Bond length (hw problem 3.85, part B)

[Steven Garcia 1H]

For this problem, wouldn't the SO3 molecule have a shorter bond length than SO2? The solution manual shows that they are approximately the same. Both the molecules only have double bonds but the SO2 molecule has a lone pair on its central S atom. Wouldn't the lone pair weaken the S-O bond in SO2 (thus its bond length would be larger relative to the bond length of SO3)?

[Chem_Mod]

The lone pair distorts the bond angle because it repels the bonds away from itself. This decreases the bond angle, but it doesn't necessarily change the bond lengths.