In a `S_(N^(2))` substitution reaction of the type
`R-Br+Cl^(-)overset("DMF")rarrR-Cl+Br^(-)`
Which one of the following has the highest relative rate?

Options

A. `{:(" "CH_(3)),(" |"),(CH_(3)-C-CH_(2)Br),(" |"),(" "CH_(3)):}`
B. `CH_(3)CH_(2)Br`
C. `CH_(3)-CH_(2)-CH_(2)Br`
D. `CH_(3)-underset(CH_(3))underset("| ")(CH)-CH_(2)Br`

Explanation

To determine which compound has the highest relative rate in an SN2 substitution reaction of the type \( R-Br + Cl^- \overset{DMF}{\rightarrow} R-Cl + Br^- \), we need to analyze the structure of the alkyl halides involved. The rate of an SN2 reaction is influenced by steric hindrance around the carbon atom that is being attacked by the nucleophile (in this case, \( Cl^- \)).

### Step-by-Step Solution:

1. **Understanding SN2 Mechanism**:
- In an SN2 reaction, the nucleophile attacks the carbon atom from the opposite side of the leaving group (Br in this case). This backside attack is essential for the reaction to occur.

2. **Steric Hindrance Consideration**:
- The rate of an SN2 reaction decreases with increasing steric hindrance. Therefore, primary (1°) alkyl halides react faster than secondary (2°), and tertiary (3°) alkyl halides are generally not reactive in SN2 reactions due to significant steric hindrance.

3. **Analyzing the Given Options**:
- We need to evaluate the four options provided to identify which one is a primary alkyl halide or has the least steric hindrance.
- **Option A**: A tertiary alkyl halide (3°) will have the highest steric hindrance.
- **Option B**: A primary alkyl halide (1-bromoethane) with minimal steric hindrance.
- **Option C**: A secondary alkyl halide (2°), which has more steric hindrance than a primary.
- **Option D**: A tertiary alkyl halide (3°) with significant steric hindrance.

4. **Identifying the Fastest Reaction**:
- Since primary alkyl halides experience the least steric hindrance, they will have the highest rate of reaction in an SN2 mechanism.
- Among the options, **Option B (1-bromoethane)** is the primary alkyl halide and will thus have the highest relative rate of reaction.

### Conclusion:
The compound with the highest relative rate in the SN2 reaction is **Option B (1-bromoethane)**.

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