a. \( \begin{array}{l}\underbrace{100.0 \mathrm{~mL}}_{\underline{\text { Initial } \mathrm{pH}}} \text { of } 0.10 \mathrm{M} \mathrm{HC}_{7} \mathrm{H}_{5} \mathrm{O}_{2}\left(\mathrm{~K}_{\mathrm{a}}=6.4 \times 10^{-5}\right) \text { titrated by } 0.10 \mathrm{M} \mathrm{NaOH} \\ \\ \mathrm{pH} \text { at halfway point }\end{array} \)

At the halfway point of a titration, where half of the weak acid has been neutralized by the strong base, the pH can be calculated using the Henderson-Hasselbalch equation. Since we are titrating benzoic acid (HC₇H₅O₂) with NaOH, at this point, the concentration of benzoic acid will equal that of its conjugate base, sodium benzoate. This results in the pH equaling the pKa. With \(K_a=6.4 \times 10^{-5}\), we can find \(pK_a \approx 4.19\). Thus, at the halfway point, the pH will be approximately 4.19. Don't forget about the practical applications! Understanding this behavior is crucial for buffer solutions in various biochemical experiments. For example, in biological systems where enzymes might depend on a narrow pH range, knowing how to control and predict pH changes during titration is invaluable. It helps in designing better buffers for reactions or protocols in laboratories where pH stability is crucial, like protein purification or enzyme assays.