For the pairs of compounds in Problem 48, which is more reactive in an SN² reaction?

SN² reaction is a nucleophilic substitution reaction where the Nucleophilic attack and bond breaking between carbon and electronegative group happens simultaneously through a 5 coordinated transition state. In this reaction, the rate equation is second order having both the concentration of nucleophile and alkyl bromide.

A reaction mechanism with an experimental compound is given below,

SN² reaction proceeds through a 5 membered transition state where bond breaking and bond making happens simultaneously. The more is the steric hindrance at transition state, the less will be the rate of the reaction. So, primary or less hindered carbocation will be more reactive.

But Vinylic halides and aryl halides (compounds in which the halogen is attached to a benzene ring) do not undergo SN² or SN¹ reactions because, as the nucleophile approaches the back side of the sp² carbon, it is repelled by the p electrons of the double bond or the benzene ring.

So, the reactivity remains same as of the SN¹ reaction, only the transition state changes.