Chapter 18.3, Problem 41SSC

Interpretation Introduction

Interpretation:

$pH$ of the solution is to be found out using given hydroxyl ion concentration.

Concept introduction:

pH gives the concentration of hydrogen ion in a solution.

It tells about acidity and basicity of a solution.

It is given by:

$\begin{array}{l}pH=-\log \left[H^{+}\right]\\ and\left[H^{+}\right]\times \left[O{H}^{-}\right]={10}^{-14}\\ \left[H^{+}\right]isconcentationofhydrogenions\\ \left[O{H}^{-}\right]isconcentationofhydroxylions\end{array}$

Answer to Problem 41SSC

pH of given solution is 5.

Explanation of Solution

Given:

$\begin{array}{c}\left[O{H}^{-}\right]=1\times {10}^{-9}mol/L\\ =1\times {10}^{-9}M\end{array}$

$pH=-\log \left[H^{+}\right]$

Therefore,

$\begin{array}{c}\left[H^{+}\right]\times \left[O{H}^{-}\right]={10}^{-14}\\ \left[H^{+}\right]=\frac{{10}^{-14}}{\left[O{H}^{-}\right]}\\ =\frac{{10}^{-14}}{1\times {10}^{-9}}\\ =1\times {10}^{-5}M\\ pH=-\log (1\times {10}^{-5})\\ =-\log 1-\log {10}^{-5}\\ =-0+5\\ =5\end{array}$

Conclusion

Thus $pH$ of given solution is 5