Question

The$\mathrm{pKa}$ of a Weak Acid$\left(\mathrm{HA}\right)\mathrm{Is}4.5$. The $\mathrm{pOH}$ of an aqueous buffer solution of $\mathrm{HA}$ in Which $50\%$ of the acid is ionized Is:

Answer 1

Step 1: Finding $\mathrm{pH}$:

$$\begin{gathered} \mathrm{HA}\left(\mathrm{aq}\right)+{\mathrm{H}}_2\mathrm{O}\left(\mathrm{l}\right)\rightleftharpoons {\mathrm{H}}_3{\mathrm{O}}^{+}\left(\mathrm{aq}\right)+{\mathrm{A}}^{-}\left(\mathrm{aq}\right) \\ \mathrm{Acid}\mathrm{conjugage}\mathrm{base} \end{gathered}$$

$$\begin{gathered} \mathrm{pH}=\mathrm{pKa}+\log \frac{\left[\mathrm{acid}\right]}{[\mathrm{Conjugate}\mathrm{base}]} \\ \mathrm{pKa}=4.5 \\ [\mathrm{Conjugate}\mathrm{base}]=\left[\mathrm{acid}\right],\mathrm{as}50\%\mathrm{ionification} \\ \mathrm{pH}=4.5+\log \frac{0.5}{0.5} \\ \mathrm{pH}=4.5 \end{gathered}$$

Step 2: Finding $\mathrm{pOH}$:

$$\begin{gathered} \mathrm{pH}+\mathrm{pOH}=14 \\ \mathrm{pOH}=14-4.5=9.5 \end{gathered}$$