ \mathit{x}\mathbf{}\xcancel{\boxed{}}\mathbf{}\mathbf{1}\mathbf{.}\mathbf{1}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{3}} \end{gathered}$$

Subpart (b) Calculation of solubility of copper (I) chloride in 0.10 M NaCl.

The ICE table for the solubility of copper chloride in 0.1M NaCl is

$$\begin{gathered} \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathit{C}\mathit{u}\mathit{C}\mathit{l}\left(s\right)\mathbf{+}\mathit{C}{\mathit{l}}^{\mathbf{-}}\left(aq\right)\mathbf{}\boxed{\xcancel{}}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathit{C}\mathit{u}\mathit{C}{\mathit{l}}_{\mathbf{2}}^{\mathbf{-}}\left(aq\right)\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}{\mathit{K}}^{\mathbf{+}}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{04}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{1}} \\ \mathit{i}\mathit{n}\mathit{i}\mathit{t}\mathit{i}\mathit{a}\mathit{l}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{0}\mathbf{.}\mathbf{10}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{0} \\ \mathit{c}\mathit{h}\mathit{a}\mathit{n}\mathit{g}\mathit{e}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{-}\mathit{x}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{+}\mathit{x} \\ \mathit{e}\mathit{q}\mathit{u}\mathit{i}{\mathit{l}}^{\mathbf{m}}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{0}\mathbf{.}\mathbf{10}\mathbf{-}\mathit{x}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathit{x} \end{gathered}$$

The equilibrium expression for the above reaction is

$\mathit{K}\mathbf{\text{'}}\mathbf{=}\frac{\left[CuC{l}_2^{-}\right]}{\left[C{l}^{-}\right]}$

Substituting the values

$$\begin{gathered} \mathbf{1}\mathbf{.}\mathbf{04}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{1}}\mathbf{=}\frac{\mathbf{x}}{\mathbf{0}\mathbf{.}\mathbf{100}\mathbf{-}\mathbf{x}} \\ \mathit{x}\mathbf{=}\mathbf{9}\mathbf{.}\mathbf{4}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{3}} \end{gathered}$$