The correct order of C-O bond length among CO, $CO_3^{2-}$, and $CO_2$ is:

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1. **Relationship:** Bond length is inversely proportional to bond order. Higher bond order implies stronger attraction and shorter bond length. 2. **Analyze CO:** Carbon monoxide has a triple bond between Carbon and Oxygen. Bond Order = 3. 3. **Analyze $CO_2$:** Carbon dioxide ($O=C=O$) has double bonds between Carbon and Oxygen. Bond Order = 2. 4. **Analyze $CO_3^{2-}$:** The carbonate ion exhibits resonance. The double bond is delocalized over three C-O bonds. Bond Order = $\frac{ ext{Total Bonds}}{ ext{Resonance Structures}} = \frac{4}{3} \approx 1.33$. 5. **Comparison:** - Bond Order: $CO (3) > CO_2 (2) > CO_3^{2-} (1.33)$ - Bond Length: $CO < CO_2 < CO_3^{2-}$

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