Calculate the pH of a solution whose concentration is $1 \times {10}^{-14}\mathit{ mol }{l}^{-1}$ in HCl? $(\mathit{Given},\mathit{ hydroxyl\; ion\; concentration}={10}^{-5})$

 

 

 

The pH of the solution whose concentration of $\left[O{H}^{-}\right]$ ions is ${10}^{-5}M$ is 9.
Concentration of $\left[O{H}^{-}\right]={10}^{-5}M$
$\left[H^{+}\right]\left[O{H}^{-}\right]={10}^{-4}\mathit{M }$ $\left[H^{+}\right]=\frac{{10}^{-14}}{\left[O{H}^{-}\right]}$           $\Rightarrow \frac{{10}^{-14}}{\left[{10}^{-5}\right]}$
          $\Rightarrow { 10}^{-9}M$
Therefore, $\mathit{pH}=-\mathit{log }\left[H^{+}\right]$                          $\Rightarrow -\mathit{log }\left[{10}^{-9}\right]$
                         $\Rightarrow 9\mathit{ log }\left(10\right)\mathit{ }(\mathit{since\; log }10 =1)$    Thus, $\mathit{pH}=9$