Final Answer:
The statement given "The rate of a SN1 reaction increases with increasing carbocation stability." is true because increased carbocation stability, associated with more alkyl substituents, accelerates the rate of SN1 reactions. (option A)
Step-by-step explanation:
In SN1 (Substitution Nucleophilic Unimolecular) reactions, the rate-determining step involves the formation of a carbocation intermediate. Carbocation stability plays a crucial role in determining the reaction rate.
Carbocations with more alkyl substituents are more stable due to hyperconjugation and inductive effects, making them more likely to form and leading to faster reactions. As the number of alkyl groups attached to the positively charged carbon increases, the carbocation becomes more stable, and the reaction rate increases.
Therefore, the statement is true: the rate of an SN1 reaction is directly proportional to the stability of the carbocation intermediate.
Option A is the answer.