The substances from lowest to highest boiling points are:
1) C₃H₇OH (lowest)
2) C₃H₆(OH)₂
3) C₃H₅(OH)₃ (highest)
The variation in boiling points is due to the fact that these substances have a different number of hydroxide groups. The hydroxide group brings about polarity in the molecule, due to the electronegative nature of oxygen. The electric charge becomes concentrated around the oxygen atom, and the adjacent hydrogen atom attains a partial positive charge. This leads to hydrogen bonding in the molecule. The more the hydroxide groups, the more the hydrogen bonding taking place, the stronger the intermolecular forces, meaning a greater boiling point.