Consider the following carbocations
(I)`C_(6)H_(5)overset(+)CH_(2)` , (II)`C_(6)H_(5)CH_(2)overset(+)CH_(2)`
(III)`C_(6)H_(5)overset(+)CHCH_(3)` , (IV) `C_(6)H_(5)overset(+)C(CH_(3))_(2)`
The correct sequence for the stability of these is

Options

A. (II) lt (I) lt (III) lt (IV)
B. (I) lt (II) lt (III) lt (IV)
C. (III) lt (II) lt (I) lt (IV)
D. (IV) lt (I) lt (III) lt (I)

Answer

To determine the stability of the given carbocations, we will analyze each structure based on resonance and hyperconjugation effects. Here’s a step-by-step breakdown of the solution:

### Step 1: Draw the Structures
First, we need to visualize the structures of the carbocations provided:

1. **Carbocation I**: `C6H5-CH2+`
2. **Carbocation II**: `C6H5-CH2-CH2+`
3. **Carbocation III**: `C6H5-CH+CH3`
4. **Carbocation IV**: `C6H5-C(CH3)2+`

### Step 2: Analyze Resonance Effects
- **Carbocation I**: The positive charge is directly attached to a carbon that is bonded to the benzene ring. This allows for resonance stabilization.
- **Carbocation II**: The positive charge is on a carbon that is not directly attached to the benzene ring. Therefore, it does not benefit from resonance stabilization.
- **Carbocation III**: The positive charge is on a carbon that is adjacent to the benzene ring, allowing for some resonance stabilization.
- **Carbocation IV**: Similar to Carbocation I, it has resonance stabilization due to the positive charge being adjacent to the benzene ring.

### Step 3: Analyze Hyperconjugation Effects
- **Carbocation I**: No hyperconjugation since it has no alkyl groups attached to the positively charged carbon.
- **Carbocation II**: No hyperconjugation since it is a primary carbocation.
- **Carbocation III**: Has one methyl group that can provide hyperconjugation.
- **Carbocation IV**: Has two methyl groups that can provide hyperconjugation, making it more stable.

### Step 4: Stability Ranking
Now, we can rank the stability of the carbocations based on the above analyses:
1. **Carbocation II**: Least stable (no resonance, primary carbocation)
2. **Carbocation I**: More stable than II (resonance but no hyperconjugation)
3. **Carbocation III**: More stable than I (resonance + some hyperconjugation)
4. **Carbocation IV**: Most stable (resonance + maximum hyperconjugation)

### Conclusion
The correct sequence for the stability of the carbocations is:
**II < I < III < IV**

### Final Answer
The correct order of stability is: **2 < 1 < 3 < 4**.

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