Step 1: Understanding the Concept:
IUPAC nomenclature requires identifying the principal functional group, the longest carbon chain, and numbering to give the functional group the lowest possible locant.
Detailed Explanation:
1. The principal functional group is the hydroxyl group (\(-OH\)).
2. The longest carbon chain containing the \(-OH\) group has 6 carbons, so the root name is "hexan-3-ol" or "hexan-4-ol".
3. Numbering from left to right: \(-OH\) is at position 3. Substituents are 1-bromo, 4-methyl, and 5-chloro.
4. Numbering from right to left: \(-OH\) is at position 4.
5. According to IUPAC rules, the functional group gets priority, so we choose the 1 to 6 numbering from left to right.
6. Alphabetical arrangement of substituents: Bromo, Chloro, Methyl.
Name: 1-bromo-5-chloro-4-methylhexan-3-ol.
Step 2: Final Answer:
The correct IUPAC name is 1-bromo-5-chloro-4-methylhexan-3-ol.