Question

You need a buffer solution that has \(\mathrm{pH}=7.00\). Which of the following buffer systems should you choose? Explain. (a) \(\mathrm{H}_{3} \mathrm{PO}_{4}\) and \(\mathrm{H}_{2} \mathrm{PO}_{4}^{-}\) (b) \(\mathrm{H}_{2} \mathrm{PO}_{4}^{-}\) and \(\mathrm{HPO}_{4}^{2-}\) (c) \(\mathrm{HPO}_{4}^{2-}\) and \(\mathrm{PO}_{4}^{3-}\)

Short answer

Choose (b) \(\mathrm{H}_{2}\mathrm{PO}_{4}^{-}\) and \(\mathrm{HPO}_{4}^{2-}\); its pKa is closest to pH 7.00.

Step-by-step solution

Understanding Buffer Systems

A buffer is a solution that can resist pH changes when small amounts of acid or base are added. It consists of a weak acid and its conjugate base or a weak base and its conjugate acid. For an ideal buffer, the pH of the solution should be close to the pKa of the weak acid/base.

Identifying pKa Values

To solve the problem, we need to know the pKa values of the mentioned acid-base pairs: 1. For (a) \(\mathrm{H}_{3}\mathrm{PO}_{4}\) and \(\mathrm{H}_{2}\mathrm{PO}_{4}^{-}\), the pKa is approximately 2.1. 2. For (b) \(\mathrm{H}_{2}\mathrm{PO}_{4}^{-}\) and \(\mathrm{HPO}_{4}^{2-}\), the pKa is approximately 7.2. 3. For (c) \(\mathrm{HPO}_{4}^{2-}\) and \(\mathrm{PO}_{4}^{3-}\), the pKa is approximately 12.4.

Matching pH with pKa

To choose the best buffer system, select the system with a pKa value close to the desired pH of 7.00. Among the given options: - (a) has a pKa far below 7.00. - (b) has a pKa of 7.2, which is very close to the desired pH of 7.00. - (c) has a pKa far above 7.00.

Conclusion

The buffer system \(\mathrm{H}_{2}\mathrm{PO}_{4}^{-}\) and \(\mathrm{HPO}_{4}^{2-}\) (option b) is the best choice because its pKa is 7.2, which is closest to the target pH of 7.00, providing effective buffering capacity at that pH level.

Key concepts

pH Level

Understanding pH is crucial when dealing with buffer solutions. The pH level measures how acidic or basic a solution is, with a scale ranging from 0 to 14. At a pH of 7, the solution is neutral, like pure water. Values lower than 7 indicate acidity, and values higher than 7 indicate basicity.
The pH scale is logarithmic, meaning each whole number change represents a tenfold change in hydrogen ion concentration. Thus, even small changes in pH indicate significant changes in acidity or basicity. To determine the best buffer solution from several options, the desired pH helps guide the selection. A buffer should have a pH close to its pKa to effectively stabilize the pH of a solution. A buffer system with a good matching pH resists drastic pH fluctuations when acids or bases are introduced.
This balance makes buffer systems essential in various chemical and biological applications.

pKa Values

The concept of pKa values is critical in understanding buffer solutions. pKa is the negative logarithm of the acid dissociation constant ( Ka). It provides insight into the strength of an acid or base in a solution.
A small pKa value indicates a strong acid readily releases protons into the solution, while a larger pKa suggests a weaker acid.

• For a good buffer, select a pair with a pKa close to the target pH.
• This is because the buffer should resist changes in pH near its pKa value.

The relationship between pH and pKa is central in finding the right buffer system. By comparing the pKa values to the desired pH, you can strategically choose a buffer system that maintains the necessary pH balance in a solution. As seen in the exercise above, assessing the pKa values helped identify the optimal buffer pair.

Weak Acids and Bases

Weak acids and bases play an essential role in forming buffer solutions. They do not completely dissociate in water, providing a balance between acid and base that stabilizes the pH level. This partial dissociation is the reason buffer solutions are able to resist sudden pH changes when the solution is exposed to external acids or bases.
In a weak acid and its conjugate base pair, only a small amount of the acid remains undissociated in the solution but is enough to bond with most again if more base is added. Similarly, weak bases release fewer hydroxide ions compared to strong bases, allowing gradual pH changes.

• The partial dissociation of weak acids and bases makes them ideal for forming buffers.
• They provide a balancing mechanism in solutions, maintaining desired pH levels.

This chemical balance ensures that buffer solutions function effectively in various settings, from biological systems to industrial applications. They allow dynamic environments to remain stable despite external fluctuations in pH.