Consider the ionization of the following acid-base indicator:
$$
\operatorname{HIn}(a q) \Longrightarrow \mathrm{H}^{+}(a
q)+\operatorname{In}^{-}(a q)
$$
The indicator changes color according to the ratios of the concentrations of
the acid to its conjugate base as described inSection \(16.5 .\) Show that the
\(\mathrm{pH}\) range over which the indicator changes from the acid color to
the base color is \(\mathrm{pH}=\mathrm{p} K_{\mathrm{a}} \pm 1,\) where
\(K_{\mathrm{a}}\) is the ionization constant of the acid.