How do polar solvent help in the first step in `S_(N)1` mechanism?

Explanation

In the first step i.e., rate determining step (r.d.s) of `S_(N)1` reaction, the substrate undergoes ionisation to form carbocation intermediate. Such ionisation process is favoured in presence of a polar solvent (i.e., solvent having high dielectric constant). Futhermore, especially the protic polar solvents stabilise the carbocation, thereby favouring the `S_(N)1` mechanism.