Step 1: Understand the reaction of carboxylic acids with sodium hydrogen carbonate.
Aryl carboxylic acids contain the functional group:
\[
-COOH
\]
Carboxylic acids are acidic in nature and react with sodium hydrogen carbonate \((NaHCO_3)\).
This reaction is commonly used as a test for the presence of carboxylic acid group.
Step 2: Write the general reaction.
The reaction between a carboxylic acid and sodium hydrogen carbonate is:
\[
RCOOH + NaHCO_3 \longrightarrow RCOONa + H_2O + CO_2
\]
In this reaction:
\[
RCOOH \rightarrow \text{Carboxylic acid}
\]
\[
RCOONa \rightarrow \text{Sodium carboxylate}
\]
The gaseous product evolved is carbon dioxide.
Step 3: Explain the formation of gas.
Hydrogen carbonate ion reacts with the acidic proton of the carboxylic acid to form unstable carbonic acid:
\[
H_2CO_3
\]
Carbonic acid immediately decomposes into:
\[
CO_2 + H_2O
\]
Thus, brisk effervescence is observed due to evolution of carbon dioxide gas.
Step 4: Identify the liberated gas.
Therefore, the gaseous molecule liberated is:
\[
CO_2
\]
Step 5: Match with the given options.
The correct option is:
\[
(2)\; CO_2
\]
Step 6: Final conclusion.
Hence, the gas evolved is:
\[
\boxed{CO_2}
\]