To determine which pair of molecules are isomers, we need to understand what isomers are.
Isomers are compounds that have the same molecular formula but differ in the arrangement of atoms.
In simpler terms, they have the same number and types of atoms (same chemical composition) but different structures.
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Consider the first pair: \( \text{CH}_3\text{OCH}_2\text{CH}_2\text{CH}_3 \) and \( \text{CH}_3\text{CH}_2\text{OCH}_2\text{CH}_3 \).
- The molecular formula for both compounds is \( \text{C}_4\text{H}_{10}\text{O} \).
- The first molecule, \( \text{CH}_3\text{OCH}_2\text{CH}_2\text{CH}_3 \), is an ether, where an oxygen atom is bonded between the methyl (\( \text{CH}_3 \)) group and a three-carbon group (\( \text{CH}_2\text{CH}_2\text{CH}_3 \)).
- The second molecule, \( \text{CH}_3\text{CH}_2\text{OCH}_2\text{CH}_3 \), is also an ether, where the oxygen atom is bonded between two ethyl (\( \text{CH}_3\text{CH}_2 \)) groups.
- Despite both having the same molecular formula, their structural arrangements differ, confirming them as isomers.
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Now, examine the other options:
- \( \text{CH}_3\text{CH}_2\text{CH}_2\text{CH}_3 \) and \( \text{CH}_3\text{CH}_2\text{OCH}_3 \) have molecular formulas \( \text{C}_4\text{H}_{10} \) and \( \text{C}_3\text{H}_8\text{O} \) respectively. These are not isomers.
- \( \text{CH}_3\text{COCH}_3 \) and \( \text{CH}_3\text{CH}_2\text{CHO} \) have the same molecular formula \( \text{C}_3\text{H}_6\text{O} \), but they are functional isomers (ketone and aldehyde).
- \( \text{CH}_3\text{CH}_2\text{CH}_2\text{OH} \) and \( \text{CH}_3\text{CH}_2\text{COOH} \) have molecular formulas \( \text{C}_3\text{H}_8\text{O} \) and \( \text{C}_3\text{H}_6\text{O}_2 \). These are not isomers.
Thus, the pair that are isomers are
\( \text{CH}_3\text{OCH}_2\text{CH}_2\text{CH}_3 \) and
\( \text{CH}_3\text{CH}_2\text{OCH}_2\text{CH}_3 \).