The ${\mathrm{pK}}_{\mathrm{a}}$ of acetic acid and ${\mathrm{pK}}_{\mathrm{b}}$ of ammonium hydroxide are 4.76 and 4.75 respectively. Calculate the pH of ammonium acetate solution.

As ${\mathrm{CH}}_3{\mathrm{COONH}}_4$ is a salt of weak acid and weak base.

$\mathrm{Given}, {\mathrm{pK}}_{\mathrm{a}} ( {\mathrm{CH}}_3\mathrm{COOH} ) = 4.76 \mathrm{and} {\mathrm{pK}}_{\mathrm{b}} ( {\mathrm{NH}}_4\mathrm{OH} ) = 4.75$

$\mathrm{The} \mathrm{reaction} \mathrm{taking} \mathrm{place} \mathrm{is}: {\mathrm{CH}}_3\mathrm{COOH} + {\mathrm{NH}}_4\mathrm{OH} \rightleftharpoons {\mathrm{CH}}_3{\mathrm{COONH}}_4 + {\mathrm{H}}_2\mathrm{O}$

$$\begin{gathered} {\mathrm{p}}^{\mathrm{H}}= 7+\frac{1}{2}\left[{\mathrm{pK}}_{\mathrm{a}}-{\mathrm{pK}}_{\mathrm{b}}\right] \\ =7+\frac{1}{2}(4.76-4.75) \\ =7+0.005=7.005 \end{gathered}$$