Problem 115 - A Complete Resource Book in Chemistry for JEE Main

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

Step-by-Step Solution

Answer

The correct order of increasing \( \mathrm{C}-\mathrm{O} \) bond length is option (c): \(\mathrm{CO}<\mathrm{CO}_{2}<\mathrm{CO}_{3}^{2-}\).

Step 1: Understand Bond Orders

The bond length of C-O bonds is related to their bond order. Higher bond order results in shorter bond lengths. We will determine the bond order for each molecule: CO, \(CO_2\) and \(CO_3^{2-}\).

Step 2: Determine Bond Order of CO

In CO, there is a triple bond between the carbon and oxygen atoms. This results in a bond order of 3.

Step 3: Determine Bond Order of CO2

In \(CO_2\), each carbon forms two double bonds with the oxygen atoms, resulting in a bond order of 2.

Step 4: Determine Bond Order of CO3^{2-}

The carbonate ion \(CO_3^{2-}\) has resonance structures, resulting in a bond order of 1.33 as the doubly bonded oxygen is shared among the three oxygens.

Step 5: Arrange Bond Orders

Arrange the molecules based on the increasing bond length: Higher bond order means shorter bond length. So the order of C-O bond lengths from shortest to longest is: CO (bond order 3), CO2 (bond order 2), and CO3^{2-} (bond order 1.33).

Step 6: Identify Correct Option

The correct order in terms of increasing bond length is \(CO < CO_2 < CO_3^{2-}\). This corresponds with option (c).

Key Concepts

C-O Bond

The C-O bond refers to the chemical bond between a carbon atom and an oxygen atom. It is a fundamental part of various important molecules such as carbon monoxide (CO), carbon dioxide (\(CO_2\)), and carbonate ion (\(CO_3^{2-}\)). Understanding the nature of these bonds is crucial for determining molecular properties such as bond length. Bond length is the distance between the nuclei of two bonded atoms. In general, the bond length of a molecule is influenced by the bond order, which is the number of chemical bonds present between a pair of atoms.

• Molecules can have single, double, or triple bonds.
• Higher bond orders usually result in shorter bond lengths.

Thus, as seen in CO, which has a triple bond, the bond length will be shorter compared to that of CO2, which contains double bonds.

Bond Order

Bond order is a critical concept in understanding bond length and stability. It is defined as the number of chemical bonds between a pair of atoms. For example, 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 helps determine various attributes of a molecule, including its bond length and strength. Generally, the higher the bond order, the shorter the bond length and the greater the bond strength.

• In carbon monoxide (\(CO\)), the C-O bond has a bond order of 3, indicating a triple bond.
• In carbon dioxide (\(CO_2\)), it features two double bonds, giving each C-O bond a bond order of 2.
• In the carbonate ion (\(CO_3^{2-}\)), the situation is more complex due to resonance, resulting in a calculated bond order of approximately 1.33.

Resonance Structures

Resonance structures are a way of describing delocalized electrons within certain molecules where the bonding cannot be expressed by a single Lewis structure. In the \(CO_3^{2-}\) (carbonate ion), resonance is a key factor.

• This ion can be represented by several structures with equivalent energy.
  
• These structures differ only in the position of electrons, not in the position of nuclei.
• Resonance structures imply that electrons are delocalized, meaning the actual bonding is a hybrid of all possible structures.

For carbonate, this resonance results in an average bond order between carbon and oxygen that is lower than a double bond but higher than a single bond. This results in a bond order of 1.33, contributing to a bond length that is intermediate between a typical single and double bond.

Triple Bond

A triple bond is a type of chemical bond where three pairs of electrons are shared between two atoms, making it one of the strongest types of covalent bonds. In the molecule carbon monoxide (\(CO\)), the C-O triple bond shows a bond order of 3.

• This high bond order means that the bond is particularly strong and short.
• Triple bonds are shorter and stronger than both single and double bonds.
• The presence of a triple bond implies a high degree of overlap between the orbitals of the bonded atoms.

Due to these properties, CO has the shortest C-O bond length among the compared molecules, resulting from this relatively strong triple bond.

Double Bond

Double bonds occur when two pairs of electrons are shared between two atoms. These types of bonds are common in organic molecules like carbon dioxide (\(CO_2\)).

• The double bond in \(CO_2\) consists of one sigma bond and one pi bond.
• Double bonds are stronger and shorter than single bonds but longer and weaker than triple bonds.
• In \(CO_2\), each C-O bond has a bond order of 2, which sets a moderate strength and intermediate bond length.

Thus, the C-O bond in CO2 is longer than in carbon monoxide but shorter than in the carbonate ion due to its double bond nature.