Sulfur Hybridization and Bonding

[Qube]

Homework Statement

http://i.minus.com/jsdp6WZ2nqRY9.jpg

Homework Equations

Sulfur is sp2 hybridized. Sulfur is also nonpolar having an AXE of AX3 and no lone pairs. It is trigonal planar.

The Attempt at a Solution

I'm not sure if sulfur can be represented by three equivalent resonance structures. If one draws the resonance structures there will be one double-bonded oxygen, and a double-bonded oxygen is going to have a shorter bond length than a single bonded oxygen to the sulfur. The problem states that all the oxygen are equidistant, so how can there be three resonance structures in which the distance of the oxygen from the sulfur differ?

 

[DrClaude]

I'm not sure if sulfur can be represented by three equivalent resonance structures. If one draws the resonance structures there will be one double-bonded oxygen, and a double-bonded oxygen is going to have a shorter bond length than a single bonded oxygen to the sulfur. The problem states that all the oxygen are equidistant, so how can there be three resonance structures in which the distance of the oxygen from the sulfur differ?

First, resonance structures are an approximation. Second, you can't see these structures as independent. As the molecule goes from one structure to the other, the average bond length will be the same for each S-O bond.

By the way, this question should've been posted in the chemistry subforum.