Which one is most reactive towards `S_(N)1` reactions ?

Options

A. `C_(6)H_(5) CH(C_(6)H_(5))`Br
B. `C_(6)H_(5) CH(CH_(3))`Br
C. `C_(6)H_(5) C(CH_(3))(C_(6)H_(5))`Br
D. `C_(6)H_(5) CH_(2)`Br

Answer

To determine which compound is most reactive towards SN1 reactions, we need to analyze the stability of the carbocations formed during these reactions. The more stable the carbocation, the more reactive the compound will be in an SN1 reaction.

### Step-by-Step Solution:

1. **Understand SN1 Mechanism**:
- SN1 (Substitution Nucleophilic Unimolecular) reactions involve the formation of a carbocation intermediate. The stability of this carbocation is crucial for the reactivity of the compound.

2. **Analyze Each Option**:
- **Option 1**: C₆H₅CH(C₆H₅)Br
- Upon losing Br, it forms a benzyl carbocation stabilized by resonance from two phenyl rings.
- Stability: High due to resonance stabilization from two phenyl groups.

- **Option 2**: C₆H₅CH(CH₃)Br
- Upon losing Br, it forms a carbocation that is stabilized by one phenyl ring and the inductive effect of the methyl group.
- Stability: Moderate due to one phenyl group and inductive effect.

- **Option 3**: C₆H₅C(CH₃)C₆H₅Br
- Upon losing Br, it forms a carbocation that is stabilized by two phenyl rings and the inductive effect of the methyl group.
- Stability: Very high due to resonance from two phenyl groups and inductive effect from the methyl group.

- **Option 4**: C₆H₅CH₂Br
- Upon losing Br, it forms a primary carbocation that is only stabilized by one phenyl ring.
- Stability: Low due to only one phenyl group providing resonance stabilization.

3. **Compare Carbocation Stability**:
- Option 1: Stabilized by 2 phenyl rings (highest stability).
- Option 2: Stabilized by 1 phenyl ring and a methyl group (moderate stability).
- Option 3: Stabilized by 2 phenyl rings and a methyl group (very high stability).
- Option 4: Stabilized by 1 phenyl ring (lowest stability).

4. **Conclusion**:
- The most stable carbocation is formed from **Option 3 (C₆H₅C(CH₃)C₆H₅Br)**, making it the most reactive towards SN1 reactions.

### Final Answer:
**Option 3 (C₆H₅C(CH₃)C₆H₅Br) is the most reactive towards SN1 reactions.**