The boiling points of substances depend on their molecular structure and intermolecular forces, particularly hydrogen bonding.
- Ethanol (I: \(\text{C}_2\text{H}_5\text{OH}\)): Ethanol is a small alcohol with hydrogen bonding and has a relatively high boiling point due to the ability to form hydrogen bonds.
- Propanol (II: \(\text{C}_3\text{H}_7\text{OH}\)): Propanol is larger than ethanol, but the additional carbon chain doesn't significantly increase the boiling point compared to ethanol.
- Ethanol (\(III: \text{CH}_3\text{CH}_2\text{OH}\)): Ethanol is slightly smaller than propanol but still capable of hydrogen bonding, so it has a boiling point lower than that of propanol.
- Butane (IV: \(\text{CH}_3\text{CH}_2\text{CH}_3\)): Butane, a non-polar molecule, has a significantly lower boiling point because it only experiences van der Waals forces, not hydrogen bonding.
Hence, the correct order of boiling points is:
\[
\text{II $>$ III $>$ IV $>$ I}.
\]