I know this undergoes an $\ce{S_{N}1}$ reaction:
Ethanol is the solvent. Weak nucleophile. Neutral nucleophile. This points toward $\ce{S_{N}1/E1}$ (competing pathways).
The leaving group is on a tertiary carbon. This precludes backside attack, $\ce{S_{N}2}$.
The professor labeled this reaction as $\ce{S_{N}1}$.
My question: where's the substitution part of this reaction? I don't see any substitution. Is there supposed to be no reaction here? From what he wrote it looks like a bromine left as bromide ion and a hydrogen appeared out of nowhere.
My expected transition state is a tertiary carbocation, which will not rearrange, and then the nucleophilic oxygen part of the ethanol molecule attacks the carbocation. Bromide ion deprotonates the oxonium ion, and I get an ether.
Who's right?