Step 1: Understanding the Concept:
The question describes a specific name reaction in organic chemistry used for the synthesis of alkanes. We need to identify the reaction based on the reactants and products.
Step 2: Identifying the Reaction Type:
The general form of the reaction is the treatment of an alkyl halide (R-X) with sodium metal in the presence of dry ether to form a symmetrical alkane (R-R) with double the number of carbon atoms.
\[ 2R-X + 2Na \xrightarrow{\text{dry ether}} R-R + 2NaX \]
Step 3: Detailed Explanation:
The given reaction is:
Reactants: Bromoethane (CH\(_{3}\)CH\(_{2}\)-Br) and metallic Sodium (Na).
Solvent: Dry ethereal solution.
Product: n-butane (CH\(_{3}\)CH\(_{2}\)CH\(_{2}\)CH\(_{3}\)).
The reaction can be written as:
\[ 2\text{CH}_3\text{CH}_2\text{-Br} + 2\text{Na} \xrightarrow{\text{dry ether}} \text{CH}_3\text{CH}_2\text{-}\text{CH}_2\text{CH}_3 + 2\text{NaBr} \]
This specific reaction, where two molecules of an alkyl halide are coupled by sodium metal in dry ether to form a higher alkane, is known as the Wurtz reaction.
Let's briefly consider the other options:
- Kolbe's reaction: Electrolysis of an aqueous solution of a sodium or potassium salt of a carboxylic acid to produce an alkane.
- Williamson reaction: Synthesis of ethers from an alkoxide and an alkyl halide.
- Fittig reaction: Similar to Wurtz, but uses aryl halides to form biaryls.
- Friedel-Crafts reaction: Alkylation or acylation of an aromatic ring using a Lewis acid catalyst.
Step 4: Final Answer:
The described synthesis of n-butane from bromoethane and sodium is a classic example of the Wurtz reaction. This corresponds to option (B).