Step 1: Dimethyl ether (\( {CH}_3{OCH}_3 \)) and ethanol (\( {CH}_3{CH}_2{OH} \)) are structural isomers, but their physical properties differ due to differences in intermolecular forces.
Step 2: Ethanol, with an -OH (hydroxyl) group, can form hydrogen bonds with other ethanol molecules. These hydrogen bonds are relatively strong and significantly increase the boiling point of ethanol. Dimethyl ether, on the other hand, lacks the -OH group and cannot form hydrogen bonds. Therefore, the intermolecular forces in dimethyl ether are weaker than those in ethanol.
Step 3: As a result of the absence of hydrogen bonding, dimethyl ether has a lower boiling point compared to ethanol, where hydrogen bonding plays a crucial role in increasing the boiling point. Thus, the correct explanation for the lower boiling point of dimethyl ether is the lack of hydrogen bonding.
Thus, the correct answer is option (E).