Final answer:
A secondary substrate undergoes an SN₂ reaction in a polar aprotic solvent with a strong nucleophile and an SN₁ reaction in a polar protic solvent with a weak nucleophile.
Step-by-step explanation:
A secondary substrate will proceed through an SN₂ mechanism if the nucleophile is strong and the solvent is polar aprotic; it will proceed through an SN₁ mechanism if the nucleophile is weak and the solvent present in it is polar protic.
In an SN₂ mechanism, the reaction occurs in one concerted step, with the nucleophile attacking the electrophilic carbon of the substrate as the leaving group departs. This reaction type is preferred in polar aprotic solvents because the nucleophiles are less solvated and thus more reactive towards the substrate.
For an SN₁ mechanism, the reaction rate is unimolecular and proportional to the substrate concentration. It typically occurs in polar protic solvents which stabilize both the cationic and anionic intermediates that form during the reaction process, even in cases with tert-butyl bromide as the substrate.