Comparison of Carbon Oxygen Double Bond Length in Organic Species

To determine the correct order of the carbon-oxygen ($\text{C}-\text{O}$) bond length in the given species, we analyze the contribution of resonance structures and the resulting bond order for each species:

1. Species $(x)$ (Tropone / 2,4,6-Cycloheptatrien-1-one):

   • The carbonyl group can polarize as follows: $\text{Tropone} \longleftrightarrow \text{Tropylium Cation} + \text{O}^-$
   • Polarisation gives a seven-membered ring carbocation containing $6\pi$ electrons. According to Hückel's rule ($(4n+2)\pi$ electrons with $n=1$), this ring is aromatic and exceptionally stable.
   • Due to this aromatic stabilization, the dipolar single-bonded resonance structure ($\text{C}^+-\text{O}^-$) contributes heavily to the resonance hybrid.
   • As a result, the $\text{C}-\text{O}$ bond has substantial single-bond character, leading to a bond order significantly less than $1.5$. Thus, it has the longest carbon-oxygen bond.

2. Species $(z)$ (Acetate ion, $\text{CH}_3\text{COO}^-$):

   • The negative charge is delocalized equally over both oxygen atoms through two equivalent canonical structures: $\text{CH}_3-\text{C}(=\text{O})-\text{O}^- \longleftrightarrow \text{CH}_3-\text{C}(\text{O}^-)=\text{O}$
   • Due to equal resonance, the carbon-oxygen bond order is exactly: $\text{Bond Order} = \frac{1 + 2}{2} = 1.5$

3. Species $(y)$ (Acetone, $(\text{CH}_3)_2\text{C}=\text{O}$):

   • It possesses a standard, highly localized carbon-oxygen double bond ($\text{C}=\text{O}$).
   • Without any aromatic stabilization or equivalent charge delocalization, the single-bond contributor is minimal.
   • Thus, the bond order is closest to $2.0$, giving it the shortest carbon-oxygen bond.

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Conclusion:

Comparing the bond orders: $\text{Bond Order: } y > z > x$

Since bond length is inversely proportional to bond order ($\text{Bond Length} \propto \frac{1}{\text{Bond Order}}$), the correct order of carbon-oxygen bond lengths is: $x > z > y$

Correct Option: D ($x > z > y$)