Solvents will change the reaction rate. Since the SN1 reaction involves formation of an unstable carbocation intermediate in the rate-determining step, anything that can help this will speed up the reaction. The normal solvents of choice are both "polar" (to stabilize ionic intermediates in general) and "protic" (to solvate the leaving group in particular). Typical polar protic solvents include water and alcohols, which will also act as nucleophiles.
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