Problem 215 - A Complete Resource Book in Chemistry for JEE Main

Question

When one of the following molecules is expected to exhibit diamagnetic behaviour? (a) \(\mathrm{O}_{2}\) (b) \(\mathrm{S}_{2}\) (c) \(\mathrm{C}_{2}\) (d) \(\mathrm{N}_{2}\)

Step-by-Step Solution

Answer

Both \( \mathrm{C}_2 \) and \( \mathrm{N}_2 \) exhibit diamagnetic behavior.

Step 1: Understanding Diamagnetism

Diamagnetic substances have all their electrons paired in their molecular orbital configuration. This means they do not have any net magnetic moment, i.e., they are not attracted to a magnetic field. Our task is to determine which of the given molecules have all electrons paired.

Step 2: Analyzing Electron Configuration of O2

The molecular orbital configuration for \( \mathrm{O}_2 \) is \[ \mathrm{(\sigma_{1s})^2 (\sigma_{1s}^*)^2 (\sigma_{2s})^2 (\sigma_{2s}^*)^2 (\sigma_{2p_z})^2 (\pi_{2p_x})^2 (\pi_{2p_y})^2 (\pi_{2p_x}^*)^1 (\pi_{2p_y}^*)^1} \] which shows that \( \mathrm{O}_2 \) has unpaired electrons in the \( \pi^* \) orbitals, making it paramagnetic.

Step 3: Analyzing Electron Configuration of S2

For \( \mathrm{S}_2 \), the electronic configuration is similar to \( \mathrm{O}_2 \) with \[ \mathrm{(\sigma_{1s})^2 (\sigma_{1s}^*)^2 (\sigma_{2s})^2 (\sigma_{2s}^*)^2 (\sigma_{2p_z})^2 (\pi_{2p_x})^2 (\pi_{2p_y})^2 (\pi_{2p_x}^*)^1 (\pi_{2p_y}^*)^1} \] indicating also presence of unpaired electrons, making \( \mathrm{S}_2 \) paramagnetic.

Step 4: Analyzing Electron Configuration of C2

The electronic configuration for \( \mathrm{C}_2 \) is \[ \mathrm{(\sigma_{1s})^2 (\sigma_{1s}^*)^2 (\sigma_{2s})^2 (\sigma_{2s}^*)^2 (\pi_{2p_x})^2 (\pi_{2p_y})^2} \] which reveals that all electrons in \( \mathrm{C}_2 \) are paired, making it diamagnetic.

Step 5: Analyzing Electron Configuration of N2

In \( \mathrm{N}_2 \), the molecular orbital configuration is \[ \mathrm{(\sigma_{1s})^2 (\sigma_{1s}^*)^2 (\sigma_{2s})^2 (\sigma_{2s}^*)^2 (\pi_{2p_x})^2 (\pi_{2p_y})^2 (\sigma_{2p_z})^2} \] which indicates all electrons are paired, meaning \( \mathrm{N}_2 \) is diamagnetic.

Step 6: Final Decision

Comparing all the molecules, \( \mathrm{C}_2 \) and \( \mathrm{N}_2 \) both have all paired electrons resulting in diamagnetic behavior. Hence, among the options, both \( \mathrm{C}_2 \) and \( \mathrm{N}_2 \) are diamagnetic.

Key Concepts

Molecular Orbital Theory

Molecular Orbital Theory (MOT) is a fundamental principle that explains how atomic orbitals combine to form molecular orbitals. This concept is crucial for understanding how electrons are arranged in a molecule and, in turn, determines the molecule's magnetic properties. In this theory:

• Atomic orbitals from two or more atoms overlap to create molecular orbitals, which can either be bonding or antibonding.
• Bonding molecular orbitals increase electron density between atomic nuclei, stabilizing the molecule.
• Antibonding molecular orbitals have electron density that tends to cancel out between atoms, potentially destabilizing the molecule.

The molecular orbitals are filled according to the Aufbau principle, which states that electrons fill lower energy orbitals before higher energy orbitals. Pairing of electrons within these orbitals follows Hund’s rule and the Pauli exclusion principle, ensuring that each orbital is filled before electrons start pairing up.
Molecular Orbital Theory is applied to determine a molecule's magnetism based on the configuration of these molecular orbitals. If all electrons are paired, the molecule is diamagnetic. However, the presence of one or more unpaired electrons makes a molecule paramagnetic.

Electron Configuration

Electron configuration in molecules extends the concept from individual atoms to molecular systems, showing how electrons are distributed in orbitals that belong to the entire molecule. For diatomic molecules like \( \mathrm{O}_2 \), \( \mathrm{S}_2 \), \( \mathrm{C}_2 \), and \( \mathrm{N}_2 \), molecular orbital diagrams help in visualizing electron distribution.
Each filling pattern comes from combining atomic orbitals:

• \(\sigma\) orbitals (sigma): These occur when orbitals overlap along the axis connecting the two nuclei.
• \(\pi\) orbitals (pi): These result from side-to-side overlap.
• Bonding orbitals \((\sigma, \pi)\): Formed from constructive interference, they are lower in energy.
• Antibonding orbitals \((\sigma^*, \pi^*)\): Formed from destructive interference, they are higher in energy.

The electrons fill into these orbitals according to the increasing energy level, obeying the same rules as atomic orbitals. Electrons fill lower energy orbitals first, pair in these energy levels, and will only occupy higher orbitals if necessary. For instance, in \( \mathrm{O}_2 \) and \( \mathrm{S}_2 \), unpaired electrons in high-energy \(\pi^*\) orbitals account for their paramagnetic nature. While for \( \mathrm{C}_2 \) and \( \mathrm{N}_2 \), all electrons are paired, making them diamagnetic.

Paramagnetism

Paramagnetism refers to a form of magnetism that occurs due to the presence of unpaired electrons in a substance. These unpaired electrons have magnetic moments that align parallel to an external magnetic field, causing an attraction.
For molecules with unpaired electrons in their molecular orbitals, such as \( \mathrm{O}_2 \), the magnetic moments do not cancel each other out. Because of this:

• The molecule exhibits a net magnetic moment.
• The magnetic moments align in an external magnetic field, enhancing the magnetic interaction.
• This makes the substance paramagnetic, meaning it is attracted to magnetic fields.

In contrast, when all electrons are paired, as is the case in diamagnetic substances, there are no unpaired electron magnetic moments available to align with a magnetic field, leading the molecule to be slightly repelled by the field. Understanding the number of unpaired electrons in a molecule is crucial because it determines whether the molecule is diamagnetic or paramagnetic, hence influencing its magnetic properties.