Step 1: Understanding the Concept:
The formula \(\text{C}_{\text{n}}\text{H}_{2\text{n}+2}\text{O}\) represents saturated open-chain alcohols or ethers. Here \(\text{n}=5\), so \(\text{H} = 2(5) + 2 = 12\). A formula of \(\text{C}_5\text{H}_{12}\text{O}\) means the compound has no rings or double bonds. Step 2: Key Formula or Approach:
Degree of unsaturation (DoU) = \(\text{C} + 1 - \frac{\text{H}}{2} = 5 + 1 - \frac{12}{2} = 6 - 6 = 0\).
A DoU of $0$ indicates a fully saturated, open-chain molecule. Step 3: Detailed Explanation:
- (A) Cyclopentanol: Has one ring. Formula is \(\text{C}_5\text{H}_{10}\text{O}\). Incorrect.
- (B) Pentan-1-ol: A straight chain of 5 carbons and 12 hydrogens. Formula is \(\text{C}_5\text{H}_{12}\text{O}\). Correct.
- (D) A ring with a double bond would have even fewer hydrogens (e.g., \(\text{C}_5\text{H}_8\text{O}\)). Incorrect.
Looking at the skeletal images:
Image B shows 5 vertices/ends (excluding oxygen) in an open zigzag chain: \(\text{CH}_3\text{-CH}_2\text{-CH}_2\text{-CH}_2\text{-CH}_2\text{-OH}\). Step 4: Final Answer:
Structure B corresponds to the formula.
