Arrange the following sets of compounds in order of their increasing boiling points:
$(a)$ Pentan$-1-$ol,butan$-1-$ol,butan$-2-$ol,ethanol,propan$-1-$ol,methanol.
$(b)$ Pentan$-1-$ol,$n-$butane,pentanal,ethoxyethane.

(N/A) The boiling point of organic compounds depends on intermolecular forces such as hydrogen bonding and dipole-dipole interactions.
$(a)$ The boiling point increases with the increase in the length of the carbon chain due to increased van der Waals forces. For isomers,branching decreases the boiling point. The order is: $\text{Methanol} < \text{Ethanol} < \text{Propan-}1\text{-ol} < \text{Butan-}2\text{-ol} < \text{Butan-}1\text{-ol} < \text{Pentan-}1\text{-ol}$.
$(b)$ The order of boiling points based on intermolecular forces (Hydrogen bonding > Dipole-dipole > van der Waals) is: $n\text{-Butane} < \text{Ethoxyethane} < \text{Pentanal} < \text{Pentan-}1\text{-ol}$.