You have the following reagents on hand: \begin{tabular}{|ll|} \hline Solids \(\left(\mathrm{p} \boldsymbol{K}_{\mathrm{a}}\right.\) of Acid Form Is Given) & Solutions \\ \hline Benzoic acid (4.19) & \(5.0 \mathrm{M} \mathrm{HCl}\) \\ Sodium acetate (4.74) & \(1.0 \mathrm{M}\) acetic acid (4.74) \\ Potassium fluoride (3.14) & \(2.6 \mathrm{M} \mathrm{NaOH}\) \\ Ammonium chloride (9.26) & \(1.0 \mathrm{M} \mathrm{HOCl}(7.46)\) \\ \hline \end{tabular} What combinations of reagents would you use to prepare buffers at the following \(\mathrm{pH}\) values? a. \(3.0\) b. \(4.0\) c. \(5.0\) d. \(7.0\) e. \(9.0\)

The Henderson-Hasselbalch equation is given by: \[pH = pKa + \log_{10}\left(\frac{[\mathrm{A}^-]}{[\mathrm{HA}]}\right)\] where: - \(pH\) is the desired pH value of the buffer solution - \(pKa\) is the acid dissociation constant of the weak acid - \([\mathrm{A}^-]\) is the concentration of the conjugate base of the weak acid - \([\mathrm{HA}]\) is the concentration of the weak acid We will use this equation to identify proper combinations of reagents for each given pH value.

For each pH value, we will look for a reagent pair whose pKa value is closest to the desired pH value. Once we have a pair, we can use the reagents to adjust the concentrations of \([\mathrm{A}^-]\) and \([\mathrm{HA}]\) to achieve the desired pH value. a. Desired pH: 3.0 The closest pKa value is 3.14 for potassium fluoride. We can combine potassium fluoride with a weak acid, such as 1.0 M acetic acid (4.74). b. Desired pH: 4.0 The closest pKa values are 4.19 for benzoic acid and 4.74 for sodium acetate. We can combine either benzoic acid or sodium acetate with a strong acid, such as 5.0 M HCl or a weak base, such as 2.6 M NaOH. c. Desired pH: 5.0 The closest pKa value is 4.74 for sodium acetate. We can combine sodium acetate with a weak acid, such as 1.0 M acetic acid (4.74). d. Desired pH: 7.0 The closest pKa value is 7.46 for 1.0 M HOCl. We can combine 1.0 M HOCl with a weak base, such as ammonium chloride (9.26). e. Desired pH: 9.0 The closest pKa value is 9.26 for ammonium chloride. We can combine ammonium chloride with a weak acid, such as 1.0 M HOCl (7.46), or a strong base, such as 2.6 M NaOH. By selecting appropriate reagents and adjusting their concentrations, we can prepare the desired buffer solutions at various pH values.