Let's solve each part step-by-step with explanations: --- ## **Part (a)** ### **Transformation** \[ (S)\text{-hexan-3-ol} \longrightarrow (R)\text{-3-methoxyhexane} \] ### **Step-by-Step Solution** 1. **Convert Alcohol to Tosylate:** - Reagent: Tosyl chloride (TsCl), pyridine - Mechanism: The alcohol reacts with TsCl to form a tosylate (a good leaving group) **without** inversion of configuration. - Intermediate: (S)-3-tosyloxyhexane 2. **Nucleophilic Substitution with Methoxide:** - Reagent: Sodium methoxide (NaOCH₃) or Methanol (CH₃O⁻) - Mechanism: The methoxide ion attacks the carbon (SN2 mechanism), **inverting** the configuration from S to R. - Product: (R)-3-methoxyhexane ### **Explanation** - **SN2 reactions** at a stereocenter result in **inversion** of configuration. - The tosylate step does not change the configuration. - Thus, overall S → R. --- ## **Part (b)** ### **Transformation** \[ (S)\text{-hexan-3-ol} \longrightarrow (S)\text{-3-methoxyhexane} \] ### **Step-by-Step Solution** 1. **Convert Alcohol to Bromide:** - Reagent: PBr₃ - Mechanism: PBr₃ converts the alcohol to an alkyl bromide **with inversion** of configuration (S → R). - Intermediate: (R)-3-bromohexane 2. **Nucleophilic Substitution with Methoxide:** - Reagent: Sodium methoxide (NaOCH₃) - Mechanism: SN2 reaction with methoxide, **inverting** configuration again (R → S). - Product: (S)-3-methoxyhexane ### **Explanation** - Two inversions (one with PBr₃, one with SN2) restore the original configuration. --- ## **Part (c)** ### **Transformation** \[ \text{hex-5-en-1-ol} \longrightarrow \text{2-methyltetrahydro-2H-pyran} \] ### **Step-by-Step Solution** 1. **Acid-Catalyzed Cyclization (Prins Cyclization):** - Reagent: Acid (H⁺, e.g., H₂SO₄) - Mechanism: - Protonation of the alcohol forms a good leaving group. - An intramolecular attack by the alkene leads to a 6-membered ring (tetrahydropyran). - Rearrangement leads to a methyl group at C-2. ### **Explanation** - The acid catalyzes the cyclization, forming the tetrahydropyran ring with a methyl group at position 2. --- ## **Summary Table** | Part | Reagents & Steps | Stereochemical Outcome | Product | |------|--------------------------------------------|-----------------------------|-------------------------------| | a | 1. TsCl, pyridine 2. NaOCH₃ | Inversion (S → R) | (R)-3-methoxyhexane | | b | 1. PBr₃ 2. NaOCH₃ | Double inversion (S → R → S)| (S)-3-methoxyhexane | | c | H⁺ (acid catalysis) | Cyclization | 2-methyltetrahydro-2H-pyran | --- ## **Final Answers** **(a)** Use TsCl/pyridine, then NaOCH₃ (SN2) to get (R)-3-methoxyhexane. **(b)** Use PBr₃ (inverts to R), then NaOCH₃ (SN2, inverts back to S) to get (S)-3-methoxyhexane. **(c)** Use acid catalysis (H⁺) to cyclize hex-5-en-1-ol into 2-methyltetrahydro-2H-pyran. --- If you need arrow-pushing mechanisms or more details for any step, let me know!