Question

Compare the structure and bonding in \(\mathrm{CO}_{2}\) and \(\mathrm{CO}_{3}^{2-}\) with regard to the \(\mathrm{O}-\mathrm{C}-\mathrm{O}\) bond angles, the \(\mathrm{CO}\) bond order, and the \(\mathrm{C}\) atom hybridization.

Short answer

\(\mathrm{CO}_2\) is linear with \(180^\circ\) angles, bond order 2, \(sp\) hybridized; \(\mathrm{CO}_3^{2-}\) is trigonal planar with \(120^\circ\) angles, average bond order \(\frac{4}{3}\), \(sp^2\) hybridized.

Step-by-step solution

Determine Molecular Geometry

The molecular geometry of \(\mathrm{CO}_2\) is linear, resulting in an \(\mathrm{O}-\mathrm{C}-\mathrm{O}\) bond angle of \(180^\circ\). In contrast, \(\mathrm{CO}_3^{2-}\) is a trigonal planar ion, with bond angles of \(120^\circ\) for each \(\mathrm{O}-\mathrm{C}-\mathrm{O}\) bond.

Analyze CO Bond Order

In \(\mathrm{CO}_2\), the carbon and each oxygen are connected by double bonds, resulting in a bond order of 2 for each \(\mathrm{C}=\mathrm{O}\) bond. In \(\mathrm{CO}_3^{2-}\), resonance structures exist: one single bond and two double bonds with an overall effect of averaging the \(\mathrm{C}-\mathrm{O}\) bond order to \(\frac{1}{3}(2+1+1)=\frac{4}{3}\).

Determine Carbon Hybridization

In \(\mathrm{CO}_2\), carbon undergoes \(sp\) hybridization, using two \(p\) orbitals to form \(\pi\)-bonds. For \(\mathrm{CO}_3^{2-}\), carbon is \(sp^2\) hybridized, because it forms three sigma bonds using \(sp^2\) orbitals and shares \(\pi\) bonds via delocalization in the resonance structures.

Key concepts

Molecular Geometry

Molecular geometry is a crucial concept in understanding the shape and structure of molecules. It refers to the spatial arrangement of atoms within a molecule.

• **Linear Geometry:** This occurs in molecules like carbon dioxide (\(\mathrm{CO}_2\)) where the central carbon atom forms double bonds with two oxygen atoms. These double bonds repel each other equally, creating a straight line of atoms and resulting in an \(\mathrm{O}-\mathrm{C}-\mathrm{O}\) bond angle of \(180^\circ\).


• **Trigonal Planar Geometry:** This is seen in carbonate ions (\(\mathrm{CO}_3^{2-}\)), where the central carbon atom is bonded to three oxygen atoms arranged in a plane. Each of these oxygen atoms forms a bond angle of \(120^\circ\) with the carbon atom. This setup is due to the resonance, which allows for even distribution of electrons across the ion.

Understanding the molecular geometry is essential for predicting the behavior and reactivity of molecules.

Carbon Hybridization

Hybridization is the mixing of atomic orbitals in an atom to generate new hybrid orbitals. These orbitals are used to form covalent bonds.

• In **carbon dioxide** (\(\mathrm{CO}_2\)), the carbon atom undergoes **sp hybridization**. This means one s orbital and one p orbital combine to form two sp hybrid orbitals. These two hybrid orbitals form sigma bonds with the oxygen atoms, while the remaining p orbitals form pi bonds.


• For the **carbonate ion** (\(\mathrm{CO}_3^{2-}\)), the carbon is **sp^2 hybridized**. Here, one s orbital and two p orbitals mix to form three sp^2t hybrid orbitals. These create the sigma bonds with the three oxygen atoms. The remaining p orbital participates in the delocalized pi bonding, which is spread across the entire molecule due to resonance.

Hybridization is key to understanding the geometry and bonding characteristics of a molecule. It explains how carbon, which has different electronic configurations, can form stable bonds in various forms.

Bond Order

Bond order is a concept that relates to the number of chemical bonds between a pair of atoms. The bond order indicates bond strength; a higher bond order means a stronger bond.

• In **carbon dioxide** (\(\mathrm{CO}_2\)), the bond order is 2. This is because there are two double bonds (each consisting of one sigma and one pi bond) between carbon and the oxygen atoms. This bond order suggests a strong, stable molecule with each carbon-oxygen link.


• In the **carbonate ion** (\(\mathrm{CO}_3^{2-}\)), the bond order averages to about \(\frac{4}{3}\). This lower bond order occurs due to resonance structures, with one double bond and two single bonds. The electrons in \(\mathrm{CO}_3^{2-}\) are distributed over the resonant forms, leading to an averaged state which makes the bonds partly double and partly single.

Bond order is essential to comprehend because it affects the stability and the length of the chemical bonds within a molecule.

Resonance Structures

Resonance structures are different ways to represent the distribution of electrons in a molecule that can't be fully described with a single Lewis structure. They help explain real molecular structure more accurately by showing possible configurations of electron distributions:

• **Carbon Dioxide** (\(\mathrm{CO}_2\)) does not have resonance structures. It can be satisfactorily depicted with double bonds in a single, fixed configuration.


• **Carbonate Ion** (\(\mathrm{CO}_3^{2-}\)) requires resonance structures. Because electrons are delocalized over the molecule, it can be represented with one double bond cycling between the three oxygen atoms. This leads to three equivalent resonance structures that together describe the electron distribution more accurately than any single Lewis structure.

Resonance structures often indicate stability, as the electrons are spread out, minimizing repulsion and lowering energy. Understanding resonance can offer insights into the molecule's reactivity and properties.