Q.Decreasing order of nucleophilicity is
Step 1. Nucleophilicity for these simple, comparably-sized anions/molecules tracks basicity, which in turn tracks how readily each species' conjugate acid gives up a proton -- the weaker the conjugate acid, the stronger the base/nucleophile.
Step 2. is the conjugate base of ammonia ( of ) -- an extremely weak acid, making an exceptionally strong base and the strongest nucleophile of the four.
Step 3. (methoxide) and (hydroxide) are conjugate bases of methanol and water respectively ( and ) -- both far weaker bases than , but methoxide is very slightly the stronger of the two, since the electron-donating () methyl group pushes extra electron density onto oxygen, making methoxide a touch more electron-rich (and hence more nucleophilic/basic) than bare hydroxide.
Step 4. is a neutral amine, not an anion -- neutral species are always markedly weaker nucleophiles than a charged (anionic) species built on the same donor atom, so it ranks last.
Step 5. Putting these together: , matching option (c).
(c) NH₂⁻ > CH₃O⁻ > OH⁻ > RNH₂
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