Question

The acid ionization constant for ${\left[Co{\left(H_{2}O\right)}_6\right]}^{\mathbf{2}\mathbf{+}}$is $\mathbf{3}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{10}}$Calculate the pH of a 0.10 M solution of Co(NO₃)₂.

Short answer

The pH of the solution is 5.26.

Step-by-step solution

The reaction of Co(NO3)2 with water

The balanced chemical equation for the reaction of Co(NO₃)₃with water:

$Co{{\left(H_{2}O\right)}_6}^{3+}\left(aq\right)+H_{2}O\left(I\right)\square {\left[Co{\left(H_{2}O\right)}_5.OH\right]}^{2+}\left(aq\right)+H_3{O}^{+}\left(aq\right)$

Construction of ICE table

$$\begin{gathered} Co{{\left(H_{2}O\right)}_6}^{3+}\left(aq\right)+H_{2}O\left(I\right)\square {\left[Co{\left(H_{2}O\right)}_5.OH\right]}^{2+}\left(aq\right)+H_3{O}^{+}\left(aq\right) \\ I:0.10M00 \\ C:-x+x+x \\ E:0.10-xxx \end{gathered}$$

$\begin{array}{rcl}{K}_a& =& \frac{x^2}{0.10-x}\\ 3\times {10}^{-10}& =& \frac{x^2}{0.10-x}\\ x& =& 5.47\times {10}^{-6}\end{array}$

The value of pH

$\begin{array}{rcl}\left[H_3{O}^{+}\right]& =& 5.47\times {10}^{-6}\\ pH& =& -\log \left(5.47\times {10}^{-6}\right)\\ & =& 5.26\end{array}$

Hence, the pH of the solution is 5.26.