Step 1: Understand the reactivity of nucleophiles.
Nucleophilicity is a measure of the reactivity of a nucleophile in a substitution or addition reaction. The order of nucleophilicity is influenced by factors such as charge, size, and electronegativity.
- Hydroxide ion \( \text{OH}^- \): A strong nucleophile because it has a negative charge and is small.
- Phenoxide ion \( \text{PhO}^- \): A strong nucleophile, but slightly weaker than hydroxide, because the negative charge is delocalized over the aromatic ring, reducing its nucleophilicity.
- Acetate ion \( \text{CH}_3\text{COO}^- \): A weaker nucleophile than \( \text{OH}^- \) and \( \text{PhO}^- \), as the negative charge is stabilized by resonance with the carbonyl group.
- Perchlorate ion \( \text{ClO}_4^- \): A very weak nucleophile because the negative charge is highly delocalized over the oxygen atoms, making it less reactive.
Step 2: Compare nucleophilicity.
From the above reasoning, the order of nucleophilicity is:
\[
\text{OH}^->\text{PhO}^->\text{CH}_3\text{COO}^->\text{ClO}_4^-
\]
Thus, the correct order of reactivity is given by option (2).