Question

Calculate the molar solubility of $\mathit{C}\mathit{o}{\left(OH\right)}_{\mathbf{3}}\mathbf{}\mathbf{,}\mathbf{}{\mathit{K}}_{\mathbf{s}\mathbf{p}}\mathbf{=}\mathbf{2}\mathbf{.}\mathbf{5}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{43}}$

Short answer

The solubility of $Co{\left(OH\right)}_3$given the $2.5\times {10}^{-46}is2.5\times {10}^{-22}mol/L$

Step-by-step solution

Definition of molar solubility

The number of moles of the solute that can be dissolved per liter of solution before the solution becomes saturated is defined as molar solubility.

Calculation of molar solubility

The dissolution equilibrium of $Co{\left(OH\right)}_3$is

$$\begin{gathered} Co{\left(OH\right)}_3\left(s\right)\iff C{o}^{+3}\left(aq\right)+3O{H}^{-}\left(aq\right) \\ {K}_{sp}=\left[C{o}^{3+}\right]{\left[O{H}^{-}\right]}^3 \\ Let‘s’mol/LrepresentthemolarsolubilityofCo{\left(OH\right)}_3 \\ \left[C{o}^{3+}\right]=smol/L \\ \left[O{H}^{-}\right]=3smol/L \\ Duetotheionizationofwater,therewillbeanincreaseinthe\left[O{H}^{-}\right]concentration \\ AtpH=7 \\ \left[H^{+}\right]=\left[O{H}^{-}\right] \\ ={10}^{-7}mol/L \\ \left[O{H}^{-}\right]=3s+{10}^{-7}mol/L \\ {K}_p=\left[C{o}^{3+}\right]\left[O{H}^{-}\right] \\ 2.5\times {10}^{-43}=\left[s\right]\left[{10}^{-7\times 3}\right] \\ s=2.5\times {10}^{-22}mol/L \end{gathered}$$