Final Answer:
The compound with the molecular formula C₅H₁₀O that meets the criteria of containing a carbon-carbon double bond, an unbranched chain, and a hydroxyl group at the end of the chain is 1-penten-5-ol.
Step-by-step explanation:
For a compound to satisfy the specified criteria of having a molecular formula C₅H₁₀O, a carbon-carbon double bond, an unbranched chain, and a hydroxyl group at the end of the chain, it must be a member of the alcohol functional group. Among the various isomers of C₅H₁₀O, 1-penten-5-ol perfectly fits the description.
The molecular formula C₅H₁₀O implies five carbon atoms, ten hydrogen atoms, and one oxygen atom. 1-Penten-5-ol possesses an unbranched chain of five carbon atoms with a carbon-carbon double bond (represented by the "-en-" in the name) located at the first carbon atom (hence "1-penten"). Moreover, the hydroxyl group (-OH) is positioned at the fifth carbon atom, indicating that it is at the end of the carbon chain, adhering to the specified criteria.
The structural formula of 1-penten-5-ol demonstrates a clear representation of the arrangement of atoms and functional groups within the molecule. The unbranched carbon chain, the presence of a carbon-carbon double bond, and the hydroxyl group at the terminal carbon satisfy all the conditions outlined in the given criteria for a compound with the molecular formula C₅H₁₀O. Therefore, 1-penten-5-ol is the appropriate compound that fulfills the specified requirements.