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Generally, a molecule has resonance structures if a double bond exists with an atom that appears twice in the structure. One example would be in NO3-, the Nitrogen has single bonds with 2 oxygen and one double bond with the third oxygen. In the Lewis structure, the double bond could be on any single Oxygen. Eahc of these would have the same energy, so none would be the dominant contributor to a resonance hybrid, but in a molecule such as SO2, the sulfur could have one double bond and one single bond, or 2 double bonds. In this case, we would calculate the formal charge of each atom within the molecule and determine which structure's atoms are closer to 0. This resonance structure would be the dominant contributor to the resonance hybrid because it is more stable and has a lower energy.
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