Problem 21 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

Which one of the following molecules is expected to exhibit diamagnetic behaviour? [Main 2013] (a) \(\mathrm{C}_{2}\) (b) \(\mathrm{N}_{2}\) (c) \(\mathrm{O}_{2}\) (d) \(\mathrm{S}_{2}\)

Step-by-Step Solution

Answer

(b) \(\mathrm{N}_2\) is diamagnetic.

Step 1: Understanding Diamagnetic and Paramagnetic

Diamagnetic substances are those where all electrons are paired, resulting in no net magnetic moment. In contrast, paramagnetic substances have one or more unpaired electrons, which cause a net magnetic moment.

Step 2: Determine Electron Configuration for Given Molecules

The first step is to write the electronic configuration for each diatomic molecule. This involves understanding the molecular orbital theory: - \(\mathrm{C}_2\): \(\sigma(1s)^2 \sigma^*(1s)^2 \sigma(2s)^2 \sigma^*(2s)^2 \pi(2p_x)^2 \pi(2p_y)^2\)- \(\mathrm{N}_2\): \(\sigma(1s)^2 \sigma^*(1s)^2 \sigma(2s)^2 \sigma^*(2s)^2 \pi(2p_x)^2 \pi(2p_y)^2 \sigma(2p_z)^2\)- \(\mathrm{O}_2\): \(\sigma(1s)^2 \sigma^*(1s)^2 \sigma(2s)^2 \sigma^*(2s)^2 \sigma(2p_z)^2 \pi(2p_x)^2 \pi(2p_y)^2 \pi^*(2p_x)^1 \pi^*(2p_y)^1\)- \(\mathrm{S}_2\): The pattern is similar to \(\mathrm{O}_2\) with more electrons.

Step 3: Identify Paired and Unpaired Electrons

Based on the molecular orbital filling:- \(\mathrm{C}_2\) has all paired electrons.- \(\mathrm{N}_2\) also has all paired electrons.- \(\mathrm{O}_2\) has unpaired electrons in the \(\pi^*\) orbitals.- \(\mathrm{S}_2\) follows a similar electronic distribution as \(\mathrm{O}_2\) with unpaired electrons.

Step 4: Determine Magnetic Behaviour

With this information:- \(\mathrm{C}_2\) is diamagnetic (all paired).- \(\mathrm{N}_2\) is diamagnetic (all paired).- \(\mathrm{O}_2\) is paramagnetic (presence of unpaired electrons).- \(\mathrm{S}_2\) is paramagnetic (presence of unpaired electrons).

Step 5: Conclusion

When comparing the molecules, both \(\mathrm{C}_2\) and \(\mathrm{N}_2\) show diamagnetic behaviour. However, we must select one. \(\mathrm{N}_2\) is typically recognized as a textbook example of a stable diamagnetic molecule without any external conditions affecting its state.

Key Concepts

Molecular Orbital Theory

Molecular Orbital (MO) Theory is a fundamental concept in chemistry that helps us understand how atoms combine to form molecules. Unlike the simpler valence bond theory, MO theory describes electrons in molecules by considering them as being spread over multiple atoms, forming molecular orbitals. These orbitals are created by the combination of atomic orbitals.
- **Bonding Orbitals**: When atomic orbitals combine constructively, they form bonding orbitals. Electrons in these orbitals help hold the molecule together.- **Anti-bonding Orbitals**: This occurs due to destructive combination, leading to higher energy levels, destabilizing the molecule.
MO theory is crucial in determining the electronic configuration of molecules, especially diatomic ones like \(\text{O}_2\), \(\text{N}_2\), and \(\text{C}_2\). By knowing the order and fill of these MO's, we can predict a molecule's stability, bond properties, and magnetic behavior. For example, the \(\sigma(2p_z)^2\pi(2p_x)^2\pi(2p_y)^2\) configuration of \(\text{N}_2\) indicates stable bonding with no unpaired electrons.

Electron Configuration

Electron Configuration is the distribution of electrons of an atom or molecule in atomic or molecular orbitals. For molecules, it's crucial to determine which electrons are paired or unpaired. This is directly related to Magnetic Properties because these configurations decide if a molecule is diamagnetic or paramagnetic.
For example, let's look at \(\text{C}_2\) molecule: it has the configuration \(\sigma(1s)^2 \sigma^*(1s)^2 \sigma(2s)^2 \sigma^*(2s)^2 \pi(2p_x)^2 \pi(2p_y)^2\), indicating all electrons are paired.
This complete pairing suggests \(\text{C}_2\) exhibits diamagnetic behavior. On the other hand, molecules like \(\text{O}_2\) have unpaired electrons, attributed to its configuration \(\pi^*(2p_x)^1\pi^*(2p_y)^1\). Understanding this electron configuration helps to determine the energy and magnetic characteristics of molecules.

Magnetic Properties

The **Magnetic Properties** of a substance depend on the arrangement of its electrons, particularly whether electrons are paired or unpaired. Here's a simple guide:
- **Diamagnetism** is seen in substances where all electrons are paired. These materials are weakly repelled by a magnetic field. Examples include \(\text{C}_2\) and \(\text{N}_2\).- **Paramagnetism** occurs in substances with unpaired electrons. These align with a magnetic field, causing the material to be attracted to it. For instance, \(\text{O}_2\) is paramagnetic due to the unpaired electrons in its \pi^*\ orbitals.
Understanding these properties is essential in fields like material science and molecular chemistry. It determines how substances interact with external magnetic fields and helps in the identification and application of different molecular systems.