In S$_N^1$ reactions, the stability of the carbocation intermediates plays a crucial role in determining the rate of the reaction. The more stable the carbocation, the faster the reaction.
Step 1: Understanding S$_N^1$ reactions.
In an S$_N^1$ reaction, the rate depends on the stability of the carbocation formed during the reaction. A more stable carbocation will lead to a faster reaction.
Step 2: Comparing the structures.
- P: The carbocation formed here will be a benzylic carbocation (due to the phenyl group) which is highly stable.
- Q: The carbocation formed here will also be a benzylic carbocation, but its stability will be less than P due to the difference in substituents.
- R: This structure will form a tertiary carbocation, which is more stable than a benzylic carbocation, making the reaction rate the highest.
- S: This structure will form a secondary carbocation, which is less stable than the tertiary carbocation, but more stable than a primary carbocation.
Step 3: Conclusion.
Thus, the order of reactivity in the S$_N^1$ reaction is R>S>P>Q, corresponding to option (2).
