Question

Which of the following combinations would be the best to buffer the pH of a solution at approximately \(7 ?\) (a) \(\mathrm{H}_{3} \mathrm{PO}_{4}\) and \(\mathrm{NaH}_{2} \mathrm{PO}_{4}\) (b) \(\mathrm{NaH}_{2} \mathrm{PO}_{4}\) and \(\mathrm{Na}_{2} \mathrm{HPO}_{4}\) (c) \(\mathrm{Na}_{2} \mathrm{HPO}_{4}\) and \(\mathrm{Na}_{3} \mathrm{PO}_{4}\)

Short answer

The best combination is (b) NaH₂PO₄ and Na₂HPO₄.

Step-by-step solution

Understanding Buffers

Buffers are solutions that resist changes in pH when small amounts of acid or base are added. They typically consist of a weak acid and its conjugate base, or a weak base and its conjugate acid. The optimal buffering occurs at the pKa of the weak acid or base, where the concentrations of the acid/base pair are equal. Thus, to buffer around a pH of 7, we need a buffer system with a pKa near this value.

Identifying pKa Values

For each potential buffer system, identify the relevant dissociation step for buffering near pH 7. The pKa values for phosphoric acid (\(\mathrm{H}_{3}\mathrm{PO}_{4}\), \(\mathrm{NaH}_{2}\mathrm{PO}_{4}\), \(\mathrm{Na}_{2}\mathrm{HPO}_{4}\), and \(\mathrm{Na}_{3}\mathrm{PO}_{4}\)) are approximately:- \(\mathrm{H}_{3}\mathrm{PO}_{4}\) to \(\mathrm{NaH}_{2}\mathrm{PO}_{4}\): pKa = 2.1 - \(\mathrm{NaH}_{2}\mathrm{PO}_{4}\) to \(\mathrm{Na}_{2}\mathrm{HPO}_{4}\): pKa = 7.2- \(\mathrm{Na}_{2}\mathrm{HPO}_{4}\) to \(\mathrm{Na}_{3}\mathrm{PO}_{4}\): pKa = 12.4The closest pKa value to 7 is 7.2.

Selecting the Best Buffer Combination

Since we're aiming to buffer at pH 7, check which combination involves the ions with a pKa nearest to 7. The combination of \(\mathrm{NaH}_{2}\mathrm{PO}_{4}\) and \(\mathrm{Na}_{2}\mathrm{HPO}_{4}\) has a pKa of 7.2, which is optimally suited for buffering around pH 7.

Conclusion

The best combination to buffer a solution at approximately pH 7 is \(\mathrm{NaH}_{2}\mathrm{PO}_{4}\) and \(\mathrm{Na}_{2}\mathrm{HPO}_{4}\) as they have a pKa closest to 7.

Key concepts

Weak Acid

A weak acid is an acid that only partially dissociates into its ions in a solution. Unlike strong acids, which almost completely dissociate, weak acids maintain an equilibrium between the un-ionized acid and its ions. A classic example of a weak acid is acetic acid, commonly found in vinegar. It's important to understand that not all molecules of a weak acid will release hydrogen ions (H⁺) into the solution. This partial dissociation is what gives weak acids their characteristic buffering ability.

Weak acids are essential in creating buffer solutions. A buffer solution can maintain a relatively constant pH when small amounts of acids or bases are added. This is because the weak acid in the buffer system can donate protons to neutralize added bases, and its conjugate base can accept protons to neutralize added acids. The relationship between the weak acid and its conjugate base is key to the buffer's function, allowing it to resist shifts in pH levels.

Conjugate Base

The conjugate base of an acid is the species that remains after the acid has donated a proton (H⁺). For example, if the weak acid is acetic acid (CH₃COOH), its conjugate base would be acetate (CH₃COO⁻). This base is formed during the dissociation of the weak acid. In buffer systems, the conjugate base plays a vital role in stabilizing the pH.

The presence of the conjugate base allows the buffer solution to neutralize added acids. When an extra acid is introduced into the solution, the conjugate base will react with the additional hydrogen ions, reducing the likelihood of a pH change. Similarly, when a base is introduced, the weak acid part of the buffer donates a proton to counter the base's effect. This dual action of the weak acid and its conjugate base working in tandem is what keeps the pH of the solution steady, an essential aspect in many chemical and biological systems, like blood pH regulation.

Understanding conjugate acids and bases is crucial for correctly selecting components of buffer solutions that can effectively resist changes in pH. By carefully choosing a weak acid and its conjugate base, one can tailor a buffer to stabilize the pH at a desired value.

pKa Value Measurement

The pKa value is a vital measure for understanding an acid's strength and its potential use in a buffer solution. It reflects the acid's ability to donate protons to the solution. Specifically, pKa is the negative logarithm of the acid dissociation constant (Ka), which measures the disassociation potential of a weak acid. When considering pKa, a smaller value indicates a stronger acid, which means it is more willing to donate a proton.

For buffer solutions, the pKa is essential because it helps to determine the pH range in which the acid and its conjugate base will effectively resist changes in pH. The Henderson-Hasselbalch equation:
\[pH = pKa + \log \left( \frac{[A⁻]}{[HA]} \right)\]
is often used to calculate the pH of buffer solutions. Here, \([A⁻]\) and \([HA]\) represent the concentrations of the conjugate base and the acid, respectively. Buffer solutions are most effective when the pH is close to the pKa of the weak acid, as this is where the solution demonstrates optimal ability to neutralize acids and bases.

Choosing a buffer system for specific pH requires selecting one with a pKa close to the target pH. For instance, in the case of buffering at pH 7, finding a system with a pKa close to this value ensures maximal effectiveness. This explains why, in the original exercise, the combination of NaH₂PO₄ and Na₂HPO₄ - with a pKa of 7.2 - is ideal for stabilizing a pH of approximately 7.