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The Lucas test for alcohols is based on the way primary, secondary and tertiary alcohols react with Lucas reagent. If on adding Lucas reagent to an alcohol, the mixture immediately becomes turbid, then it is a tertiary alcohol.

I am aware that alcohols get converted to alkyl chlorides on reaction with concentrated HCl, and that it the alkyl chloride that is insoluble and hence responsible for the turbidity.

But why do tertiary alcohols react the fastest with HCl?

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The tertiary alcohol has more R groups compared to primary & secondary alcohols, there by removing the C-O Bond from a tertiary alcohol is more easier. (the tertiary carbocation is more stable)

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