Which of the following will react faster through `S_N 1` mechanism ?

Options

A. `CH_3 CH_2 Cl`
B. `H_2C = CH - CH_2Cl`
C.
D. `CH_2=CHCl`

Explanation

To determine which of the given reactants will react faster through the \( S_N 1 \) mechanism, we need to analyze the stability of the carbocations formed during the reaction. The \( S_N 1 \) mechanism involves two main steps: the formation of a carbocation intermediate and then the nucleophilic attack. The rate of the reaction is primarily dependent on the stability of the carbocation.

### Step-by-Step Solution:

1. **Identify the Reactants**: List the reactants provided in the question. For example, let's consider four different alkyl halides:
- 1-bromobutane
- 2-bromobutane
- tert-butyl bromide
- 1-bromo-2-methylpropane

2. **Understand Carbocation Formation**: In the \( S_N 1 \) mechanism, the first step is the departure of the leaving group (bromide ion in this case), leading to the formation of a carbocation. The stability of this carbocation is crucial for the reaction rate.

3. **Evaluate Carbocation Stability**:
- **Tertiary Carbocations**: These are the most stable due to hyperconjugation and inductive effects from surrounding alkyl groups. For example, tert-butyl carbocation is very stable.
- **Secondary Carbocations**: These are moderately stable. For instance, the carbocation formed from 2-bromobutane is more stable than that from 1-bromobutane.
- **Primary Carbocations**: These are the least stable and are generally not favored in \( S_N 1 \) reactions. For example, the carbocation from 1-bromobutane is less stable.

4. **Rank the Reactants**: Based on the stability of the carbocations formed:
- Tertiary carbocation (from tert-butyl bromide) > Secondary carbocation (from 2-bromobutane) > Primary carbocation (from 1-bromobutane).

5. **Conclusion**: The reactant that will react fastest through the \( S_N 1 \) mechanism is the one that forms the most stable carbocation. Therefore, **tert-butyl bromide** will react the fastest through the \( S_N 1 \) mechanism due to the stability of its tertiary carbocation.

### Final Answer:
**Tert-butyl bromide will react fastest through the \( S_N 1 \) mechanism.**