Butylamine(I), diethylamine(II) and  N,N-dimethylamine(III) have the same molar mass . The increasing order of their boiling point is 

III < II < I

The correct answer is option 1. III < II < I.

To understand why butylamine (I), diethylamine (II), and N,N-dimethylamine (III) have different boiling points, let us dive into their structures and the nature of their intermolecular forces.

Butylamine (I)

Intermolecular Forces:

Hydrogen Bonding: Primary amines have an \(NH_2\) group, which allows them to form hydrogen bonds with other molecules. Hydrogen bonding occurs between the hydrogen of the \(NH_2\) group and the lone pair of electrons on the nitrogen of another molecule or within the same molecule.

Dipole-Dipole Interactions: Present because of the polar \(NH_2\) group.

Effect on Boiling Point: Hydrogen bonding is a strong intermolecular force, which significantly increases the boiling point.

2.Diethylamine (II)

Intermolecular Forces:

Hydrogen Bonding: Secondary amines have an \(NH\) group, allowing for hydrogen bonding, but not as extensive as in primary amines because there is only one NH group available for bonding.

Dipole-Dipole Interactions: Present due to the polar \(NH\) group.

Effect on Boiling Point: Secondary amines have hydrogen bonding but less extensive compared to primary amines, leading to a lower boiling point than primary amines.

3. N,N-Dimethylamine (III)

Intermolecular Forces:

Hydrogen Bonding: Tertiary amines lack an \(NH\) bond, which means they cannot form hydrogen bonds. Thus, the only intermolecular forces are dipole-dipole interactions and van der Waals forces.

Dipole-Dipole Interactions: Present due to the polar \(NH\) group, but weaker compared to hydrogen bonding.

Effect on Boiling Point: The absence of hydrogen bonding results in a lower boiling point compared to primary and secondary amines.

Comparison and Order of Boiling Points

N,N-Dimethylamine (III) has the lowest boiling point because it lacks hydrogen bonding. The only forces present are dipole-dipole interactions, which are weaker.

Diethylamine (II) has a higher boiling point than N,N-dimethylamine due to the presence of hydrogen bonding, but it is less extensive compared to primary amines.

Butylamine (I) has the highest boiling point because it is a primary amine and can form strong hydrogen bonds, which significantly raises its boiling point.

Conclusion

The boiling points are influenced by the strength of intermolecular forces. Since hydrogen bonding is stronger than dipole-dipole interactions, the order of boiling points is:
\(\text{N,N-Dimethylamine (III)} < \text{Diethylamine (II)} < \text{Butylamine (I)} \)

Thus, the increasing order of boiling points is: III < II < I