Question

Predict the ordering of the \(\mathrm{C}-\mathrm{O}\) bond lengths in \(\mathrm{CO}, \mathrm{CO}_{2}\), and \(\mathrm{CO}_{3}^{2-}\).

Short answer

The predicted ordering of the C-O bond lengths in CO, CO2, and CO3^(2-) is: CO (bond order = 3) < CO2 (bond order = 2) < CO3^(2-) (bond order = 4/3). This is based on the molecular structures, resonance structures, and bond orders of each molecule or ion. Higher bond orders correlate with shorter bond lengths.

Step-by-step solution

Determining the Molecular Structure

To understand the bond lengths of each molecule, we need to know the structures first: 1. CO (Carbon Monoxide) - CO is a diatomic molecule where a carbon atom is triple-bonded to an oxygen atom. 2. CO2 (Carbon Dioxide) - CO2 is a linear molecule, where a carbon atom is double-bonded to two oxygen atoms on either side. 3. CO3^(2-) (Carbonate ion) - CO3^(2-) is a planar molecule in which a central carbon atom is single-bonded to three oxygen atoms, which are positioned at the vertices of an equilateral triangle.

Resonance Structures

In order to analyze and compare the bonds in these molecules, let's look for resonance structures: 1. CO - There is only one resonance structure for CO, with a triple bond between C and O atoms. 2. CO2 - There is only one resonance structure for CO2, with a double bond between the carbon atom and each oxygen atom. 3. CO3^(2-) - The carbonate ion has three equivalent resonance structures, where each of the three single bonds between the central carbon atom and the oxygen atoms can be replaced by one double bond in each resonance structure.

Bond Order

Now let's determine the bond order for the C-O bonds in each molecule/ion: 1. CO - The bond order in CO is 3, due to the triple bond between the carbon and oxygen atoms. 2. CO2 - The bond order in CO2 is 2, because of the double bond between the carbon atom and each oxygen atom. 3. CO3^(2-) - The bond order in the carbonate ion is 4/3 (4 bonds distributed over 3 C-O bonds). This value is obtained by considering the presence of one double bond and two single bonds in the resonance structures.

Predict the Ordering of the C-O Bond Lengths

Finally, we can predict the ordering of the C-O bond lengths. Generally, higher bond orders correlate with shorter bond lengths. Therefore, we can list the C-O bond lengths in order from shortest to longest: 1. CO (Triple bond, bond order = 3) 2. CO2 (Double bond, bond order = 2) 3. CO3^(2-) (Average of single and double bonds, bond order = 4/3) Thus, the predicted ordering of the C-O bond lengths is: CO < CO2 < CO3^(2-).

Key concepts

Molecular Structure

To accurately predict bond lengths, understanding the molecular structure of each compound is key. Let's take a closer look at the three molecules in question:

• CO (Carbon Monoxide): This is a simple diatomic molecule composed of just one carbon and one oxygen atom. These atoms are joined by a triple bond, making the molecule linear.
• CO2 (Carbon Dioxide): This molecule consists of one carbon atom double-bonded to two oxygen atoms on either side, forming a straight, linear structure. This layout affects how the electrons are shared between atoms, influencing the bond length.
• CO3^2- (Carbonate Ion): Here, the central carbon atom is surrounded by three oxygen atoms, forming a planar triangular shape. In this arrangement, the carbon shares single bonds with each oxygen, but due to resonance, one of these can occasionally manifest as a double bond. This delocalization across the structure impacts the bond lengths as well.

By understanding these structures, we can already anticipate differences in the bond lengths due to the quantity and type of bonds between carbon and oxygen.

Resonance Structures

Resonance is a concept that helps us understand the distribution of electrons within a molecule. It plays a crucial role in determining the bond characteristics, such as bond length.

• CO (Carbon Monoxide): There is only one resonance structure available here, characterized by a triple bond between carbon and oxygen. This lack of resonance means there's one dominant electron configuration affecting the bond length.
• CO2 (Carbon Dioxide): Similar to CO, there is only one primary resonance structure for CO2, with double bonds between the carbon and each oxygen atom. The lack of resonance options keeps the bond length uniform.
• CO3^2- (Carbonate Ion): Unlike the previous two, the carbonate ion presents three equivalent resonance structures. In these, the placement of a double bond shifts between the various oxygen atoms. This movement of electrons creates an average effect in bond characteristics called resonance stabilization, influencing average bond lengths.

Resonance structures allow bonds to share characteristics, making lengths uniform across similar connections, although averaged.

Bond Order

Bond order is directly connected to the strength and length of the bond between atoms. When discussing C-O bonds, understanding bond order helps in predicting bond lengths:

• CO (Carbon Monoxide): This molecule boasts a bond order of 3 due to its triple bond, indicating strong and short bonds.
• CO2 (Carbon Dioxide): Here, the bond order is 2, corresponding to the double bonds present. These bonds are shorter and stronger than single bonds but longer than triple bonds.
• CO3^2- (Carbonate Ion): The carbonate ion's bond order comes out to be approximately 4/3. This fractional bond order results from the averaging effect of resonance, where some C-O links feature double bond characteristics periodically.

The higher the bond order, the stronger and shorter the bond. Therefore, when comparing molecules like CO, CO2, and CO3^2-, you can predict C-O bond lengths by examining their bond orders: shortest in CO, followed by CO2, and longest in CO3^2-. This understanding connects structural concepts to measurable physical properties.