Describe the bonding in the \(\mathrm{CO}_{3}^{2-}\) ion using the localized electron model. How would the molecular orbital model describe the \(\pi\) bonding in this species?

Begin by drawing the Lewis structure of the carbonate ion (CO₃²⁻). This structure contains 24 valence electrons: 4 from carbon, 6 from each of 3 oxygen atoms, and 2 extra electrons due to the -2 charge. The central carbon atom is bonded to 3 oxygen atoms, each of which has one double bond and two lone pairs of electrons. Since the double bond can exist between the central carbon and any of the three oxygen atoms, there are 3 possible resonance structures: Resonance Structure 1: O=C-O^- O^- Resonance Structure 2: O^-=C-O^- O Resonance Structure 3: O^- O=C-O^- In each resonance structure, there is one C=O double bond and two C-O single bonds, with negative charges on the unshared oxygen atoms. To explain the bonding in \(\mathrm{CO}_{3}^{2-}\), we need to consider the contribution from all these resonance structures.

To determine the hybridization of the atoms in CO₃²⁻, look at the central carbon atom, which is bonded to 3 oxygen atoms. We can treat the entire ion as a molecule with one central atom and 3 surrounding atoms. This arrangement indicates that the carbon atom must be sp² hybridized, leading to the formation of 3 sigma bonds. Similarly, the three oxygen atoms also exhibit sp² hybridization as they form double bonds with carbon in the resonance structures. The lone pairs in these oxygen atoms occupy the remaining hybrid orbitals in sp² hybridization.

In the localized electron model, the bonding in CO₃²⁻ can be described as follows: 1. The sigma (σ) bonds: The sp² hybrid orbitals from the carbon atom overlap with the sp² hybrid orbitals from each oxygen atom, forming 3 sigma (σ) bonds. 2. The pi (π) bonds: In each resonance structure, one of the three oxygen atoms shares a double bond (C=O) with the carbon atom. In addition to the sigma bond, a double bond contains a π bond as well. The π bond is formed by the side-by-side overlap of unhybridized 2p orbitals on the carbon atom and the doubly-bonded oxygen atom. Since there are three possible resonance structures, the π bonding is delocalized over the entire ion, giving a partial double bond character to all the C-O bonds.

The molecular orbital model describes the bonding by considering the constructive and destructive interference of the atomic orbitals from the bonded atoms. In the case of CO₃²⁻, the three atomic p orbitals on oxygen atoms interact and combine with the p orbital on the central carbon atom to form π molecular orbitals. The resultant molecular orbitals would involve three bonding orbitals and one antibonding orbital. The electrons in the π bonding molecular orbitals are delocalized over the entire ion, sharing the electron density between the central carbon and all three oxygen atoms, giving a partial double bond character to the C-O bonds. In conclusion, both the localized electron model and the molecular orbital model describe the π bonding in the CO₃²⁻ ion as delocalized, giving partial double bond character to all the C-O bonds in the structure.