Step 1: Understanding the Concept:
Vigorous oxidation of alkylbenzenes with alkaline $KMnO_4$ converts the entire side chain into a carboxylic acid group ($-COOH$).
Step 2: Formula Application:
$Ar-R \xrightarrow{KMnO_4} Ar-COOH$. This happens as long as there is at least one benzylic hydrogen.
Step 3: Explanation:
Ethylbenzene ($C_6H_5-CH_2-CH_3$) has two benzylic hydrogens on the first carbon. Regardless of the length of the alkyl chain (methyl, ethyl, propyl, etc.), the chain is "chopped off," and the benzylic carbon is oxidized to a carboxyl group, forming Benzoic acid.
Step 4: Final Answer:
The product is Benzoic acid ($C_6H_5-COOH$).