Problem 138 - A Complete Resource Book in Chemistry for JEE Main

Question

The following amino acid has characteristic pKa values \(\mathrm{H}_{3} \mathrm{~N}^{\oplus}-\mathrm{CH}_{2}-\mathrm{CH}_{2}-\mathrm{CH}_{2}-\mathrm{CH}_{2}-\mathrm{CH}-\mathrm{COOH}\) (3) [C-] \(\mathrm{NH}_{3}\) (2) \(\mathrm{pK}_{\mathrm{a}(1)}=2.18 ; \mathrm{pK}_{a(2)}=8.95\) and \(\mathrm{pK}_{\mathrm{a}(3)}=10.79\) The isoelectric point pI of the above amino acid is (a) \(5.56\) (b) \(9.87\) (c) \(11.13\) (d) \(12.97\)

Step-by-Step Solution

Answer

The isoelectric point of the amino acid is 9.87 (option b).

Step 1: Identify Relevant pKa Values

To find the isoelectric point (pI), we need to consider only the pKa values involved in the transition between the charged states. For amino acids with three pKa values, the relevant ones for calculating the pI are the ones that involve the neutral form. This will be between the pKa values where the molecule transitions from positive to neutral and from neutral to negative.

Step 2: Determine Transition Points

The three given pKa values are 2.18, 8.95, and 10.79. Generally, amino acids have a zwitterionic form that is neutral, so we look for two values that are close between the positive (fully protonated) and the negative state (fully deprotonated). Thus, the relevant pKa values for the zwitterionic form transition, which affect the pI, are pKa2 and pKa3.

Step 3: Calculate Isoelectric Point (pI)

The isoelectric point is the average of the pKa values that describe the state transitions from the positive to neutral and neutral to negative forms of the amino acid. Therefore, calculate the pI using the formula: \[ pI = \frac{pK_{a2} + pK_{a3}}{2} \]Substitute the values:\[ pI = \frac{8.95 + 10.79}{2} \]

Step 4: Compute Average

Perform the calculation to find the average:\[ pI = \frac{8.95 + 10.79}{2} = \frac{19.74}{2} = 9.87 \]

Key Concepts

pKa Values

Understanding pKa values is fundamental when studying amino acids and their behavior in different pH environments. A pKa value is a measure of the strength of an acid; it tells us the pH at which a particular proton can be removed or added to a molecule.
The lower the pKa value, the stronger the acid, meaning it can donate a proton more easily. In the case of amino acids, we are often concerned with multiple pKa values because these molecules usually contain more than one ionizable group.

• pKa1: Generally, this is for the carboxyl group ( ext{-COOH})
• pKa2: Appears for the amino group ( ext{-NH}_3^{+})
• pKa3: If present, is usually related to side chains if they have ionizable groups

Recognizing which pKa values are relevant in transitions from charged to zwitterionic to another charged form is critical for understanding their behavior at specific pH levels.

Amino Acid Zwitterion

At its core, a zwitterion is an ion that contains both a positive and a negative charge but is overall electrically neutral. Amino acids often exist in this form in physiological conditions.
The existence of a zwitterion form is due to the ability of amino acids to donate and accept protons, which interchangeably affects the charges on the amino and carboxyl groups.

• This unique property derives from their amphoteric nature, meaning they can act as either an acid or a base
• Zwitterionic form is typically most stable for many amino acids around a neutral pH

Being amphi-protic makes amino acids versatile, allowing them to adapt to various pH environments and making them crucial in biological processes such as protein building.

pI Formula

Calculating the isoelectric point (pI) of an amino acid is fundamental to understanding at which pH the amino acid carries no net electric charge. This is particularly important for processes such as protein purification and electrophoresis.
The formula used to find the pI involves averaging the pKa values that describe transitions from positive to zwitterion (neutral) and from zwitterion to negative forms. For the presented exercise:

• The relevant pKa values used are 8.95 ( ext{pKa2}) and 10.79 ( ext{pKa3})
• The pI is calculated using: \[ pI = \frac{pKa2 + pKa3}{2} = \frac{8.95 + 10.79}{2} \]
• The resulting isoelectric point for the given amino acid is 9.87

This concept is essential because at its pI, an amino acid is least soluble and moves the slowest in an electric field, helping in various separation techniques.

Acid-Base Chemistry

Acid-base chemistry forms the backbone for understanding the behavior of amino acids under different pH conditions. It assesses how compounds donate or accept protons in these contexts.
For amino acids, this involves understanding their behavior as they switch from acting as acids (proton donors) to bases (proton acceptors) depending on their structure and the surrounding environment's pH.

• This understanding helps determine the charge state of an amino acid at any given pH
• Ions of amino acids result from dissociation of hydrogens in acidic groups or association in basic groups
• Amino acids in solution can exist in multiple states, such as protonated, zwitterionic, or deprotonated

Grasping these principles is crucial for predicting reactions and interactions in biochemistry and molecular biology.