Question

You need to carry out an enzymatic reaction at pH \(7.5 .\) A friend suggests a weak acid with a \(\mathrm{p} K\) of 3.9 as the basis of a buffer. Will this substance and its conjugate base make a suitable buffer? Why or why not?

Short answer

No, because the effective buffer range (2.9 to 4.9) is not close to the desired pH of 7.5.

Step-by-step solution

Understand Buffer and pKa

Buffers are solutions that resist changes in pH when small amounts of acid or base are added. The effectiveness of a buffer is highest when its pH is close to the pKa of the weak acid. Generally, a buffer works most effectively within a pH range of ±1 of its pKa value.

Identify the Given pKa Value

The pKa of the weak acid provided is 3.9.

Calculate the Effective Buffer Range

Using the pKa of 3.9, we calculate the effective buffer range as 3.9 ± 1, which gives a range from 2.9 to 4.9.

Compare the Desired pH with the Buffer Range

The desired pH for the reaction is 7.5. Compare this with the effective buffer range of 2.9 to 4.9.

Conclusion

Since the desired pH of 7.5 is not within the effective buffer range of 2.9 to 4.9, the weak acid with a pKa of 3.9 will not make a suitable buffer for this reaction.

Key concepts

pKa and buffer effectiveness

Buffers are essential in biochemical reactions to stabilize the pH. Buffers work best when the pH of the solution is close to the pKa of the acid in the buffer. The pKa is a measure of the strength of an acid in solution and is the pH at which half of the acid is dissociated.
The general rule of thumb is that a buffer shows optimal resistance to pH changes within a pH range of ±1 from its pKa. This means if you have a weak acid with a pKa of 4, the buffer is most effective between pH 3 and pH 5.
For effective buffering in your solutions, always choose the weak acid whose pKa is as close as possible to your desired pH. This ensures that the buffer can neutralize added acids or bases, maintaining a stable pH environment.

Weak acids in buffer solutions

A buffer solution is typically made from a weak acid and its conjugate base, or a weak base and its conjugate acid. Weak acids, by definition, do not fully dissociate in water. This partial dissociation helps the buffer absorb excess hydrogen ions (H+) or hydroxide ions (OH−).
For example, acetic acid (a weak acid) can combine with its conjugate base, acetate, to create a buffer solution. When an acid is added to this buffer, the acetate ions can react with the hydrogen ions to form acetic acid, thus minimizing the change in pH.
Let's recall our exercise: A weak acid with a pKa of 3.9 is suggested for a reaction at pH 7.5. Since 7.5 is far away from the pKa of 3.9, this buffer system will not effectively stabilize the pH at 7.5, making it a poor choice for the reaction.

pH and buffer range

The pH of a solution is a measure of the hydrogen ion concentration. In buffer systems, the effective pH range is generally ±1 from the pKa of the buffering agent. In simpler terms, if the pKa is 5, the effective buffer range is from pH 4 to pH 6.
This range is critical because within these limits, the buffer can neutralize small additions of acids or bases. If the pH goes beyond this range, the buffer's ability to stabilize pH diminishes rapidly.
Returning to our exercise, the weak acid with a pKa of 3.9 has an effective buffer range of pH 2.9 to 4.9. Since the desired pH for the reaction is 7.5, which lies well outside this range, the buffering capacity is inadequate. So, always ensure the buffer's pH range aligns with your required pH to maintain the biochemical reaction conditions effectively.