Predict the major products (including stereochemistry) when cis-3-methylcyclohexanol reacts with the following reagents.
(a) PBr₃
(b) SOCl₂ 
(c) Lucas reagent

Verified step by step guidance

1. Step 1: Analyze the structure of cis-3-methylcyclohexanol. It is a cyclohexane ring with a hydroxyl (-OH) group and a methyl (-CH3) group attached. The hydroxyl group is in the cis configuration relative to the methyl group, meaning both substituents are on the same side of the ring.
2. Step 2: For reaction (a) with PBr3 (phosphorus tribromide), understand that PBr3 is used to convert alcohols into alkyl bromides via an SN2 mechanism. The hydroxyl group will be replaced by a bromine atom. Since the reaction proceeds via inversion of configuration (due to the SN2 mechanism), the stereochemistry of the product will be inverted relative to the starting material.
3. Step 3: For reaction (b) with SOCl2 (thionyl chloride), recognize that SOCl2 converts alcohols into alkyl chlorides. This reaction typically proceeds via an SN2 mechanism when pyridine is present, leading to inversion of configuration. The hydroxyl group will be replaced by a chlorine atom, and the stereochemistry of the product will be inverted.
4. Step 4: For reaction (c) with Lucas reagent (a mixture of ZnCl2 and concentrated HCl), note that this reagent is used to convert alcohols into alkyl chlorides. The reaction mechanism depends on the type of alcohol. Since cis-3-methylcyclohexanol is a secondary alcohol, the reaction proceeds via an SN1 mechanism, forming a carbocation intermediate. The stereochemistry of the product will be racemic due to the planar nature of the carbocation intermediate.
5. Step 5: Summarize the major products for each reaction: (a) 3-bromo-3-methylcyclohexane with inverted stereochemistry, (b) 3-chloro-3-methylcyclohexane with inverted stereochemistry, and (c) racemic 3-chloro-3-methylcyclohexane due to the SN1 mechanism.

Key Concepts

Reactions of Alcohols

Alcohols can undergo various reactions, including substitution and elimination. In the presence of reagents like PBr3 and SOCl2, alcohols are converted into alkyl halides through nucleophilic substitution. Understanding the mechanism of these reactions is crucial for predicting the products formed, including the stereochemistry of the resulting compounds.

Stereochemistry

Stereochemistry refers to the spatial arrangement of atoms in molecules and how this affects their chemical behavior. In the case of cyclic compounds like cyclohexanol, the orientation of substituents can lead to different stereoisomers. Recognizing the stereochemical implications of reactions is essential for accurately predicting the major products, especially when dealing with chiral centers.

Lucas Test

The Lucas test is a qualitative test used to classify alcohols based on their reactivity with Lucas reagent (a mixture of zinc chloride and hydrochloric acid). This reagent facilitates the conversion of alcohols to alkyl chlorides, with tertiary alcohols reacting faster than secondary and primary. Understanding the Lucas test helps in predicting the outcome of reactions involving alcohols and their corresponding halides.