Which of the following alkyl halides undergoes the fastest `S_(N^(1))` reaction ?

Options

A. Methyl chloride
B. Ethyl chloride
C. Isobutyl chloride
D. tert-Butyl chloride

Explanation

To determine which of the given alkyl halides undergoes the fastest SN1 reaction, we need to analyze the stability of the carbocations that would be formed during the reaction. The options provided are:

1. Methyl chloride
2. Ethyl chloride
3. Isobutyl chloride
4. Tert-butyl chloride

### Step-by-Step Solution:

**Step 1: Understand the SN1 Mechanism**
- The SN1 reaction is a two-step process:
1. Formation of a carbocation by the departure of the leaving group (in this case, the halide).
2. Nucleophilic attack on the carbocation.

**Hint:** Remember that the stability of the carbocation is crucial for the rate of the SN1 reaction.

**Step 2: Analyze Carbocation Stability**
- The stability of carbocations increases with the degree of substitution:
- Tertiary (3°) carbocations are the most stable.
- Secondary (2°) carbocations are less stable than tertiary but more stable than primary (1°).
- Primary (1°) carbocations are the least stable.

**Hint:** Recall that more alkyl groups attached to the positively charged carbon stabilize the carbocation through hyperconjugation and inductive effects.

**Step 3: Identify the Carbocation for Each Alkyl Halide**
- **Methyl chloride (CH3Cl)**: Forms a methyl carbocation (1°) - least stable.
- **Ethyl chloride (C2H5Cl)**: Forms an ethyl carbocation (1°) - still not very stable.
- **Isobutyl chloride (C4H9Cl)**: Forms a secondary carbocation (2°) - more stable than 1°.
- **Tert-butyl chloride (C4H9Cl)**: Forms a tertiary carbocation (3°) - most stable.

**Hint:** Compare the structure of each alkyl halide to determine the type of carbocation formed.

**Step 4: Conclusion**
- Since the rate of the SN1 reaction is directly related to the stability of the carbocation, the tert-butyl chloride, which forms a tertiary carbocation, will undergo the fastest SN1 reaction.

**Final Answer:**
- The alkyl halide that undergoes the fastest SN1 reaction is **tert-butyl chloride**.