Arrange the following carbocations in order of stability
`{:("benzyl allyl methyl vinyl"),(" I II III IV"):}`

Options

A. `IV gt III gt II gt I`
B. `I gt II gt III gt IV`
C. `II gt IV gt III gt I`
D. `III gt II gt I gt IV`

Answer

To arrange the given carbocations (benzyl, allyl, methyl, and vinyl) in order of stability, we can analyze each carbocation based on resonance and hybridization effects. Here’s a step-by-step breakdown of the solution:

### Step 1: Identify the Carbocations
- **Benzyl Carbocation (I)**: This has a positive charge on a carbon that is directly attached to a benzene ring.
- **Allyl Carbocation (II)**: This has a positive charge on a carbon that is adjacent to a carbon-carbon double bond.
- **Methyl Carbocation (III)**: This has a positive charge on a carbon that is attached to three hydrogens (no resonance).
- **Vinyl Carbocation (IV)**: This has a positive charge on a carbon that is part of a double bond (sp-hybridized).

### Step 2: Analyze Resonance Stabilization
- **Benzyl Carbocation**: The positive charge can be delocalized over the benzene ring through resonance. This results in multiple resonance structures, enhancing stability.
- **Allyl Carbocation**: The positive charge can also be delocalized through resonance with the adjacent double bond, but it has fewer resonance structures compared to the benzyl carbocation.
- **Methyl Carbocation**: This carbocation has no resonance stabilization; it is a simple structure with a positive charge on a carbon.
- **Vinyl Carbocation**: Similar to the methyl carbocation, it has no resonance stabilization. Additionally, the carbon bearing the positive charge is sp-hybridized, which is less stable due to higher s-character (50%).

### Step 3: Compare Stability
- **Benzyl (I)**: Most stable due to extensive resonance.
- **Allyl (II)**: More stable than methyl and vinyl due to resonance but less stable than benzyl.
- **Methyl (III)**: More stable than vinyl due to lower s-character.
- **Vinyl (IV)**: Least stable due to lack of resonance and high s-character.

### Step 4: Order of Stability
Based on the analysis:
1. **Benzyl (I)** - Most stable
2. **Allyl (II)**
3. **Methyl (III)**
4. **Vinyl (IV)** - Least stable

Thus, the order of stability of the carbocations is:
**Benzyl > Allyl > Methyl > Vinyl**

### Final Answer
The correct order of stability is:
**I > II > III > IV**

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