Question

Consider the following bond lengths: $$\mathrm{C}-\mathrm{O} \quad 143 \mathrm{pm} \quad \mathrm{C}=\mathrm{O} \quad 123 \mathrm{pm} \quad \mathrm{C} \equiv \mathrm{O} \quad 109 \mathrm{pm}$$ In the \(\mathrm{CO}_{3}^{2-}\) ion, all three \(\mathrm{C}-\mathrm{O}\) bonds have identical bond lengths of 136 \(\mathrm{pm} .\) Why?

Short answer

In the carbonate ion (CO₃²⁻), there are three possible resonance structures with double bonds between the carbon atom and one of the oxygen atoms. The actual structure is a resonance hybrid of these three structures, where all C-O bonds have a mixture of single and double bond character, resulting in identical bond lengths. These C-O bonds have a length of 136 pm, which is intermediate between the typical C-O single bond (143 pm) and C=O double bond (123 pm) lengths, as all resonance structures contribute equally to the hybrid.

Step-by-step solution

Lewis Structure of CO₃²⁻

To understand the bond lengths in the carbonate ion (CO₃²⁻), we first need to draw its Lewis structure. The total number of valence electrons in the ion is 24 (4 from the carbon atom, 18 from the three oxygen atoms, and 2 extra electrons due to the 2- charge). We can complete the octets of the oxygen atoms by forming single bonds between each oxygen and the central carbon, and adding two lone pairs to the carbon atom and three lone pairs to each oxygen. After completing the octets, we'll find that the central carbon atom still has one lone pair.

Resonance Structures

The lone pair on the carbon atom can be moved to form a double bond with one of the oxygen atoms, while the double bonded oxygen returns one of its bonding electrons as a lone pair. This results in three possible resonance structures for the CO₃²⁻ ion, differing in the location of the double bond.

Resonance Hybrid

No single resonance structure is an accurate representation of the CO₃²⁻ ion. Instead, the true structure is a resonance hybrid of all three resonance structures, where all C-O bonds are delocalized between single and double bond character.

Bond Length Explanation

In the resonance hybrid, the C-O bonds are not purely single or double bonds, but rather a mixture of both. Consequently, their bond lengths are intermediate between those of single and double bonds. Since all three resonance structures contribute equally to the resonance hybrid, all three C-O bonds in the CO₃²⁻ ion have the same bond length, which is 136 pm – a value between the typical C-O single bond (143 pm) and C=O double bond (123 pm) lengths.

Key concepts

Lewis structure

Lewis structures are drawings used to represent molecules visually. They illustrate how atoms are connected, the types of bonds between them, and where lone pairs of electrons are located.
For the carbonate ion, \(\text{CO}_3^{2-}\), it is essential to account for all the valence electrons.

• Carbon contributes 4 electrons.
• Each oxygen contributes 6 electrons, totaling 18 from three oxygens.
• The 2- charge adds 2 more electrons to the pool.

That brings us to a total of 24 valence electrons to arrange in the structure. The goal is to satisfy the octet rule for each atom while keeping track of the total electron count. In a carbonate ion, each oxygen is singly bonded to the carbon, initially leaving carbon with only 6 electrons. Completing the octets ensures proper electron distribution without losing sight of the overall charge.

bond length

Bond length refers to the distance between the centers of two bonded atoms. It's significant because it affects the stability and reactivity of molecules. In general, single bonds are longer than double bonds, and double bonds are longer than triple bonds.
For example, in carbon-oxygen bonds:

• A C-O single bond typically measures around 143 picometers (pm).
• A C=O double bond is around 123 pm long.
• A C≡O triple bond is approximately 109 pm.

In the carbonate ion \(\text{CO}_3^{2-}\), all C-O bonds are 136 pm, which is an average length between a single and a double bond. This occurs due to resonance, where electronic structure enables a shared character between bond types.

carbonate ion

The carbonate ion, \(\text{CO}_3^{2-}\), is a polyatomic ion featuring one carbon atom centered between three oxygen atoms. It carries a 2- charge overall and plays a vital role in various chemical processes, such as limestone formation and aquatic buffering systems.
Due to its charge, the carbonate ion must be depicted with extra electrons in its Lewis structure, representing this ionic characteristic. The presence of resonance in the carbonate ion leads to equal bond lengths across its C-O bonds. These bonds are neither single nor double completely but illustrate a resonant average due to electron delocalization.

• This equalizes the bond strength and length.
• Each resonance form contributes equally to the overall structure.

This phenomenon contributes to the carbonate ion's stability and uniform geometry.

chemical bonding

Chemical bonding explains the forces holding atoms together in molecules and includes several bond types like ionic, covalent, and metallic bonds. In the context of the carbonate ion, covalent bonding predominates.
Covalent bonds result from the sharing of electron pairs between atoms, as seen in carbon's bonds with oxygen in \(\text{CO}_3^{2-}\). The ion's charge affects how electrons are distributed and shared. Another critical aspect of covalent bonds is resonance, where electrons can shift locations, allowing the molecule to exist in multiple equivalent forms.
Facts about chemical bonding in resonance:

• Resonance structures are different valid ways to draw a molecule, each conforming to electron rules.
• Resonance hybrids are more accurate depictions, merging these forms into a singular, averaged structure showing delocalized electron sharing.

This leads to bond lengths that reflect an average of all potential structures, rather than exact single or double bonds.