3.85 part b

[Jade Corpus-Sapida 1G]

In this problem it asks to arrange the following molecules/ions in order of decreasing lengths: SO₂, SO₃, and SO₃^2-. The answer is SO₃^2- > SO₂ ~SO₃. I understand why SO₃^2- has the longest length, however I don't understand why the other two would have equal/same lengths? If this were to be on a test how would we know that they were equal?

[Jade Corpus-Sapida 1G]

or would this just be known by looking up these values in the back of the book/online? or can it be calculated?

[Emma Leshan 1B]

Both Lewis structures have one double bonded O and the other(s) are single bonded. Because of resonance, the double bonds are shared throughout the molecule. This makes the bond lengths approximately equal in the molecules even though technically SO2 should be a little shorter due to the double bond being shared at 2 bonds instead of 3.

[ErinKim1I]

When there is resonance, electrons are delocalized and so the bond length distribution is somewhere between the single and double bond in the structure.