To determine which compound undergoes solvolysis the most readily with methanol, we need to consider the structure and stability of the carbocations that would form during the reaction. Solvolysis involves the nucleophilic attack of the solvent (in this case, methanol) on the substrate, leading to the formation of a carbocation intermediate.
Among the provided options:
- 1-bromo-1-butene: This compound can form a tertiary carbocation, which is quite stable due to hyperconjugation and inductive effects.
- 2-bromo-1-butene: This would form a secondary carbocation, which is less stable than a tertiary carbocation, thus it undergoes solvolysis more slowly.
- 3-bromo-1-butene: This compound can form a primary carbocation, making it the least favorable for solvolysis.
- 4-bromo-1-butene: Also forms a primary carbocation and has similar stability issues as 3-bromo-1-butene.
Considering these factors, 1-bromo-1-butene is the compound that most readily undergoes solvolysis with methanol because it forms a highly stable tertiary carbocation, thereby facilitating a quicker reaction.