Which of the following carbocations is least stable ?

Options

A. `Ph overset (oplus) CH_2`
B. `overset C H = CH_2`
C. `Me_2 overset (oplus) C H`
D. `CH_2 = CH - overset C H_2`

Explanation

To determine which carbocation is the least stable, we will analyze the stability of each carbocation based on three main factors: the +I effect (inductive effect), resonance, and hyperconjugation.

### Step 1: Identify the Carbocations
We have four carbocations to analyze:
1. **Carbocation A**: CH2+ on a benzene ring
2. **Carbocation B**: CH2=CH+
3. **Carbocation C**: CH(CH3)2+
4. **Carbocation D**: CH2=CH-CH2+

### Step 2: Analyze Carbocation A (Benzyl Carbocation)
- **Structure**: CH2+ attached to a benzene ring.
- **Stability Factors**:
- **Resonance**: The positive charge can be delocalized over the benzene ring, providing significant stability.
- **Conclusion**: This carbocation is relatively stable due to resonance.

### Step 3: Analyze Carbocation B (Vinyl Carbocation)
- **Structure**: CH2=CH+
- **Stability Factors**:
- **Hybridization**: The carbon with the positive charge is sp hybridized, which has a linear geometry.
- **Stability**: sp hybridized carbons have less p character and cannot stabilize the positive charge effectively, making this carbocation less stable.
- **Conclusion**: This carbocation is the least stable due to its hybridization and lack of resonance.

### Step 4: Analyze Carbocation C (Tertiary Carbocation)
- **Structure**: CH(CH3)2+
- **Stability Factors**:
- **+I Effect**: The two CH3 groups donate electrons towards the positively charged carbon.
- **Hyperconjugation**: There are 6 alpha hydrogens available for hyperconjugation, leading to multiple stabilizing interactions.
- **Conclusion**: This carbocation is very stable due to the +I effect and hyperconjugation.

### Step 5: Analyze Carbocation D (Allyl Carbocation)
- **Structure**: CH2=CH-CH2+
- **Stability Factors**:
- **Resonance**: The positive charge can be delocalized over the adjacent double bond, providing stability.
- **Conclusion**: This carbocation is stable due to resonance.

### Final Conclusion
After analyzing all four carbocations, we find that **Carbocation B (CH2=CH+)** is the least stable due to its sp hybridization and lack of resonance stabilization.