Acid chlorides are more reactive than anhydrides towards nucleophiles.

Solution

Chemistry ma’am · 4 steps

Judge the leaving group: the weaker the base that leaves, the faster the nucleophile attacks.

1. Same mechanism. Acid chlorides and anhydrides both react by nucleophilic acyl substitution. The nucleophile adds to the carbonyl carbon, and then a leaving group is pushed out.
2. Compare leaving groups. An acid chloride loses Cl⁻, the conjugate base of HCl (pKₐ ≈ -7). An anhydride loses RCOO⁻, the conjugate base of a carboxylic acid (pKₐ ≈ 4.8). Cl⁻ is the much weaker base, so it leaves far more easily.
3. Carbonyl carbon. In RCOCl the chlorine 3p lone pair overlaps poorly with the carbon 2p orbital, so it gives almost no resonance stabilisation. Its strong -I effect leaves the carbonyl carbon very electron-poor. In an anhydride the oxygen lone pair donates partly into each carbonyl, which makes that carbon a little less positive.
4. So. The reactivity order is acid chloride > anhydride > ester > amide, and the statement is true.

The idea to keep. For acid derivatives, the better the leaving group and the less resonance into the C=O, the more reactive the derivative: RCOCl > (RCO)₂O > RCOOR' > RCONH₂.

Answer from the NTA final answer key. Solution by PrepWiser.