Step 1: Understanding Aspartame
Aspartame is a dipeptide formed by the condensation of aspartic acid and phenylalanine. The methyl ester group is added to the carboxyl group of the phenylalanine residue.
Step 2: Structural Features of Aspartame
Step 3: Verifying the Structure
Structure (B) correctly shows the peptide bond between aspartic acid and phenylalanine, with the methyl ester group on phenylalanine.
Conclusion
The correct structure of aspartame is represented by option (B).
To solve the problem, we need to determine the correct structure of aspartame, which is a dipeptide consisting of aspartyl phenylalanine methyl ester.
1. Understanding the Components:
Aspartame is made from aspartic acid and phenylalanine, with the phenylalanine part esterified as a methyl ester.
- Aspartic acid has two carboxyl groups, one of which forms a peptide bond.
- Phenylalanine contains a phenyl (Ph) group attached to the alpha carbon.
2. Structure of Aspartame:
- The amino group of phenylalanine bonds with the carboxyl group of aspartic acid.
- The free carboxyl group of phenylalanine is converted to methyl ester (–COOCH₃).
- The resulting structure is a dipeptide: aspartyl-phenylalanine methyl ester.
3. Identifying the Correct Option:
Among the given options, option (B) correctly shows:
- Aspartic acid with free amino and carboxyl groups.
- Phenylalanine linked via peptide bond.
- Methyl ester group at the carboxyl terminal of phenylalanine.
Thus, option (B) is the correct structure of aspartame.
Final Answer:
Option (B)
Let $ S $ denote the locus of the point of intersection of the pair of lines $$ 4x - 3y = 12\alpha,\quad 4\alpha x + 3\alpha y = 12, $$ where $ \alpha $ varies over the set of non-zero real numbers. Let $ T $ be the tangent to $ S $ passing through the points $ (p, 0) $ and $ (0, q) $, $ q > 0 $, and parallel to the line $ 4x - \frac{3}{\sqrt{2}} y = 0 $.
Then the value of $ pq $ is