Problem 70 - A Complete Resource Book in Chemistry for JEE Main

Question

Which of the following has the highest bond order? (a) \(\mathrm{N}_{2}\) (b) \(\mathrm{O}_{2}\) (c) \(\mathrm{He}_{2}\) (d) \(\mathrm{H}_{2}\)

Step-by-Step Solution

Answer

\(\mathrm{N}_2\) has the highest bond order: 3.

Step 1: Understanding Bond Order

Bond order is defined as the difference between the number of bonding and antibonding electrons, divided by two. It can be expressed with the formula: \( ext{Bond Order} = \frac{( ext{Number of bonding electrons} - ext{Number of antibonding electrons})}{2} \). A higher bond order indicates a stronger bond.

Step 2: Counting Electrons for Each Molecule

To find the bond order of each molecule, we need to first count the total number of electrons for each of them:- \( \text{N}_2 \) has 14 electrons.- \( \text{O}_2 \) has 16 electrons.- \( \text{He}_2 \) has 4 electrons.- \( \text{H}_2 \) has 2 electrons.

Step 3: Electron Configuration in Molecular Orbitals

Using molecular orbital theory, we fill the bonding and antibonding orbitals:- \( \text{N}_2 \): \(( ext{\sigma}_{1s})^2 ( ext{\sigma}_{1s}^*)^2 ( ext{\sigma}_{2s})^2 ( ext{\sigma}_{2s}^*)^2 ( ext{\pi}_{2p})^4 ( ext{\sigma}_{2p})^2 \)- \( \text{O}_2 \): \(( ext{\sigma}_{1s})^2 ( ext{\sigma}_{1s}^*)^2 ( ext{\sigma}_{2s})^2 ( ext{\sigma}_{2s}^*)^2 ( ext{\sigma}_{2p})^2 ( ext{\pi}_{2p})^4 ( ext{\pi}_{2p}^*)^2 \)- \( \text{He}_2 \): \(( ext{\sigma}_{1s})^2 ( ext{\sigma}_{1s}^*)^2 \)- \( \text{H}_2 \): \(( ext{\sigma}_{1s})^2 \)

Step 4: Calculating Bond Order

Now, calculate the bond order for each molecule:- \( \text{N}_2 \): Bond Order = \( \frac{10 - 4}{2} = 3 \)- \( \text{O}_2 \): Bond Order = \( \frac{10 - 6}{2} = 2 \)- \( \text{He}_2 \): Bond Order = \( \frac{2 - 2}{2} = 0 \)- \( \text{H}_2 \): Bond Order = \( \frac{2 - 0}{2} = 1 \)

Step 5: Comparing Bond Orders

Comparing the bond orders calculated:- \( \text{N}_2 \): 3- \( \text{O}_2 \): 2- \( \text{He}_2 \): 0- \( \text{H}_2 \): 1The highest bond order is for \( \text{N}_2 \), which is 3.

Key Concepts

Molecular Orbital Theory

Molecular Orbital Theory provides a more holistic way to understand how electrons are distributed in molecules compared to earlier models like Lewis structures. It allows us to predict the behaviors and properties of molecules more accurately.
This theory postulates that atomic orbitals combine to form molecular orbitals, which belong to the entire molecule and not just to a single atom. Molecular orbitals are classified into two main types:

• Bonding orbitals, which result from the constructive interference of atomic orbitals and lead to an increase in electron density between the nuclei. These orbitals typically have lower energy and stabilize the molecule.
• Antibonding orbitals, which arise from the destructive interference. They are usually higher in energy and can destabilize a molecule if they are occupied.

When atoms are close together, their atomic orbitals overlap to form these molecular orbitals. To find a molecular orbital diagram of a diatomic molecule like N2 or O2, we fill the lower-energy bonding orbitals first following the Aufbau principle, and check to see if higher-energy antibonding orbitals are filled. This filling pattern helps determine the overall stability and bond order of the molecule.

Electron Configuration

Electron configuration is key to understanding how electrons fill different energy levels and orbitals in a molecule. In molecular orbital theory, electrons fill the molecular orbitals in a specific sequence, starting with the lowest energy orbitals first. This distribution is dictated by Pauli's exclusion principle, which states that each orbital can hold a maximum of two electrons with opposite spins. As electrons fill in these molecular orbitals, a pattern of the overall electronic arrangement emerges. For diatomic molecules like N2 and O2, this often involves filling s and p orbitals, with a specific focus on bonding and antibonding interactions. Many concepts from atomic electron configuration carry over to molecular orbital theory, including Hund's Rule: electrons will occupy degenerate orbitals singly and with parallel spins before pairing up. Understanding the electron configuration in molecular orbital terms allows chemists to calculate important properties like bond order, magnetism, and reactivity.

Chemical Bonding

Chemical bonding occurs due to interactions that allow atoms to reach more stable electron configurations. In molecular orbital theory, chemical bonding is explained via the overlap of atomic orbitals to form molecular orbitals, where the strength and type of the bond are linked to the distance between nuclei and the number of shared electrons. Different types of bonding include:

• Covalent Bonds: These involve the sharing of electron pairs between atoms that results in the formation of single, double, or triple bonds. The number of shared electron pairs determines the bond order, reflecting the bond’s strength.
• Ionic Bonds: Although not directly related to molecular orbitals, ionic bonds are formed when electrons are transferred from one atom to another, often resulting in substances like salts.
• Metallic Bonds: In metals, a "sea of electrons" flows freely, providing metals their distinct properties like conductivity.

Bond order is a particularly useful concept derived from molecular orbital theory, used to predict the strength and stability of a bond. A higher bond order usually indicates a stronger bond. By comparing the number of electrons in bonding and antibonding orbitals, chemists can determine this ordering. For instance, the bond order of N2 is higher than that of O2, which corresponds to its greater bond strength.