To determine the correct order of carbon-oxygen double bond lengths in the given molecules/species, we need to consider the resonance and electronic structure of each molecule:
- Resonance and Bond Order:
- Molecule \((x)\): This is a ketone, specifically a cyclic ketone (benzophenone), where there's no significant resonance with the double bond. The bond order is typical of a carbonyl group.
- Molecule \((y)\): Acetone exhibits less resonance stabilization than \((x)\). The bond order remains essentially 2 (a double bond).
- Molecule \((z)\): This is an enolate ion, where resonance plays an important role. The negative charge is delocalized between the oxygen atoms, decreasing the effective bond order of the carbon-oxygen double bond compared to the carbonyl groups in \((x)\) and \((y)\).
- Carbon-Oxygen Bond Length:
The bond length is inversely related to the bond order. Higher bond order means more shared electrons between atoms, leading to shorter bond lengths.
- In enolate ion \((z)\), the bond order is reduced due to resonance, resulting in a longer bond length than typical carbonyls.
- Molecule \((y)\)'s bond length is shorter than \((z)\) due to no resonance affecting the carbonyl group significantly.
- Molecule \((x)\) is a typical carbonyl with a normal bond length for a double bond, between \((y)\) and \((z)\).
Conclusion: Thus, the increasing order of carbon-oxygen bond length is \(z > x > y\)