Question

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?

Short answer

The bonding in the carbonate ion (\(\mathrm{CO}_{3}^{2-}\)) can be described using both the localized electron model and the molecular orbital model. In the localized electron model, the central carbon atom is sp² hybridized, forming 3 sigma (σ) bonds with the 3 sp² hybridized oxygen atoms. The π bond is formed by the side-by-side overlap of unhybridized 2p orbitals on the carbon and the doubly-bonded oxygen atom, and the π bonding is delocalized over the entire ion. The molecular orbital model describes the π bonding through the interaction of the atomic p orbitals on the carbon and oxygen atoms, forming delocalized π molecular orbitals, giving partial double bond character to all the C-O bonds in the structure.

Step-by-step solution

Draw the Lewis structure and identify resonance structures of \(\mathrm{CO}_{3}^{2-}\)

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.

Determine the hybridization and the σ bonding

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.

Describe the σ and π bonding in CO₃²⁻ using the localized electron model

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.

Describe the π bonding in CO₃²⁻ using the molecular orbital model

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.

Key concepts

Localized Electron Model

The Localized Electron Model (LEM) is handy for visualizing molecular bonding as it simplifies observing individual electron pairs between atoms.
In the case of the carbonate ion (\(\mathrm{CO}_{3}^{2-}\)), each atom is considered individually with reference to the specific resonance structures.
This model allows us to see that the central carbon is sp² hybridized, meaning it forms three sigma (\(σ\)) bonds with the surrounding oxygen atoms.
For each of the resonance structures, one oxygen forms a pi (\(π\)) bond with carbon, while lone pairs reside on the other oxygen atoms.
These resonance structures show the shifting positions of pi bonds and lone pairs, emphasizing the delocalization nature of the electron density in carbonate.
Ultimately, even though the bonds seem unique to each resonance structure, they contribute equally, which is how LEM provides a mix of realism and simplicity when explaining bondings in molecules.

Molecular Orbital Model

Unlike the Localized Electron Model, the Molecular Orbital Model (MOM) extends bonding concepts across the entire molecule.
In this model, the electrons are considered as spreading over the whole ion rather than staying within bond pairs.
For the carbonate ion, the p orbitals of the oxygen atoms interact with the p orbital of carbon to form molecular orbitals.
This interaction leads to the formation of bonding and antibonding orbitals.
Electrons fill these orbitals, and those in the bonding orbitals are shared across the entire molecule.
Because of this electron sharing, the bonds between carbon and oxygen have partial double bond character rather than being limited to one strong double bond and weaker single bonds like in a localized model.
This delocalization indicates why the carbonate ion has special chemical stability and bonding character.

Resonance Structures

Resonance structures are ways of expressing molecules that cannot be depicted with a single Lewis structure.
For the carbonate ion, there are three resonance structures.
Each features a different oxygen double-bonded to carbon while the others carry negative charges.
No single structure is a true representation, but the actual electron positioning is a hybrid of all resonance forms.
This delocalization of electrons across multiple structures increases the ion’s stability.
In practice, none of the resonance structures exist alone; they simply illustrate possible configurations that combine to form the real distribution of electrons in the ion.
Resonance emphasizes that electrons in the carbonate ion aren't fixed but fluid, sharing between the carbon and oxygen atoms.

Hybridization

Hybridization is a concept that helps explain the geometry and bonding of molecules.
In the carbonate ion, the carbon atom exhibits sp² hybridization.
This comes from mixing one s orbital and two p orbitals, resulting in three sp² hybrid orbitals.
This hybridization gives the carbonate ion a planar trigonal structure with bond angles of approximately 120 degrees.
Each sp² orbital on the carbon overlaps with the sp² orbitals of the oxygen atoms to form sigma bonds.
Meanwhile, unhybridized p orbitals are involved in forming the pi bonds associated with each resonance structure.
The matching of hybrid orbitals with the ion’s geometry illustrates a clear relationship between structure and hybridization.

Delocalized Bonding

Delocalized bonding occurs when electrons are not confined to a particular bond between two atoms but spread over several atoms.
In the carbonate ion, the pi electrons are delocalized across the carbon and all three oxygen atoms.
This delocalization means the bond order between carbon and oxygen is not a simple integer; rather, it sits between a single and double bond.
The result gives the ion increased stability and resonance stabilization energy.
As the electron cloud is shared among all oxygen atoms rather than being localized in single or double bonds, the molecular structure benefits from this distribution of charge.
Delocalized bonding is crucial for understanding why certain molecules are exceptionally stable despite what individual resonance structures might suggest.