Which of the following is most reactive towards `S_(N)1` reaction?

Options

A. `C_6 H_5 C(CH_3)C_6 H_5 Br `
B. `C_8 H_5 CH_2 Br `
C. `C_6 H_5 CH 9(C_6 H_5) Br `
D. `C_6 H_5 CH ( CH_3)Br`

Explanation

To determine which compound is most reactive towards an \( S_N1 \) reaction, we need to analyze the stability of the carbocations that would form when the leaving group (in this case, a halide) departs. The stability of the carbocation is crucial because \( S_N1 \) reactions proceed through a carbocation intermediate.

### Step-by-Step Solution:

1. **Identify the Leaving Group**:
In an \( S_N1 \) reaction, the leaving group is typically a halide (e.g., Br, Cl, I). When the halide leaves, it generates a carbocation.

2. **Carbocation Formation**:
The stability of the carbocation formed after the leaving group departs is the key factor in determining the reactivity of the compound. The more stable the carbocation, the more reactive the compound will be towards \( S_N1 \) reactions.

3. **Evaluate Carbocation Stability**:
Carbocations can be classified based on their degree of substitution:
- **Tertiary Carbocations**: Most stable due to hyperconjugation and inductive effects from surrounding alkyl groups.
- **Secondary Carbocations**: Less stable than tertiary but more stable than primary.
- **Primary Carbocations**: Least stable and generally not formed in \( S_N1 \) reactions.
- **Methyl Carbocations**: Also very unstable and not favored.

4. **Consider Resonance Effects**:
If the carbocation can be stabilized by resonance (e.g., adjacent double bonds or aromatic systems), this will further increase its stability. For example, a carbocation adjacent to a benzene ring can be stabilized by resonance.

5. **Analyze Given Compounds**:
Suppose we have several compounds to analyze:
- Compound A: Tertiary halide
- Compound B: Secondary halide with resonance stabilization
- Compound C: Primary halide
- Compound D: Methyl halide

Based on the above analysis:
- **Compound A** would form a tertiary carbocation, which is very stable.
- **Compound B** would form a secondary carbocation, which is less stable but could be stabilized by resonance.
- **Compound C** would form a primary carbocation, which is quite unstable.
- **Compound D** would form a methyl carbocation, which is also very unstable.

6. **Conclusion**:
The compound that forms the most stable carbocation will be the most reactive towards \( S_N1 \) reactions. In this case, **Compound A (the tertiary halide)** is likely the most reactive due to the stability of the tertiary carbocation formed.

### Final Answer:
The most reactive compound towards \( S_N1 \) reaction is the one that forms the most stable carbocation, which is typically a tertiary halide.