Ether Cleavage with HI: Mechanism and Product Selectivity

The reaction involves the acid-catalyzed cleavage of an ether, tert-butyl methyl ether ($(CH_3)_3C – O – CH_3$), using hydrogen iodide ($HI$). The products formed are tert-butyl iodide ($(CH_3)_3CI$) and methanol ($CH_3OH$), not methyl iodide ($CH_3I$) and tert-butyl alcohol ($(CH_3)_3C – OH$). This selectivity is explained by the reaction mechanism and the stability of intermediate carbocations.

Reaction Mechanism

The reaction proceeds in two main steps:

1. Protonation: The ether oxygen is protonated by $HI$ to form an oxonium ion. $(CH_3)_3C – O – CH_3 + HI \rightarrow (CH_3)_3C – O^+(H) – CH_3 + I^-$
2. C-O Bond Cleavage: The protonated ether undergoes heterolytic cleavage of one of the carbon-oxygen bonds. Two pathways are possible:
   • Cleavage of the tert-butyl C-O bond: This forms a tert-butyl carbocation $((CH_3)_3C^+)$ and methanol ($CH_3OH$).
   • Cleavage of the methyl C-O bond: This forms a methyl carbocation ($CH_3^+$) and tert-butyl alcohol ($(CH_3)_3C – OH$).

Carbocation Stability

The stability of carbocations follows the order: tertiary $(3^\circ)$ $>$ secondary $(2^\circ)$ $>$ primary $(1^\circ)$ $>$ methyl ($CH_3^+$). This stability is due to inductive effects and hyperconjugation.

• The tert-butyl carbocation $((CH_3)_3C^+)$ is tertiary and thus relatively stable.
• The methyl carbocation ($CH_3^+$) is highly unstable.

Explanation of Product Formation

The reaction favors the pathway that forms the more stable carbocation. Therefore, the tert-butyl C-O bond cleaves, leading to the formation of $(CH_3)_3C^+$ and subsequently $(CH_3)_3CI$ upon reaction with $I^-$. The other fragment yields $CH_3OH$.

Analysis of Options

• Statement (A): "in step 2 of the reaction the departure of leaving group ($HO – CH_3$) creates less stable carbocation." This statement is incorrect. The pathway leading to the observed products involves the formation of a *more* stable carbocation $((CH_3)_3C^+)$. The alternative pathway (forming $CH_3^+$) would create a less stable carbocation, but (A) is false in the context of explaining the *given* products.
• Statement (B): "in step 2 of the reaction the departure of leaving group ($HO – CH_3$) creates more stable carbocation." This statement is correct. The cleavage of the tert-butyl C-O bond generates the more stable tert-butyl carbocation $((CH_3)_3C^+)$.
• Statement (C): "the reaction follows $S_N1$ mechanism." This statement is correct. The formation of a stable carbocation intermediate (tert-butyl carbocation) is characteristic of the $S_N1$ mechanism.
• Statement (D): "the reaction follows $S_N2$ mechanism." This statement is incorrect. $S_N2$ mechanisms do not involve stable carbocation intermediates and are disfavored by steric hindrance at the tertiary carbon.

Therefore, statements (B) and (C) correctly explain why the reaction produces $(CH_3)_3CI$ and $CH_3OH$.