Step 1: Analyze Statement (I).
Statement (I) claims that oligopeptides yield a smaller number of \( \alpha \)-amino acids upon hydrolysis, while proteins yield a large number of \( \beta \)-amino acids. Oligopeptides are short chains of amino acids linked by peptide bonds. Hydrolysis of oligopeptides breaks these peptide bonds, resulting in the constituent amino acids.
These amino acids are \( \alpha \)-amino acids, characterized by the amino group and the carboxyl group attached to the same carbon atom (the \( \alpha \)-carbon). The number of \( \alpha \)-amino acids produced is equal to the number of peptide bonds broken plus one (the original N-terminal amino acid), which is a small number for oligopeptides. Proteins are long chains (polymers) of amino acids. Upon hydrolysis, proteins also yield \( \alpha \)-amino acids, and the number of these amino acids is large due to the large size of protein molecules. Proteins do not yield \( \beta \)-amino acids upon hydrolysis. \( \beta \)-amino acids have the amino group attached to the carbon atom adjacent to the carboxyl group (\( \beta \)-carbon).
Peptide bonds in proteins are formed between the \( \alpha \)-carboxyl group of one amino acid and the \( \alpha \)-amino group of the next. Therefore, Statement (I) is incorrect because proteins yield \( \alpha \)-amino acids, not \( \beta \)-amino acids, upon hydrolysis.
Step 2: Analyze Statement (II).
Statement (II) claims that natural proteins are denatured by acids, converting water-soluble fibrous proteins to their water-insoluble form. Denaturation of proteins involves the disruption of their secondary, tertiary, and quaternary structures, leading to a loss of their native conformation and biological activity. Acids are indeed denaturing agents for proteins as they can disrupt ionic bonds and hydrogen bonds within the protein structure.
However, the statement specifically mentions fibrous proteins becoming water-insoluble upon denaturation. Many fibrous proteins, such as keratin and collagen, are inherently water-insoluble due to their structure and amino acid composition, which often involves a high proportion of hydrophobic residues and extensive cross-linking. Denaturation might cause further aggregation or structural changes but does not necessarily convert a water-soluble fibrous protein to a water-insoluble form, especially since many are already insoluble. Furthermore, denaturation can affect both globular (often water-soluble) and fibrous proteins. The outcome on solubility depends on the specific protein and the nature of the denaturation process.
Therefore, Statement (II) is also incorrect as it presents an oversimplified and potentially misleading view of protein denaturation and solubility changes, particularly for fibrous proteins.
Step 3: Determine the correctness of both statements.
Based on the analysis, Statement (I) is incorrect, and Statement (II) is also incorrect.
Step 4: Choose the appropriate option.
The option that states both Statement I and Statement II are incorrect is (3).
Consider the following molecules:
The order of rate of hydrolysis is: