Which of the following is an `S_(N^(2))` reaction:-

Options

A. `CH_(3)CH_(2)Br +KOH rarr CH_(3)CH_(2)OH +KBr`
B. `CH_(3)CH_(2)Br +CH_(3)CH_(2)ONa rarr CH_(3)CH_(2)OCH_(2)CH_(3)+NaBr`
C. `(CH_(3))_(3)CBr +KOH rarr (CH_(3))_(3) COH +KBr`
D. `CH_(3)-CH_(2)-overset(CH_(3))overset(|)underset(CH_(3))underset(|)(C)-Br +KOH rarr CH_(3)CH_(2)-overset(CH_(3))overset(|)underset(CH_(3))underset(|)(C)-OH +KBr`

Answer

To determine which of the given reactions is an \( S_N2 \) reaction, we need to analyze each option based on the characteristics of \( S_N2 \) mechanisms. Here’s a step-by-step solution:

### Step 1: Understand the \( S_N2 \) Mechanism
The \( S_N2 \) (Substitution Nucleophilic Bimolecular) reaction is characterized by a single concerted step where the nucleophile attacks the electrophile (alkyl halide) from the opposite side of the leaving group, leading to a transition state where both the nucleophile and the leaving group are partially bonded to the carbon atom. This mechanism typically occurs with primary alkyl halides due to steric hindrance.

### Step 2: Analyze Each Option
1. **Option A**: A primary alkyl halide reacting with KOH.
- **Analysis**: Primary alkyl halides are favorable for \( S_N2 \) reactions. The nucleophile \( OH^- \) can effectively attack the carbon, resulting in an \( S_N2 \) reaction.
- **Conclusion**: This is an \( S_N2 \) reaction.

2. **Option B**: A tertiary alkyl halide undergoing Williamson ether synthesis.
- **Analysis**: Williamson ether synthesis generally requires a primary alkyl halide to proceed via \( S_N2 \). Tertiary alkyl halides do not undergo \( S_N2 \) due to steric hindrance and typically follow \( S_N1 \) mechanisms instead.
- **Conclusion**: This is NOT an \( S_N2 \) reaction.

3. **Option C**: A secondary alkyl halide reacting with a strong nucleophile.
- **Analysis**: Secondary alkyl halides can undergo both \( S_N1 \) and \( S_N2 \) reactions, but they are more likely to follow the \( S_N1 \) pathway due to steric hindrance. The reaction conditions and the nature of the nucleophile will influence the pathway, but generally, secondary alkyl halides are less favorable for \( S_N2 \).
- **Conclusion**: This is NOT a clear \( S_N2 \) reaction.

4. **Option D**: A tertiary alkyl halide reacting with a nucleophile.
- **Analysis**: Tertiary alkyl halides are not suitable for \( S_N2 \) reactions due to steric hindrance. They typically undergo \( S_N1 \) reactions where the leaving group departs first, forming a carbocation.
- **Conclusion**: This is NOT an \( S_N2 \) reaction.

### Final Conclusion
Based on the analysis, **Option A** is the only reaction that represents an \( S_N2 \) mechanism.