Step 1: Understanding the Concept:
Carboxylic acids are strong enough to react with weak bases like sodium bicarbonate to release \(CO_2\) gas, whereas esters do not show this reaction.
Step 2: Detailed Explanation:
1. Test with \(NaHCO_3\): Add a small amount of aqueous sodium bicarbonate solution to both compounds.
2. Benzoic Acid: Being a carboxylic acid, it reacts to give brisk effervescence due to the evolution of carbon dioxide gas.
\[ C_6H_5COOH + NaHCO_3 \rightarrow C_6H_5COONa + H_2O + CO_2\uparrow \]
3. Ethyl Benzoate: Being an ester, it does not react with sodium bicarbonate; hence no effervescence is observed.
Step 3: Final Answer:
Benzoic acid gives brisk effervescence with sodium bicarbonate solution, while ethyl benzoate does not.