The acid-catalyzed cleavage of an ether using hydroiodic acid HI involves the following steps:1. Protonation of the ether: The first step in the mechanism is the protonation of the ether oxygen by the strong acid, hydroiodic acid HI . This occurs because the oxygen atom in the ether has a lone pair of electrons that can act as a Lewis base, making it susceptible to protonation by a strong acid. The protonation of the ether oxygen increases its electrophilicity, making it more susceptible to nucleophilic attack.2. Nucleophilic attack by iodide ion: After protonation, the positively charged oxygen atom becomes more electrophilic and susceptible to nucleophilic attack. The iodide ion I- present in the solution acts as a nucleophile and attacks one of the carbon atoms connected to the oxygen atom. This leads to the formation of a new carbon-iodine bond and the breaking of the carbon-oxygen bond.3. Deprotonation: The final step in the mechanism is the deprotonation of the protonated oxygen atom. This can be achieved by the iodide ion I- acting as a base and abstracting a proton from the oxygen atom, or by the solvent usually water acting as a base. The end result is the formation of two alkyl iodides and water.Overall, the acid-catalyzed cleavage of an ether using hydroiodic acid results in the conversion of the ether into two alkyl iodides. This reaction is particularly useful for the synthesis of alkyl halides from ethers, which can be further used in various organic transformations.