For solutions containing salts of the form \(\mathrm{NH}_{4} \mathrm{X}\), the \(\mathrm{pH}\) is determined by using the equation

\[\mathrm{pH}=\frac{\mathrm{p} K_{\mathrm{a}}\left(\mathrm{NH}_{4}^{+}ight)+\mathrm{p} K_{\mathrm{a}}(\mathrm{HX})}{2}\]

a. Derive this equation. (Hint: Review Section 8.7 on the \(\mathrm{pH}\) of solutions containing amphoteric species.)

b. Use this equation to calculate the \(\mathrm{pH}\) of the following solutions: ammonium formate, ammonium acetate, and ammonium bicarbonate. See Appendix 5 for \(K_{\mathrm{a}}\) values.

c. Solutions of ammonium acetate are commonly used as \(\mathrm{pH}=7.0\) buffers. Write equations to show how an ammonium acetate solution neutralizes added \(\mathrm{H}^{+}\)and \(\mathrm{OH}^{-}\).