Which of the following reactions involve a decrease in the length of the carbon chain:-

Options

A. Schmidt reaction
B. Hofmann's bromamide reaction
C. Hell-Volhard-Zelinski reaction
D. All of these

Answer

To determine which reactions involve a decrease in the length of the carbon chain, we need to analyze each reaction provided in the question.

### Step-by-Step Solution:

1. **Understanding the Reactions**:
- We need to identify reactions that lead to a reduction in the number of carbon atoms in the reactants compared to the products.

2. **Smith Reaction**:
- The Smith reaction involves the conversion of a carbonyl compound (like benzoic acid) to an amine (like aniline).
- Example: Benzoic acid (C7H6O2) reacts with hydrozoic acid (HN3) in an acidic medium to form aniline (C6H5NH2).
- Here, we start with 7 carbon atoms in benzoic acid and end up with 6 carbon atoms in aniline.
- **Conclusion**: This reaction results in a decrease in the carbon chain length.

3. **Hoffman Bromamide Reaction**:
- This reaction involves the degradation of amides to primary amines using a strong base and bromine (Br2).
- Example: An amide (RCONH2) reacts to yield a primary amine (RNH2) with one less carbon atom.
- **Conclusion**: This reaction also results in a decrease in the carbon chain length.

4. **Hell-Volhard-Zelinsky (HVZ) Reaction**:
- This reaction involves the halogenation of the alpha carbon of a carboxylic acid.
- Example: A carboxylic acid (RCOOH) reacts with bromine (Br2) in the presence of red phosphorus, resulting in the alpha-bromo carboxylic acid.
- In this case, the number of carbon atoms remains unchanged as we are substituting a hydrogen atom with a bromine atom.
- **Conclusion**: This reaction does not decrease the carbon chain length.

5. **Final Answer**:
- The reactions that involve a decrease in the length of the carbon chain are:
- **Smith Reaction**
- **Hoffman Bromamide Reaction**

### Summary:
The answer to the question is that the Smith Reaction and the Hoffman Bromamide Reaction involve a decrease in the length of the carbon chain.