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How do ethanol and methyl ether differ even though they have the same molecular formula?

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representations of molecular structure — molecule Several methods of representing a molecule's structure. In Lewis structures, element symbols represent atoms, and dots represent electrons surrounding them. A pair of shared electrons (covalent bond) may also be shown as a single dash. The ball-and-stick model better illustrates the spatial arrangement of the atoms. For aromatic compounds, the Kekulé structure is common, in which each bond is represented by a dash, carbon atoms are implied where two or more lines meet, and hydrogen atoms are usually omitted. Bond-line formulas, similar to the Kekulé structure, are often used for complex nonaromatic organic compounds. Sugars are often drawn as Fischer projections, in which the carbon “backbone” is drawn as a straight vertical line, with carbon atoms implied where horizontal lines intersect the vertical one.

Ethanol and methyl ether (commonly known as dimethyl ether) are constitutional isomers. While they share the same molecular formula, they differ in the connectivity of their atoms, which results in distinct chemical and physical properties.1

The primary structural difference lies in their functional groups:

Ethanol (CH $_{3}$ CH $_{2}$ OH) contains a hydroxyl group (–OH). This group allows ethanol molecules to engage in hydrogen bonding with one another, which significantly increases its boiling point and makes it miscible with water.2
Methyl ether (CH $_{3}$ –O–CH $_{3}$ ) is an ether, characterized by an oxygen atom bonded to two alkyl groups. Because it lacks a hydroxyl group, it cannot form hydrogen bonds with other ether molecules. Consequently, it has a much lower boiling point than ethanol.3

In chemistry, such compounds are defined as isomers, meaning they possess the same number and types of atoms but are arranged differently, leading to different behaviors in chemical reactions and physical states.1