Give the reaction of $CH_3-C(CH_3)_2-OCH_3$ with the following:
$(i)$ Anhydrous $HI$ in ether
$(ii)$ Concentrated $HI$

(N/A) The reaction of tert-butyl methyl ether with $HI$ proceeds via the protonation of the ether oxygen atom.
$(i)$ With anhydrous $HI$ (or $HI$ in ether),the reaction follows an $S_N2$ mechanism. The nucleophile $I^-$ attacks the less sterically hindered methyl group,resulting in the formation of tert-butyl alcohol and methyl iodide $(CH_3I)$.
$(ii)$ With concentrated $HI$,the reaction follows an $S_N1$ mechanism. The protonated ether undergoes cleavage to form a stable tert-butyl carbocation,which then reacts with $I^-$ to form $2-$iodo$-2-$methylpropane,while the methyl group forms methanol $(CH_3OH)$.