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The final answer for this textbook problem was that SO3^2- had the longest S-O bond length and SO2 and SO3 had equal S-O bond lengths. In these problems, should we always try to draw oxygen with a double bond because it has a lower Formal Charge? Initially, I had drawn the SO2 and SO3 structure with only one double bond so my answer wasn't the same.
Whenever you are drawing a structure you want to minimize formal charge as much as you can. If you do have to have charges than any negative charge should go on the more electronegative atom while any positive charges would go on the least electronegative atom in the molecule. Whenever you begin to draw a structure, calculate the formal charges and see if there are any lone pairs you can move to create multiple bonds to minimize them to make the structure more stable.
The other answers are correct that you should always try to minimize formal charge as much as you can. I just wanted to add that you also need to make sure the central atom can hold an expanded octet when you do this! In this case, sulfur can hold an expanded octet because it is in Period 3 and therefore has access to the D orbitals.
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