Chapter 18, Problem 96A

Interpretation Introduction

Interpretation:

The $\mathrm{pH}$ of hypobromous acid is to be calculated for given 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:

$\begin{array}{l}pH=-\log \left[H^{+}\right]\\ \left[H^{+}\right]isconcentationofhydrogenions\end{array}$

Answer to Problem 96A

The $pH$ of hypobromousis $4.63$.

Explanation of Solution

Hypobromous acid has one replaceable hydrogen ion.

Therefore,

$\begin{array}{l}HBrO\rightleftharpoons Br{O}^{-}+H^{+}\\ Therfore,\\ k_a=\frac{\left[Br{O}^{-}\right]\left[H^{+}\right]}{\left[HBrO\right]}\\ k_a=\frac{{\left[H^{+}\right]}^2}{\left[HBrO\right]}\\ {\left[H^{+}\right]}^2=k_a\times \left[HBrO\right]\end{array}$

Given data:

$\begin{array}{c}\left[HBrO\right]=0.200M\\ k_a=2.8\times {10}^{-9}\\ \left[H^{+}\right]=\sqrt{2.8\times {10}^{-9}\times 0.200}\\ =2.4\times {10}^{-5}M\end{array}$

$\begin{array}{c}pH=-\log (2.4\times {10}^{-5})\\ =-\log 2.4-\log {10}^{-5}\\ =-0.37+5\\ =4.63\end{array}$

Conclusion

Thus $pH=4.63$