Problem 148 - A Complete Resource Book in Chemistry for JEE Main

Question

Which of the pairs have identical values of bond order? (a) \(\mathrm{F}_{2}\) and \(\mathrm{Ne}_{2}\) (b) \(\mathrm{N}_{2}^{+}\)and \(\mathrm{O}_{2}^{+}\) (c) \(\mathrm{O}_{2}^{2-}\) and \(\mathrm{B}_{2}\) (d) \(\mathrm{C}_{2}\) and \(\mathrm{N}_{2}\)

Step-by-Step Solution

Answer

Pairs (b) and (c) have identical bond orders: \(\mathrm{N}_2^{+}\) and \(\mathrm{O}_2^{+}\); \(\mathrm{O}_2^{2-}\) and \(\mathrm{B}_2\).

Step 1: Understand Bond Order

Bond order is a measure of the number of chemical bonds between a pair of atoms. It's typically calculated as \(( ext{number of bonding electrons} - \text{number of antibonding electrons})/2\).

Step 2: Bond Order of \(\mathrm{F}_2\) and \(\mathrm{Ne}_2\)

Calculate for \(\mathrm{F}_2\): Both bonding and antibonding molecular orbitals are filled, with \(10\) bonding and \(8\) antibonding electrons, so bond order is \((10-8)/2 = 1\).\(\mathrm{Ne}_2\) has fully filled orbitals, \(10\) bonding and \(10\) antibonding electrons, yielding a bond order of \((10-10)/2 = 0\).

Step 3: Bond Order of \(\mathrm{N}_2^+\) and \(\mathrm{O}_2^+\)

For \(\mathrm{N}_2^+\): Remove one electron from \(\mathrm{N}_2\), thus it has \(9\) bonding and \(4\) antibonding electrons, giving a bond order of \((9-4)/2 = 2.5\).\(\mathrm{O}_2^+\) removes one electron from \(\mathrm{O}_2\), leaving \(10\) bonding and \(5\) antibonding electrons, bond order is \((10-5)/2 = 2.5\). They are identical.

Step 4: Bond Order of \(\mathrm{O}_2^{2-}\) and \(\mathrm{B}_2\)

For \(\mathrm{O}_2^{2-}\): Add two electrons to \(\mathrm{O}_2\), which gives \(10\) bonding and \(8\) antibonding electrons, bond order is \((10-8)/2 = 1\).\(\mathrm{B}_2\) has \(6\) bonding and \(4\) antibonding electrons, thus bond order is \((6-4)/2 = 1\). They are identical.

Step 5: Bond Order of \(\mathrm{C}_2\) and \(\mathrm{N}_2\)

For \(\mathrm{C}_2\): It has \(8\) bonding and \(4\) antibonding electrons, so bond order is \((8-4)/2 = 2\).\(\mathrm{N}_2\) has \(10\) bonding and \(4\) antibonding electrons, resulting in a bond order of \((10-4)/2 = 3\). They are not identical.

Key Concepts

Molecular Orbitals

Molecular orbitals are at the heart of understanding chemical bonding. They form when atomic orbitals overlap as atoms approach each other. Unlike atomic orbitals, which are associated with a single atom, molecular orbitals cover the whole molecule. Think of them like clouds where electrons reside around pairs of atoms.

Some key points to remember about molecular orbitals:

• They are divided into bonding and antibonding orbitals.
• Bonding orbitals are lower in energy and increase stability when filled.
• Antibonding orbitals are higher in energy and decrease stability when populated.

This is why when calculating bond order, the number of electrons in bonding and antibonding orbitals are considered. Molecular orbitals help us understand whether a bond will form, and the bond order tells us the strength of that bond.

Bonding Electrons

Bonding electrons play a crucial role in the formation of a chemical bond. These electrons reside in bonding molecular orbitals, which form when atomic orbitals constructively interfere. These orbitals are at a lower energy level.

Characteristics of bonding electrons include:

• Lying between the nuclei of bonding atoms, thus minimizing repulsion and enhancing attraction.
• Contributing to the stability and strength of a bond.
• Influencing molecular shape and properties.

In a solid molecular structure, the more electrons in bonding orbitals, the higher the bond order, translating into a stronger bond.

Antibonding Electrons

Antibonding electrons occupy molecular orbitals that form when atomic orbitals overlap in a way that is not conducive to bonding. These orbitals are marked with an asterisk (e.g., \( ext{σ}^*\), \( ext{π}^*\)) and are higher in energy.

Key features of antibonding electrons:

• They exist outside the region between the bonded nuclei.
• They can counteract the stability provided by bonding electrons.
• Filling these orbitals can weaken or even prevent bond formation.

In bond order calculations, antibonding electrons are subtracted from bonding electrons, showing that their presence reduces bond strength.

Chemical Bonds

Chemical bonds are the connections that hold atoms together in a molecule. These bonds arise from the sharing or transferring of electrons, allowing atoms to attain more stable electron configurations.

Types of chemical bonds include:

• Covalent bonds, where electrons are shared between atoms.
• Ionic bonds, where electrons are transferred, creating charged ions.
• Metallic bonds, involving a 'sea' of electrons that bind metal atoms together.

The bond order concept helps us quantify these bonds by showing the number of electron pairs shared between atoms. A higher bond order usually signifies a stronger chemical bond. Through these interactions, chemical bonds dictate the structures and behavior of molecules.