The reaction involves the elimination of a halide ion (\( \text{Br}^- \)) from a substrate in the presence of sodium methoxide (NaOCH₃), which results in the formation of an alkene.
Step 1: Mechanism of reaction.
Sodium methoxide is a strong base and will dehydrohalogenate alkyl halides. The base will abstract a hydrogen atom from a carbon adjacent to the carbon bearing the halogen, leading to the formation of a double bond and expulsion of the halide ion.
Step 2: Reaction with tert-butyl bromide.
When sodium methoxide reacts with tert-butyl bromide, the result is the elimination of hydrogen from the carbon adjacent to the one with the bromine, resulting in the formation of 2-methylpropene.
Step 3: Conclusion.
Therefore, the correct answer is (C) tert-butyl bromide, as it leads to the formation of 2-methylpropene under elimination conditions.
Final Answer:} (C) tert-butyl bromide