Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
In their best Lewis structures, the perchlorate ion has three bonds, the sulfate ion two bonds and the phosphate ion one bond. The rest are single bonds, and resonance makes them all equal. Find each bond order and rank the bonds by length.
For the same two atoms, a higher bond order means a shorter, stronger bond. With resonance, the bond order is the number of bond pairs from the central atom divided by the number of outer atoms.
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. Perchlorate. bond pairs over oxygens: .
Step 2. Sulfate. over : .
Step 3. Phosphate. over : .
Step 4. Rank. A higher bond order means a shorter bond: . The central atoms also grow in that order, which pushes the same way.
Answer: , and ; perchlorate has the shortest bonds.
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