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?

In the Localized Electron Model, we consider bonds as localized between two adjacent atoms as a result of the sharing of electrons. There are three resonance structures for the CO₃²⁻ ion, each structure having one double bond (∏ bond) and two single bonds (σ bonds). It is important to understand that these resonance structures do not imply that the molecule switches between the different forms but rather that the resulting structure is a resonance hybrid of the three possibilities where the double bond is evenly distributed over all three oxygen atoms.

The electron configuration of carbon is \([He]2s^2 2p^2\). In order to form three sigma bonds with the oxygen atoms, carbon must hybridize its valence orbitals into three equivalent orbitals, involving 2s and two 2p orbitals. This is called sp² hybridization. Each of the three sp² orbitals on the carbon atom will form a sigma bond with one of the p orbitals on the oxygen atom. In terms of the LE Model, all six electrons are located within these sigma bonds.

In the LE Model, we use the concept of resonance structures to describe the distribution of the pi bonding electrons over the CO₃²⁻ ion. The π bonding originates from the overlap of the remaining p orbitals of the carbon atom and one of the oxygen atoms. There are three possible distributions for the location of the double bond among the three oxygens. These three resonance structures equally contribute to the actual molecule, spreading the π bonding electrons evenly across the oxygen atoms.

In the Molecular Orbital Model, we consider that electrons are delocalized over the entire molecule in molecular orbitals. In the case of the CO₃²⁻ ion, the molecular orbitals are formed by the combination of the 2p orbitals of the carbon atom and the 2p orbitals from the oxygen atoms. Since the 2p orbitals are perpendicular to the plane formed by the sp² hybrid orbitals, they create new molecular orbitals that are delocalized over all three oxygen atoms. There are three new molecular orbitals formed: one bonding (∏ bonding), one non-bonding, and one antibonding (∏* antibonding) molecular orbital. The ∏ bonding molecular orbitals have lower energy and can hold two electrons each. For CO₃²⁻, there are two electrons delocalized over the entire ion in the ∏ bonding molecular orbitals. That means the bond order of the pi bonding equals to 2/3, showing the partial double bond character in the CO₃²⁻ ion. In conclusion, the Localized Electron Model describes the bonding in CO₃²⁻ ion using resonance structures, where the double bond appears in a single location among the three oxygen atoms. In contrast, the Molecular Orbital Model gives a more accurate depiction of the delocalized nature of π bonding, where the electrons are shared evenly over all three oxygen atoms.