Final answer:
Methyl bromide is the alkyl halide not predicted to react by the E2 mechanism because it predominantly undergoes the SN2 reaction due to the absence of steric hindrance, which is favorable for backside attack by a nucleophile.
Step-by-step explanation:
The E2 mechanism is a type of elimination reaction in organic chemistry where an alkyl halide eliminates hydrogen and a halide to form an alkene. The ease of this reaction varies depending on the structure of the alkyl halide substrate. For the E2 mechanism, tertiary alkyl halides are the most reactive due to lesser steric hindrance for the base to abstract the β-hydrogen, while secondary alkyl halides are less reactive, and both E2 and SN2 reactions may compete. In contrast, primary and methyl halides are not prone to E2 reactions, since there is no steric hindrance to prevent backside attack by a nucleophile which makes SN2 the more favorable pathway. In summary, the E2 mechanism is least likely, actually very rare, to occur with methyl bromide because it prefers a substitution reaction (SN2) over an elimination one (E2).