Problem 34 - Chemistry and Chemical Reactivity

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 CO bond order, and the C atom hybridization.

Step-by-Step Solution

Answer

CO2 is linear with 180° bond angles and sp hybridization; CO3^(2-) is trigonal planar with ~120° bond angles and sp2 hybridization. CO bond order is 2 in CO2 and 1.33 in CO3^(2-).

Step 1: Understanding Molecular Geometry - CO2

CO2 has a linear molecular geometry. The central carbon atom is bonded to two oxygen atoms with double bonds. Due to the linear arrangement, the bond angle \( \angle O-C-O \) is 180 degrees.

Step 2: Understanding Molecular Geometry - CO3^(2-)

CO3^{2-} or carbonate ion is a trigonal planar molecule. Here, the C atom is bonded to three oxygen atoms. The arrangement leads to bond angles \( \angle O-C-O \approx 120 \) degrees due to symmetry.

Step 3: Analyzing CO Bond Order in CO2

CO2 has two double bonds (C=O). Therefore, both C-O bonds are equivalent with a bond order of 2.

Step 4: Analyzing CO Bond Order in CO3^(2-)

In CO3^{2-}, resonance structures distribute the double bond character among three C-O bonds. Each bond has an equivalent bond order of 1.33 due to resonance.

Step 5: Hybridization of C atom in CO2

In CO2, the central carbon is \( sp \) hybridized, forming two equivalent \( sp \) hybridized orbitals, leading to a linear shape.

Step 6: Hybridization of C atom in CO3^(2-)

In CO3^{2-}, the central carbon is \( sp^2 \) hybridized, distributing charge among three bonds, resulting in a planar trigonal shape.

Key Concepts

Bond Order

Bond order is a concept used to describe the number of chemical bonds between a pair of atoms. It is an indication of the bond's stability and strength. Higher bond orders generally mean stronger and more stable bonds.

For the molecule \(CO_2\), the carbon atom forms two double bonds with two oxygen atoms. Double bonds translate to a bond order of 2 for each \(C-O\) bond. This means that in \(CO_2\), each bond is quite strong and stable.

In contrast, the carbonate ion \(CO_3^{2-}\) showcases resonance, which influences bond order. Resonance allows the double bond character to be spread out among all three oxygen atoms. Thus, each \(C-O\) bond in \(CO_3^{2-}\) has a bond order of approximately 1.33. This lower bond order compared to \(CO_2\) suggests relatively weaker bonds, which is due to the even distribution of the electron pairs across the three \(C-O\) bonds.

Hybridization

Hybridization is a model that explains the observed molecular geometry by considering the combination of atomic orbitals.

In \(CO_2\), the central carbon atom is \(sp\) hybridized. It utilizes two \(sp\) hybrid orbitals to form sigma bonds with each oxygen atom. The linear arrangement dictated by the \(sp\) hybridization results in a bond angle of 180 degrees.

On the other hand, in the carbonate ion \(CO_3^{2-}\), the central carbon atom is \(sp^2\) hybridized. This hybridization involves mixing one s orbital and two p orbitals. It leads to the formation of three sigma bonds with the oxygen atoms, creating a planar trigonal geometry. This \(sp^2\) hybridization is responsible for the \(120\) degree bond angles between the \(O-C-O\) bonds.

Resonance Structures

Resonance structures are different Lewis structures for molecules that can be drawn to depict the same molecule or ion. Resonance helps explain phenomena like bond length equality and charge distribution that aren't apparent from a single structural representation.

In the molecule \(CO_2\), resonance is notably absent, as its linear shape involves only distinct double bonds with defined electron locations. This means little to no electron delocalization occurs.

Conversely, resonance is a significant aspect of the carbonate ion \(CO_3^{2-}\). It has three possible equal resonance structures. In these structures, the position of the double bond shifts among the oxygen atoms, effectively distributing the double bond character and giving each \(C-O\) bond identical partial double bond character. This resonance contributes to bond strength, bond length uniformity, and the overall stability of the carbonate ion.