Why is the reactivity of all the three classes of alcohols with conc. HCl and `ZnCl_(2)` (Lucas reagent) different ?

Explanation

The reaction of alcohols with Lucas reagent (conc. HCl and `ZnCl_(2)`) follow `S_(N)^(1)` mechanism. `S_(N)^(1)` mechanism depends upon the stability of carbocations (intermediate). More stable the intermediate carbocation, more reactive is the alcohol.
Tertiary carbocations are most stable among the three classes of carbocations and the order of the stability of carbocation is `3^(@) gt 2^(@) gt 1^(@)`. This order, intrun, reflects the order of reactivity of three classes of alcohols i.e., `3^(@) gt 2^(@) 1^(@)`.
Thus, as the stability of carbocations are different so the reactivity of all the three classes of alcohols with Lucas reagent is different.