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What determines the boiling point of a substance is how strongly the molecules of the substance attracts each other. With this in mind, and since nitrogen is a more electronegative molecule, the more exposed nitrogen is, the more polar the molecule would be and this polarity would cause slightly more ionic interactions between molecules, causing them to attract each other more.

Trimethylamine has H-H interactions which are fairly weak and can be neglected. Since the structure of the molecule is like a pyramid, there is a dipole but compared to n-propylamine, this dipole is not as strong, since the nitrogen is more exposed.

Basically, because n-propylamine can act as both a H-bond donor AND a H-bond acceptor (while trimethylamine only acts as a H-bond acceptor) this makes n-propylamine have a higher boiling point.

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