Answer
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The reason why all three C-O bonds in the CO3^2- ion have identical bond lengths of 136 pm is due to the resonance structure of the carbonate ion.
In the carbonate ion (CO3^2-), the carbon atom is bonded to three oxygen atoms. The key to understanding the identical bond lengths is the concept of resonance.
The carbonate ion can be represented by the following resonance structures:
O=C-O^- ⇌ O-C=O^- ⇌ O-C-O
These resonance structures show that the carbon-oxygen bonds have partial double bond character, rather than being purely single or double bonds.
The partial double bond character is a result of the delocalization of the negative charge and the sharing of electrons among the three oxygen atoms. This delocalization of the electrons leads to the three C-O bonds having the same bond length of 136 pm, which is intermediate between the typical C-O single bond length (143 pm) and the C=O double bond length (123 pm).
The resonance stabilization of the carbonate ion results in the three C-O bonds having the same length, as the electron density is evenly distributed among the three bonds. This is in contrast to the individual C-O, C=O, and C≡O bond lengths provided in the question, which represent the typical bond lengths for these specific bond types.
