If in an amino acid, the carboxylic group ionizes at \(\mathrm{pKa}_{1}=2.34\) and the ammonium ion at \(\mathrm{pKa}_{2}=9.60\). The isoelectric point of the amino acid is: (a) \(2.36\) (b) \(5.97\) (c) \(6.86\) (d) \(7.58\)

Amino acids are the building blocks of proteins and play a crucial role in biological processes. They consist of a central carbon atom (the \(\alpha\)-carbon), an amino group (\(NH_2\)), a carboxyl group (\(COOH\)), a hydrogen atom, and an R group or side chain that varies between different amino acids and determines their unique characteristics.

In the context of the isoelectric point, the amino group, which can act as a base, and the carboxyl group, which can act as an acid, are particularly important because they can gain or lose protons (\(H^+\)) depending on the pH of the environment. As a result, they exist in different ionic forms which affect the overall charge of the amino acid at varying pH levels. Understanding the behavior of these groups in different pH conditions is essential for the determination of the isoelectric point.

The pKa value is a measure that indicates the strength of an acid, specifically the tendency of the acid to donate a proton. Every ionizable group of an amino acid has an associated pKa value; it is the pH at which half of the molecules of that group are deprotonated. For amino acids with non-ionizable side chains, there are typically two pKa values to consider: one for the carboxyl group and one for the amino group.

Significance of pKa in Amino Acids

For the carboxyl group, the associated pKa (let's call it \(\mathrm{pKa}_{1}\)) is a reflection of when the group starts to lose a proton and becomes negatively charged. Similarly, the pKa for the amino group (\(\mathrm{pKa}_{2}\)) represents the point at which it starts accepting a proton, gaining a positive charge. It's at the pH between these two values that an amino acid can be found in its zwitterionic form, where it has both a positive and a negative charge but the overall charge is zero.

The pH is a scale used to specify how acidic or basic (alkaline) a water-based solution is. Mathematically, pH is the negative logarithm, base 10, of the molar concentration of hydrogen ions (\(H^+\)) in a solution. The pH scale typically runs from 0 to 14, with 7 being neutral. Below 7 indicates acidity, and above 7 indicates alkalinity.

In relation to amino acids, the isoelectric point, or pI, is the specific pH at which an amino acid has no net electric charge. Calculating the pI is especially simple when the amino acid does not have an ionizable side chain, as it will then depend only on the two core pKa values. The pI is found by averaging the pKa values: \[ pI = \frac{\mathrm{pKa}_{1} + \mathrm{pKa}_{2}}{2} \]

Applying this calculation to our exercise, we take the given pKa values, \(\mathrm{pKa}_{1} = 2.34\) and \(\mathrm{pKa}_{2} = 9.60\), and average them to find the pI. This yields a pI of 5.97, which corresponds to choice (b) in the multiple-choice exercise. At this pH, the amino acid’s overall charge is neutral, which is an important concept for processes such as protein purification and understanding enzyme activity.