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

Question

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

Step-by-Step Solution

Answer

C2 is diamagnetic due to all electrons being paired.

Step 1: Understand Diamagnetic Behaviour

A molecule is diamagnetic if all of its electrons are paired. If the molecule has any unpaired electrons, it will exhibit paramagnetic behavior instead.

Step 2: Write the Molecular Orbital Configuration

Write the molecular orbital configuration for each molecule. Oxygen (O_{2}) is (1s)_2 (1s^*)_2 (2s)_2 (2s^*)_2 (2p_z)_2 (2p_x)_2 (2p_y)_2 (2p_z^*)_2 (2p_x^*)_1 (2p_y^*)_1, with unpaired electrons in antibonding orbitals. Nitrogen (N_{2}) is (1s)_2 (1s^*)_2 (2s)_2 (2s^*)_2 (2p_z)_2 (2p_x)_1 (2p_y)_1, with no unpaired electrons in antibonding orbitals. Carbon (C_{2}) is (1s)_2 (1s^*)_2 (2s)_2 (2s^*)_2 (2p_x)_2 (2p_y)_2 (2p_z)_0, with no unpaired electrons. Sulfur (S_{2}) follows a similar pattern to O_{2}.

Step 3: Identify Molecules with All Paired Electrons

Identify which molecules have all electrons paired. According to their configurations, N_{2} and C_{2} have all electrons paired, while O_{2} and S_{2} each have unpaired electrons.

Step 4: Conclusion

Since diamagnetic molecules have all electrons paired, N_{2} and C_{2} are expected to be diamagnetic. However, the problem asks for one such molecule, thus any answer between them is valid. In most contexts, N_{2} is the molecule that aligns with typical expectations.

Key Concepts

Molecular Orbital Theory

Molecular Orbital Theory (MOT) is a powerful tool for understanding the behavior of electrons in molecules. This theory helps in predicting molecular properties such as bond order, stability, and magnetism by considering electrons in molecular orbitals that extend over the entire molecule.
MOT describes electrons as spread out over an entire molecule in orbitals, which can be bonding, non-bonding, or antibonding. These orbitals are formed by the constructive or destructive interference of atomic orbitals. Bonding orbitals result in electron density between the nuclei, stabilizing the molecule. In contrast, antibonding orbitals have electron density that pulls nuclei apart, destabilizing the molecule.
Molecular Orbital Theory allows us to predict that molecules with unpaired electrons in these orbitals will be paramagnetic, while those with all electrons paired will be diamagnetic.

Electron Pairing

Electron pairing is a concept where two electrons occupy the same orbital, but with opposite spins. This is crucial because electron pairing largely determines the magnetic properties of a molecule.
When all electrons in a molecule are paired, the net spin is zero, leading to diamagnetism. In such cases, the molecule does not have unpaired electrons to align with a magnetic field. This characteristic is what we observe in diamagnetic substances: they create an induced magnetic field that opposes an externally applied magnetic field, hence showing no net attraction.
However, if there are unpaired electrons, the molecule will exhibit paramagnetic properties. These unpaired electrons contribute a net magnetic moment that aligns with an external magnetic field, leading to attraction.

Paramagnetic Behavior

Paramagnetic behavior is observed in substances that have one or more unpaired electrons. These unpaired electrons generate a net magnetic moment since each electron has a magnetism associated with its spin.
Such substances, unlike diamagnetic substances, are attracted to magnetic fields. The degree of this attraction depends on the number of unpaired electrons present. In Molecular Orbital Theory, when electrons occupy antibonding molecular orbitals, they often remain unpaired, leading to this behavior.
Consider oxygen \( \mathrm{O}_{2} \). According to its molecular orbital configuration, it has unpaired electrons in antibonding orbitals, making it paramagnetic. This is why a strong attraction to a magnetic field occurs, unlike diamagnetic nitrogen \( \mathrm{N}_{2} \), which has all electrons paired.

Antibonding Orbitals

Antibonding orbitals play a significant role in determining the magnetic properties of a molecule. These orbitals, indicated by an asterisk (*), have higher energy than their corresponding bonding orbitals and often contain unpaired electrons in paramagnetic substances.
When electrons populate these orbitals, they increase the energy and destabilize the molecule. In molecular terms, filling antibonding orbitals can lead to net magnetic moments, giving rise to paramagnetism.
For example, in oxygen \( \mathrm{O}_{2} \), electrons in antibonding orbitals are unpaired, making it paramagnetic. Conversely, nitrogen \( \mathrm{N}_{2} \) lacks unpaired electrons in such orbitals, supporting its diamagnetic nature. Understanding which electrons are in antibonding orbitals is essential for predicting whether a molecule will be paramagnetic or diamagnetic.