Problem 54 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

Write the M.O. electron distribution of \(\mathrm{O}_{2}\). Specify its bond order and magnetic property.

Step-by-Step Solution

Answer

The bond order is 2, and O_2 is paramagnetic with two unpaired electrons.

Step 1: Determine Molecular Orbitals for O2

Molecular Oxygen ( O_2 ) consists of two oxygen atoms. Each oxygen atom in its ground state configuration has the electron configuration 1s^2 2s^2 2p^4 . For the diatomic molecule O_2 , these atomic orbitals combine to form molecular orbitals (MOs).

Step 2: Write Electron Configuration Based on MO Energy Levels

For O_2 , the energy order of molecular orbitals is σ_{1s}, σ^*_{1s}, σ_{2s}, σ^*_{2s}, σ_{2p_z}, π_{2p_x} = π_{2p_y}, π^*_{2p_x} = π^*_{2p_y}, σ^*_{2p_z} . Add the 16 valence electrons from two oxygen atoms into these orbitals to get: σ_{2s}^2 σ^*_{2s}^2 σ_{2p_z}^2 π_{2p_x}^2 π_{2p_y}^2 π^*_{2p_x}^1 π^*_{2p_y}^1 .

Step 3: Calculate Bond Order

The bond order is calculated as: \((N_{b} - N_{a}) / 2\) where N_b is the number of electrons in bonding molecular orbitals and N_a is the number of electrons in antibonding orbitals. Here, N_b = 10 and N_a = 6, so the bond order is \((10 - 6) / 2 = 2\).

Step 4: Determine Magnetic Properties

An important property to analyze is if the molecule is paramagnetic or diamagnetic. O_2 has two unpaired electrons in the π^*_{2p_x} and π^*_{2p_y} orbitals, which makes it paramagnetic.

Key Concepts

Bond Order

Bond order is a concept that helps us understand the strength of a bond between two atoms. In simple terms, it indicates how many bonds exist between a pair of atoms. The higher the bond order, the stronger and shorter the bonds. For diatomic molecules, the bond order can be found using molecular orbital (MO) theory by comparing the number of bonding and antibonding electrons.
To calculate bond order, use the formula:

• \( ext{Bond Order} = \frac{N_b - N_a}{2} \)

where \( N_b \) is the number of electrons in bonding orbitals and \( N_a \) is the number of electrons in antibonding orbitals.
In the case of \( \mathrm{O}_{2} \), we know from the molecular orbital configuration that \( N_b = 10 \) and \( N_a = 6 \). Substituting these values into the formula gives:

• \( \text{Bond Order} = \frac{10 - 6}{2} = 2 \)

This shows that molecular oxygen forms a double bond, which is relatively strong and stable.

Electron Configuration

Electron configuration is a fundamental concept, which helps us understand how electrons are distributed within an atom or molecule. For \( \mathrm{O}_{2} \), the distribution of electrons can be represented using molecular orbitals. These orbitals form when atomic orbitals overlap as the atoms in \( \mathrm{O}_{2} \) bond together.
Let's outline the order of molecular orbitals in \( \mathrm{O}_{2} \):

• \( \sigma_{1s}, \sigma^*_{1s}, \sigma_{2s}, \sigma^*_{2s}, \sigma_{2p_z}, \pi_{2p_x} = \pi_{2p_y}, \pi^*_{2p_x} = \pi^*_{2p_y}, \sigma^*_{2p_z} \)

This order shows the relative energy levels of each molecular orbital.
For \( \mathrm{O}_{2} \), 16 valence electrons are distributed into these orbitals as follows:

• \( \sigma_{2s}^2 \sigma^*_{2s}^2 \sigma_{2p_z}^2 \pi_{2p_x}^2 \pi_{2p_y}^2 \pi^*_{2p_x}^1 \pi^*_{2p_y}^1 \)

This configuration shows that all low-energy orbitals are filled first in accordance with the Aufbau principle, with the remaining electrons occupying higher-energy antibonding orbitals.

Paramagnetism

Paramagnetism explains the magnetic properties of materials due to unpaired electrons. Molecules like \( \mathrm{O}_{2} \) demonstrate paramagnetism because they have unpaired electrons which contribute to magnetic properties.
The presence of these unpaired electrons in \( \mathrm{O}_{2} \) is revealed by looking at its molecular orbital configuration:

• \( \pi^*_{2p_x}^1 \) and \( \pi^*_{2p_y}^1 \) each contain one unpaired electron.

This shows that there are two unpaired electrons in the molecule, making \( \mathrm{O}_{2} \) paramagnetic. It's important because it allows \( \mathrm{O}_{2} \) to be attracted to magnetic fields.
Unlike diamagnetic substances, which are repelled by a magnetic field due to all electrons being paired, paramagnetic substances like \( \mathrm{O}_{2} \) align with magnetic fields due to their unpaired electrons. This magnetic attraction in \( \mathrm{O}_{2} \) confirms its paramagnetic nature.