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Which is not a good nucleophile, phenoxide ion or acetate ion?
In general, the better nucleophile should have electron density that is more concentrated onto a single atom so that it is easier to donate.
Whereas the phenoxide ion is simply the aromatic phenol anion, ##"C"_6"H"_5-"O"^(-)##, with a "well-defined" HOMO (located on the negatively-charged oxygen), the acetate ion has delocalized electron density across its two oxygens. That is, it is shared between the two oxygens, and its HOMO is less "well-defined".
Since the electron density is more disperse on the acetate ion, it is more difficult to donate it onto an electrophile's LUMO during the reaction mechanism (it's like saying "protip: . . . " and not having anything to show for it!).
One way you could understand what that means is to realize that when electron density is not gathered in one place (the nucleophilic atom), it becomes harder to move it onto another place (the electrophilic atom) because you have to gather it first.
Hence, the phenoxide ion should be the better nucleophile. Not necessarily GOOD, but better than the acetate ion.
Always treat nucleophilicity as relative!