Step 1: Understanding the Concept
Primary amines have two N-H bonds and form the most hydrogen bonds. Tertiary amines have no N-H bond and cannot form hydrogen bonds with each other.
Step 2: Compare the amines
All four compounds are isomers of formula \(\text{C}_4\text{H}_{11}\text{N}\).
n-Butylamine is a primary amine with a long straight chain.
Diethylamine is secondary, the tertiary amine has no H-bonding, and tert-butylamine is primary but highly branched, giving a smaller surface area.
Step 3: Compare the options
n-Butylamine has the highest boiling point of about 78 \(^{\circ}\)C.
Final Answer:
n-Butylamine has the highest boiling point because of strong hydrogen bonding and a straight chain.
\[ \boxed{\text{(A) }n-\text{C}_{4}\text{H}_{9}\text{NH}_{2}} \]