Why do SN2 reactions prefer aprotic solvents?

Let's first look at polar protic solvents.

Protic solvents can H-bond to nucleophiles.

They form a solvation shell around the nucleophile. This shell hinders the nucleophile from attacking the substrate.

Nucleophiles are #bbcolor(red)("less")# nucleophilic in #bbcolor(red)("protic"# solvents.

Here are some typical polar aprotic solvents.

The negative ends of the dipoles are the #"O"# of the #"C=O"# and #"S=O"# groups and the #"N"# of the #"C≡N"# group.

They point away from the body of the molecule. This makes it easy for them to solvate cations.

The positive ends are the #"C"# atoms of the #"C=O"# and #"C≡N"# groups and the #"S"# of the #"S=O"# group.

They are "buried" in the body of the molecule.

The #"CH"_3# groups hinder access by anions. So the molecules are less able to solvate anions (nucleophiles).

The nucleophiles are almost unsolvated, so it is much easier for them to attack the substrate.

Nucleophiles are #bbcolor(red)("more"# nucleophilic in #bbcolor(red)("aprotic"# solvents.

So, #"S"_"N"2# reactions "prefer" aprotic solvents.