The primary sulfonate ester shown is treated with $\mathrm{NaN}{}_3$ at the same concentration in four different solvents. In which solvent is the $\mathrm{S}{}_{\mathrm{N}}2$ reaction fastest?

The compound is butyl methanesulfonate. In protic solvents (water, methanol, acetic acid) azide is hydrogen-bonded and its nucleophilicity is lowered. In the polar aprotic solvent DMF, the anion is poorly solvated (a naked nucleophile) and the $\mathrm{S}{}_{\mathrm{N}}2$ rate rises by orders of magnitude. DMF is fastest.