Is ethoxide a better nucleophile in methanol or acetone?
Ethoxide is a better nucleophile in acetone.
The solvent affects the nucleophilicity of ethoxide ion.
A polar protic solvent like methanol can participate in hydrogen bonding with a nucleophile like ethoxide ion, creating a “shell” of solvent molecules around the ion.
This decreases the nucleophilicity of the ethoxide, because the nucleophile must push these solvent molecules out of the way in order to attack the substrate.
A polar aprotic solvent like acetone does not hydrogen bond to ethoxide ion to a significant extent.
So the ethoxide ion is almost a "bare" nucleophile.
It is better able to attack the substrate and is therefore a stronger nucleophile.
WARNING: Ethoxide ion is also a strong base, so you will get a competing reaction in acetone — the aldol condensation.