Which of these carbocation will undergo favourable rearrangement?

Options

A.
B.
C.
D.

Answer

To determine which carbocation will undergo favorable rearrangement, we need to analyze the stability of each carbocation based on the number of alpha hydrogens and the potential for rearrangement. Here’s a step-by-step breakdown of the solution:

### Step 1: Identify the Carbocations
We have four different carbocations to analyze. Each carbocation is associated with a specific structure, which we will evaluate for stability and potential rearrangement.

### Step 2: Analyze the First Carbocation
- **Structure**: A cyclohexane ring with a carbocation.
- **Alpha Hydrogens**: Count the alpha hydrogens around the carbocation.
- Methyl group contributes 3 hydrogens.
- Other groups contribute additional hydrogens.
- **Total Alpha Hydrogens**: 6.
- **Rearrangement**: If we shift a hydride, the total alpha hydrogens remain the same (6). Thus, no favorable rearrangement occurs.

### Step 3: Analyze the Second Carbocation
- **Structure**: A cyclohexane ring with a methyl and ethyl group.
- **Alpha Hydrogens**: Count the alpha hydrogens.
- Methyl contributes 3 hydrogens.
- Ethyl contributes 2 hydrogens.
- **Total Alpha Hydrogens**: 5.
- **Rearrangement**:
- If we shift the methyl group, we get a new carbocation with 6 alpha hydrogens.
- If we shift the ethyl group, we also get a carbocation with 6 alpha hydrogens.
- **Conclusion**: The rearrangement is favorable since we increase the stability of the carbocation.

### Step 4: Analyze the Third Carbocation
- **Structure**: A cyclohexane ring with two methyl groups.
- **Alpha Hydrogens**: Count the alpha hydrogens.
- Each methyl group contributes 3 hydrogens.
- **Total Alpha Hydrogens**: 5.
- **Rearrangement**:
- Shifting a methyl group results in a carbocation with 4 alpha hydrogens.
- Shifting the ethyl group results in a carbocation with 5 alpha hydrogens.
- **Conclusion**: No favorable rearrangement occurs as the stability does not increase.

### Step 5: Analyze the Fourth Carbocation
- **Structure**: No carbocation present.
- **Conclusion**: Since there is no carbocation, no rearrangement can occur.

### Final Conclusion
The only carbocation that undergoes a favorable rearrangement is from the **second option**. The other options do not provide a more stable carbocation upon rearrangement.

### Summary of Findings
- **Favorable Rearrangement**: Second option.
- **Unfavorable Rearrangement**: First, third, and fourth options.