Problem 27 - Chemistry in 30 days

Question

The correct order of increasing \(\mathrm{C}-\mathrm{O}\) bond length of \(\mathrm{CO}, \mathrm{CO}_{3}^{2-}, \mathrm{CO}_{2}\) is (a) \(\mathrm{CO}_{3}^{2}<\mathrm{CO}_{2}<\mathrm{CO}\) (b) \(\mathrm{CO}_{2}<\mathrm{CO}_{3}^{2-}<\mathrm{CO}\) (c) \(\mathrm{CO}<\mathrm{CO}_{3}^{2-}<\mathrm{CO}_{2}\) (d) \(\mathrm{CO}<\mathrm{CO}_{2}<\mathrm{CO}_{3}^{2-}\)

Step-by-Step Solution

Answer

(d) \(\mathrm{CO}<\mathrm{CO}_{2}<\mathrm{CO}_{3}^{2-}\).

Step 1: Understanding Bond Length

The bond length between two atoms is determined by the bond order. A higher bond order usually means a shorter bond length, as more electron pairs are shared between the atoms, pulling them closer together.

Step 2: Analyzing CO

Carbon monoxide (CO) has a triple bond between the carbon and oxygen atoms. This triple bond indicates a bond order of 3, which correlates with a short bond length.

Step 3: Analyzing CO2

Carbon dioxide (CO2) features two double bonds between carbon and each oxygen atom. Each double bond has a bond order of 2. Thus, the \( \mathrm{C}-\mathrm{O} \) bond in CO2 is longer than that in CO.

Step 4: Analyzing CO3^2-

In the carbonate ion (CO3^2-), resonance causes the \( \mathrm{C}-\mathrm{O} \) bonds to be equal and behave as if each bond has a bond order of approximately 1.33 (a situation between a single and a double bond). This results in longer \( \mathrm{C}-\mathrm{O} \) bonds than in both CO and CO2.

Step 5: Determining Correct Bond Length Order

Based on bond orders, the increasing order of \( \mathrm{C}-\mathrm{O} \) bond length is determined. CO, having the shortest bond, is followed by CO2, and CO3^2- has the longest bond length due to its partial double bond character.

Key Concepts

Bond Order

Bond order is a crucial concept in understanding chemical bonding, as it reflects the number of chemical bonds between a pair of atoms. It is typically calculated based on the difference between the number of bonding and antibonding electrons divided by two. For instance, a single bond has a bond order of 1, a double bond has a bond order of 2, and a triple bond has a bond order of 3. The bond order can directly impact the bond length, which is the distance between two bonded atoms:

• A higher bond order usually results in a shorter bond length.
• This occurs because more electron pairs are involved in holding the atoms together more tightly.

Therefore, understanding bond order is pivotal for predicting how tightly two atoms are bound and how far they are from each other in a molecule.

Carbon Monoxide

Carbon monoxide (CO) is a simple and well-known molecule. It consists of one carbon atom and one oxygen atom linked by a triple bond, which is quite unusual compared to other simple diatomic molecules. The triple bond means carbon monoxide has a bond order of 3. This high bond order suggests that the bond is very short and strong because it involves:

• A sigma bond, which is a single bond that allows for head-on overlapping of orbitals.
• Two pi bonds, which add additional electron sharing, leading to increased attraction between the carbon and oxygen atoms.

This molecular structure explains the very short bond length characteristic of CO, making it extremely stable and less reactive than one might expect for a small molecule consisting only of two atoms.

Carbon Dioxide

Carbon dioxide (CO2) is a linear molecule where the carbon atom forms two double bonds, one with each oxygen atom. Each of these double bonds in CO2 is characterized by a bond order of 2. A double bond involves:

• One sigma bond, providing the primary connection between the carbon and oxygen.
• One pi bond, adding further stability and electron density between the atoms.

In comparison to CO's triple bond, the double bonds in CO2 result in a longer bond length, due to fewer shared electron clouds holding the carbon and oxygen atoms together. This indicates that while CO2 has significant stability as a molecule, its bond length is longer than that found in CO.

Carbonate Ion

The carbonate ion ( ext{CO}_3^{2-}) is an interesting example of a molecule where resonance plays a crucial role. It consists of one carbon atom bonded to three oxygen atoms with equal bond lengths due to resonance. Resonance in this molecule implies that the electrons are delocalized across the different oxygen bonds, creating:

• A blend of single and double bond characteristics.
• An effective bond order of approximately 1.33 per ext{C}- ext{O} bond.

As a result of this resonance, each ext{C}- ext{O} bond is neither a full single nor a full double bond, but instead, all are equal intermediate lengths. Thus, the ext{C}- ext{O} bonds are longer than the double bonds in CO2. This phenomenon illustrates how resonance can create unique situations where a bond length is influenced by the collective behavior of several atomic bonds.