7.51  The degree of ionization of a 0.1 M bromoacetic acid solution is 0.132. Calculate the pH of the solution and the $p{K}_{a}$ of bromacetic acid.

Degree of ionization, a=0.132
Concentration, c=0.1 M
Thus, the concentration of ${H}_{3}{O}^{+}$=c.a
$=0.1×0.132\phantom{\rule{0ex}{0ex}}=0.0132\phantom{\rule{0ex}{0ex}}pH=-\mathrm{log}\left[{H}^{+}\right]\phantom{\rule{0ex}{0ex}}=-\mathrm{log}\left(0.0132\right)\phantom{\rule{0ex}{0ex}}=-1.879:1.88$
Now,
${K}_{a}=C{a}^{2}\phantom{\rule{0ex}{0ex}}=0.1×{\left(0.132\right)}^{2}\phantom{\rule{0ex}{0ex}}{K}_{a}=0.0017\phantom{\rule{0ex}{0ex}}p{K}_{a}=2.75$