Concept:
Chemistry (Organic Chemistry) - Physical Properties of Amines (Boiling Points).
Step 1: Classify each of the given isomeric amines.
First, determine the degree of each amine ($C_4H_{11}N$ isomers):
- n-Butylamine: $CH_3-CH_2-CH_2-CH_2-NH_2$ (Primary, $1^\circ$)
- tert-Butylamine: $(CH_3)_3C-NH_2$ (Primary, $1^\circ$, highly branched)
- Ethyldimethylamine: $CH_3-CH_2-N(CH_3)_2$ (Tertiary, $3^\circ$)
- Diethylamine: $CH_3-CH_2-NH-CH_2-CH_3$ (Secondary, $2^\circ$)
Step 2: Analyze the effect of hydrogen bonding classes.
The boiling point heavily depends on intermolecular hydrogen bonding. Primary ($1^\circ$) and secondary ($2^\circ$) amines have N-H bonds, allowing them to form hydrogen bonds. Tertiary ($3^\circ$) amines lack N-H bonds and cannot form intermolecular hydrogen bonds, giving them the lowest boiling points among isomers. Thus, Ethyldimethylamine has the lowest boiling point.
Step 3: Compare primary versus secondary amines.
Primary amines possess two hydrogen atoms attached to the highly electronegative nitrogen atom ($-NH_2$), enabling them to form more extensive hydrogen bonding networks than secondary amines, which only have one such hydrogen atom ($-NH-$). Therefore, the $1^\circ$ amines (n-Butylamine and tert-Butylamine) will have higher boiling points than the $2^\circ$ amine (Diethylamine).
Step 4: Analyze the effect of steric hindrance and branching.
We are left with two primary amines: n-Butylamine (straight chain) and tert-Butylamine (heavily branched). Branching forces molecules into a more compact, spherical shape, which significantly reduces the effective surface area for intermolecular Van der Waals (dispersion) forces.
Step 5: Conclude which isomer maximizes all intermolecular forces.
Because n-Butylamine has a long, straight carbon chain, it maximizes its surface area for strong Van der Waals interactions while simultaneously possessing the optimal $-NH_2$ group for extensive hydrogen bonding. Combining these two dominating factors results in n-Butylamine having the highest boiling point of the group.
$$
\therefore \text{n-Butylamine has the highest boiling point.}
$$