Final answer:
The correct statement about the E1 mechanism is that the identity of the leaving group affects the rate of reaction, as the rate-determining step is the dissociation of the leaving group to form a carbocation.
Step-by-step explanation:
The statement about an E1 mechanism that is true is a) the identity of the leaving group affects the rate of reaction. An E1 mechanism involves the formation of a carbocation intermediate when the leaving group departs, and this step is the rate-determining step of the reaction, making it unimolecular. Consequently, the nature of the leaving group can have a significant impact on the rate at which this step proceeds. Tertiary substrates are more likely to undergo E1 reactions due to the increased stability of the resulting carbocation. Polar aprotic solvents tend to favor SN1 and E1 mechanisms because they can stabilize the charged intermediates without participating significantly in hydrogen bonding with the substrate or the leaving group.