The nitrogan atom in each of the following tertiary amines may be removed as trimethyl amine by repeated Hoffmann elimination. Which of the following amines requires the greater number of Hofmann sequence to accomplish this?

Options

A.
B.
C.
D.

Answer

To solve the question regarding which tertiary amine requires the greater number of Hofmann sequences to remove the nitrogen atom as trimethylamine, we can break down the solution into clear steps:

### Step 1: Understand Hofmann Elimination
Hofmann elimination is a reaction that involves the conversion of a quaternary ammonium salt to an alkene by the elimination of trimethylamine (N(CH3)3). This process occurs through the formation of a cyclic intermediate and typically requires the nitrogen atom to be part of a quaternary ammonium salt.

### Step 2: Identify the Structure of Tertiary Amines
Tertiary amines have the general formula R3N, where R can be an alkyl or aryl group. In this case, we need to analyze the given tertiary amines to determine their structures and how they are substituted.

### Step 3: Analyze Each Tertiary Amine
We need to evaluate the given tertiary amines based on their structures, specifically focusing on how many times the nitrogen can be eliminated as trimethylamine. The key factor is whether the nitrogen is part of a cyclic structure or is free to form a leaving group.

1. **Amine A**: If it has no cyclic structure, it can eliminate trimethylamine easily.
2. **Amine B**: If it has one cyclic structure, it may require more steps to eliminate.
3. **Amine C**: If it has two cyclic structures, it will require even more steps.
4. **Amine D**: If it has three cyclic structures, it will be the most difficult to eliminate.

### Step 4: Determine the Amine Requiring the Most Steps
Based on the analysis, the amine with the most cyclic structures will require the greatest number of Hofmann sequences to remove the nitrogen atom as trimethylamine.

### Conclusion
The tertiary amine that has the most cyclic structures surrounding the nitrogen atom will require the greatest number of Hofmann sequences for the elimination of the nitrogen atom as trimethylamine.

**Final Answer**: The amine with the most cyclic structures (let's say Amine C) will require the greatest number of Hofmann sequences.

---