Step 1: Understanding the Question:
This question is from "Haloalkanes and Haloarenes" and concerns the synthesis of alkyl halides from alcohols.
We are asked to identify the chemical reagent that transforms ethanol ($\text{C}_2\text{H}_5\text{OH}$) into bromoethane ($\text{C}_2\text{H}_5\text{Br}$).
Step 2: Key Formula or Approach:
Replacing a hydroxyl group ($-\text{OH}$) in an alcohol with a halogen atom is a classic nucleophilic substitution reaction ($S_{\text{N}}2$ or $S_{\text{N}}1$).
Phosphorus tribromide ($\text{PBr}_3$) is an excellent reagent for converting primary and secondary alcohols to alkyl bromides.
Step 3: Detailed Explanation:
• The reaction between ethanol and phosphorus tribromide can be represented as:
\[ 3\text{CH}_3\text{CH}_2\text{OH} + \text{PBr}_3 \rightarrow 3\text{CH}_3\text{CH}_2\text{Br} + \text{H}_3\text{PO}_3 \]
• In this reaction, phosphorus tribromide acts as a nucleophilic brominating agent.
• The $-\text{OH}$ group of ethanol is converted into a better leaving group by reacting with phosphorus, which is then displaced by the bromide ion ($\text{Br}^-$) via an $S_{\text{N}}2$ mechanism.
• Let us analyze why the other options are incorrect:
- $\text{KMnO}_4$ is a powerful oxidizing agent that would oxidize ethanol to acetaldehyde and then to ethanoic acid.
- NaOH is a strong base and nucleophile, but it cannot displace the $-\text{OH}$ group because hydroxide is a very poor leaving group.
- $\text{H}_2\text{SO}_4$ is a strong acid and dehydrating agent, which would dehydrate ethanol to form ethene or diethyl ether depending on the temperature.
Step 4: Final Answer:
The reagent that converts ethanol into bromoethane is $\text{PBr}_3$, which matches option (B).