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

Short answer

The correct order is (d) CO < CO2 < CO3^{2-}.

Step-by-step solution

Analyze Bond Order

The bond order is the number of chemical bonds between a pair of atoms. Higher bond order generally corresponds to a shorter bond length. In this exercise, we need to determine the bond order of each compound to establish the order of bond lengths.

Determine Bond Order of CO

For carbon monoxide (CO), there is a triple bond between carbon and oxygen. Thus, the bond order of CO is 3.

Determine Bond Order of CO2

In carbon dioxide (CO2), each carbon-oxygen bond is a double bond due to resonance, so the bond order is 2.

Determine Bond Order of CO3^{2-}

For the carbonate ion (CO3^{2-}), resonance leads to an average bond order of 1.33 (due to three resonance structures where one C-O bond is a double bond and two C-O bonds are single bonds).

Order Bonds by Increasing Length

Since bond length inversely correlates with bond order, CO with bond order 3 will have the shortest bond length, CO2 with bond order 2 will have a longer bond length, and CO3^{2-} with bond order 1.33 will have the longest bond length. Thus, the order of increasing bond length is: CO, CO2, CO3^{2-}.

Choose Correct Option

According to the analysis, the correct order is: CO < CO2 < CO3^{2-}. So, the correct answer is (d).

Key concepts

Bond Order

In chemistry, bond order refers to the number of chemical bonds between a pair of atoms. The higher the bond order, the stronger the bond, which results in a shorter bond length.
For example:

• A single bond has a bond order of 1.
• A double bond has a bond order of 2.
• A triple bond has a bond order of 3.

When assessing molecules such as CO, CO₂, and CO₃²⁻, understanding their bond orders helps us predict the length of their bonds. Higher bond orders correlate with shorter bond lengths. This is why CO, with a bond order of 3, has a shorter bond length than CO₂, which has a bond order of 2, and much shorter than CO₃²⁻, which has an average bond order of 1.33.

Resonance Structures

Resonance structures are a way of representing a molecule where two or more valid Lewis structures can exist. These structures help to describe delocalized electrons within the molecule, which can't be captured by a single Lewis structure alone.
In the case of CO₃²⁻, there are three resonance structures. One has a C-O double bond, while the other two have single C-O bonds. The resonance stabilizes the molecule, distributing the charge more evenly.
The concept of resonance is crucial because it affects the bond order. In CO₃²⁻, the presence of resonance means that the actual bond order is the average of the bonds present in predominant structures. This results in an average bond order of 1.33, showing how resonance lowers the bond order compared to having only double bonds.

C-O Bond Length

The bond length between carbon (C) and oxygen (O) varies depending on the bond order. Generally, the higher the bond order, the shorter the bond length:

• In carbon monoxide (CO), the C-O bond is a triple bond, resulting in the shortest bond length among the three species discussed.
• In carbon dioxide (CO₂), the C-O bonds are double, making them longer than the triple bond in CO, but shorter than the average C-O bond length in a carbonate ion (CO₃²⁻).
• The carbonate ion (CO₃²⁻) has resonance structures resulting in an average bond order of 1.33, creating the longest bond length in our comparison.

Understanding these variations in C-O bond length helps chemists predict molecular behavior and reactivity.

Carbonates

Carbonates are a group of inorganic compounds containing the carbonate ion (CO₃²⁻). They play a vital role in many geological and biological processes due to their stability and reactivity.
The carbonate ion consists of one carbon atom covalently bonded to three oxygen atoms. The presence of resonance in carbonate ions allows for more accurate predictions of their chemical behavior. The resonance makes the bonds partially double and stabilizes the ion.
This stabilization is a hallmark of carbonates, affecting their bond lengths and bond orders, as noted in CO₃²⁻. Understanding the behavior of carbonates is essential in fields ranging from environmental science to pharmaceuticals, as they are involved in buffering the pH of natural waters and are integral components of Earth's crust.