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The reaction of ‘tert-butyl methyl ether’ with one equivalent of HI gives
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tert-butyl iodide and methanol
When tert-butyl methyl ether reacts with HI, it will formed tert-butyl iodide and methanol.
Since, the tertiary carbocation forms which is stable. So, $\mathrm{S}_{\mathrm{N}} 1$ mechanism followed. Iodine is attached to tertiary C-atom and $-\mathrm{OH}$ group is attached to methyl group.

Since, the tertiary carbocation forms which is stable. So, $\mathrm{S}_{\mathrm{N}} 1$ mechanism followed. Iodine is attached to tertiary C-atom and $-\mathrm{OH}$ group is attached to methyl group.

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