to consider the effect of polar solvent, you must consider its effect on all reactants. below is just an example:
molecular structure also plays an important role. For example, ethanol, being polar and heavier than water, binds to OH-, thus preventing the SN1 substitution of Cl with OH in a teritiary chloroalkane Comparing the case of aq medium, it would be water molecules binding the OH- ions. Each ethanol molecule is 14amu more heavier than water molecule, ie. 78% heavier. This results in much reduced mobility of the hydroxide ions, and thus reduces the nucleophilic strength.
At the same time, the solvent molecules stabilise the tertiary cation intermediate formed, and faciliates the abstraction of hydrogen (H+) to produce an alkene. Hence, the effect of heavy polar solvent brings about elimination of HCl in tertiary chloroalkane.