Problem 92 - Chemistry: An Atoms-Focused Approach

Question

Rank the following substances in order of increasing carbon-oxygen bond energy: \(\mathrm{CO}, \mathrm{CO}_{2},\) and \(\mathrm{CO}_{3}^{2-}.\)

Step-by-Step Solution

Answer

Question: Rank the following substances in order of increasing carbon-oxygen bond energy: carbon monoxide (CO), carbon dioxide (CO2), and the carbonate ion (CO3^2-). Answer: The correct order of substances in increasing carbon-oxygen bond energy is: CO3^2- < CO < CO2.

Step 1: Understand the Structure of Each Compound

CO is a linear molecule with one carbon atom double bonded to the oxygen atom. CO2 is also a linear molecule, in which the carbon atom is double bonded to two oxygen atoms. The CO3^2- ion, called the carbonate ion, has a trigonal planar geometry with a central carbon atom. The carbon atom is single bonded to two oxygen atoms and double bonded to the remaining oxygen atom. Due to resonance, the true bond order is 1.333, representing an average of the single and double bonds.

Step 2: Determine the Carbon-Oxygen Bond Energies

In general, bond energy increases with bond order (the number of electron pairs shared between atoms). In CO, the carbon-oxygen bond is a double bond with a bond order of 2. In CO2, two double bonds with bond order 2, and in CO3^2-, the average bond order is 1.333.

Step 3: Rank the Compounds

Based on their bond orders, we can now rank the compounds in order of increasing carbon-oxygen bond energy as follows: 1. CO3^2- ion (average bond order 1.333) 2. CO molecule (bond order 2) 3. CO2 molecule (bond order 2) Note that CO and CO2 both have a bond order of 2. However, the electronegativity difference between carbon and oxygen is greater in CO2 as compared to CO, which makes the double bond in CO2 stronger. Thus, CO2 has a higher bond energy than CO.

Step 4: Conclusion

The substances can be ranked in order of increasing carbon-oxygen bond energy as: CO3^2- < CO < CO2.

Key Concepts

Bond Order

The concept of bond order helps us understand the stability and strength of a chemical bond. Bond order is defined as the number of chemical bonds between a pair of atoms. This typically refers to the number of pairs of electrons shared between the atoms.
For example, in a single bond, one pair of electrons is shared, giving a bond order of 1. In a double bond, two pairs are shared, resulting in a bond order of 2.

Bond energy is directly related to bond order. A higher bond order usually implies a stronger bond, as more electron pairs are shared between the involved atoms. Therefore, compounds with high bond orders tend to have higher bond energies. This helps us predict which bonds will require more energy to break, based on their bond order.

• Single bond: Bond order 1
• Double bond: Bond order 2
• Triple bond: Bond order 3

Each bond type has its specific amount of shared electron pairs, which determines its bond order and thereby its bond energy.

Electronegativity

Electronegativity is a measure of how strongly an atom can attract and hold onto electrons within a bond. The higher the electronegativity, the stronger an atom attracts electrons towards itself.
Carbon and oxygen have different electronegativities, with oxygen being more electronegative. This difference is crucial in determining bond characteristics.

In the context of the CO and CO2 bonds:

• CO has a significant electronegativity difference, but not as much as CO2.
• In CO2, oxygen atoms pull electrons with a greater force than in CO, due to its linear symmetric structure increasing this effect.

Though both CO and CO2 have a bond order of 2, the more significant electronegativity difference in CO2 results in a stronger bond due to increased pulling of shared electrons. This translates to a higher bond energy in CO2 compared to CO.

Molecular Geometry

Molecular geometry refers to the three-dimensional arrangement of atoms in a molecule. It dictates how molecules form bonds and their resulting properties, including bond energy.

The geometry of a molecule affects how it interacts with other molecules and its overall stability.
Here’s a breakdown of the geometries mentioned:

• CO: Linear geometry. A simple double bond between carbon and oxygen.
• CO2: Also linear, but with two double bonds on either side of a central carbon, leading to symmetry that complements its high bond energy.
• CO$_3^{2-}$: Trigonal planar geometry. The carbonate ion has resonance, meaning it doesn't have static single or double bonds. Instead, it has bonds that average out to about 1.333, causing overall lower bond energy compared to CO and CO2.

Understanding molecular geometry is essential for predicting molecule behavior and reactivity, as it directly influences the chemical bond energies and the compound's stability.