Step 1: Understanding the Concept
\(\text{NaNO}_2 + \text{HCl}\) forms nitrous acid. Primary aliphatic amines react to give an unstable diazonium salt, which gives an alcohol and \(\text{N}_2\).
Step 2: Reaction
\( \text{C}_2\text{H}_5\text{NH}_2 + \text{HNO}_2 \rightarrow \text{C}_2\text{H}_5\text{OH} + \text{N}_2 + \text{H}_2\text{O} \)
Step 3: Check the Others
N-ethylethanamine is a secondary amine and gives an N-nitrosoamine. Benzenamine gives a stable diazonium salt at 273-278 K. N,N-Dimethylmethanamine is tertiary and gives a nitrite salt.
Step 4: Compare the options
The answer is ethanamine, option (A).
Final Answer:
Ethanamine gives ethanol and nitrogen gas.
\[ \boxed{\text{(A) }\text{Ethanamine}} \]