Williamson's synthesis of preparing dimethyl ether is an :

Options

A. `S_(N)1` reaction
B. Elimination reaction
C. `S_(N)2` reaction
D. Nucleophilic addition reaction

Explanation

To solve the question regarding Williamson's synthesis of dimethyl ether, we will break down the process step by step.

### Step-by-Step Solution:

1. **Understanding Williamson's Synthesis**:
Williamson's synthesis is a method used to prepare ethers. It involves the reaction of an alkoxide ion with a haloalkane (alkyl halide).

**Hint**: Remember that ethers are formed from the reaction of an alkoxide with a haloalkane.

2. **Identify the Reactants**:
For the synthesis of dimethyl ether (CH3-O-CH3), we need to use methyl chloride (CH3Cl) and sodium methoxide (CH3O-Na+).

**Hint**: Identify the specific haloalkane and alkoxide that will yield the desired ether.

3. **Dissociation of Sodium Methoxide**:
Sodium methoxide (CH3O-Na+) dissociates into methoxide ion (CH3O-) and sodium ion (Na+).

**Hint**: Recognize that the alkoxide ion is the nucleophile in this reaction.

4. **Nucleophilic Attack**:
The methoxide ion (CH3O-) acts as a nucleophile and attacks the carbon atom of the methyl chloride (CH3Cl) from the backside. This is characteristic of an SN2 mechanism, where the nucleophile attacks the electrophile, leading to the displacement of the leaving group (Cl-).

**Hint**: In SN2 reactions, the nucleophile attacks from the opposite side of the leaving group.

5. **Formation of Dimethyl Ether**:
As a result of the nucleophilic attack, the chlorine atom is displaced, and dimethyl ether (CH3-O-CH3) is formed. The chloride ion (Cl-) is captured by the sodium ion (Na+), forming sodium chloride (NaCl).

**Hint**: Keep track of the products formed during the reaction.

6. **Final Reaction Equation**:
The overall reaction can be summarized as:
\[ CH3Cl + CH3O-Na^+ \rightarrow CH3-O-CH3 + NaCl \]

**Hint**: Write down the complete reaction to visualize the reactants and products clearly.

7. **Mechanism Confirmation**:
The reaction follows an SN2 mechanism because it does not involve the formation of a carbocation intermediate. Instead, it proceeds through a single concerted step.

**Hint**: Remember that SN2 reactions are characterized by a single step and do not form intermediates like carbocations.

### Conclusion:
The Williamson's synthesis of dimethyl ether is an SN2 reaction involving the nucleophilic attack of methoxide ion on methyl chloride, resulting in the formation of dimethyl ether and sodium chloride.