Problem 205 - A Complete Resource Book in Chemistry for JEE Main

Question

Which of the following species exhibits the diamagnetic behaviour? (a) \(\mathrm{O}_{2}^{+}\) (b) \(\mathrm{O}_{2}\) (c) NO (d) \(\mathrm{O}_{2}^{2-}\)

Step-by-Step Solution

Answer

\( \mathrm{O}_{2}^{2-} \) is diamagnetic.

Step 1: Understanding Diamagnetism

Diamagnetism refers to the property of a substance that is not attracted to a magnetic field because all its electrons are paired. In contrast, paramagnetic substances are attracted to a magnetic field due to the presence of unpaired electrons.

Step 2: Writing Electronic Configuration for Each Species

1. For \( \mathrm{O}_{2}^{+} \), remove one electron from \( \mathrm{O}_2 \), resulting in the electronic configuration: \( \sigma_{1s}^2\sigma_{1s}^2\sigma_{2s}^2\sigma_{2s}^2\sigma_{2p_z}^2\pi_{2p_x}^2\pi_{2p_y}^1\pi_{2p_x}^1 \). 2. For \( \mathrm{O}_{2} \), the configuration is: \( \sigma_{1s}^2\sigma_{1s}^2\sigma_{2s}^2\sigma_{2s}^2\sigma_{2p_z}^2\pi_{2p_x}^2\pi_{2p_y}^2\). 3. For NO, the configuration is: \( \sigma_{1s}^2\sigma^{*}_{1s}^2\sigma_{2s}^2\sigma^{*}_{2s}^2\sigma_{2p_z}^2\pi_{2p_x}^2\pi_{2p_y}^1 \). 4. For \( \mathrm{O}_{2}^{2-} \), add two electrons to \( \mathrm{O}_2 \), having the configuration: \( \sigma_{1s}^2\sigma_{1s}^2\sigma_{2s}^2\sigma_{2s}^2\sigma_{2p_z}^2\pi_{2p_x}^2\pi_{2p_y}^2 \).

Step 3: Identifying Unpaired Electrons

- \( \mathrm{O}_{2}^{+} \) has two unpaired electrons, indicating paramagnetism.- \( \mathrm{O}_{2} \) has two unpaired electrons, indicating paramagnetism.- NO has one unpaired electron, indicating paramagnetism.- \( \mathrm{O}_{2}^{2-} \) has all paired electrons, suggesting diamagnetism.

Step 4: Conclusion

Since only \( \mathrm{O}_{2}^{2-} \) has all its electrons paired, it is the only species that exhibits diamagnetic behavior.

Key Concepts

Molecular Orbital Theory

Molecular Orbital Theory offers a comprehensive understanding of how electrons are distributed in a molecule. Instead of focusing on individual atoms, this theory examines molecules as a whole. The core idea is that atomic orbitals from different atoms combine to form molecular orbitals. These molecular orbitals can be occupied by electrons that are shared across the entire molecule. With this perspective:

• Bonding orbitals: When atomic orbitals combine constructively, they form bonding molecular orbitals, increasing electron density between nuclei and stabilizing the molecule.
• Antibonding orbitals: In contrast, destructive combinations result in antibonding orbitals, which are higher in energy and can destabilize the molecule if occupied.
• Nonbonding orbitals: Some orbitals don’t change a molecule's energy and remain unaffected during bonding.

Understanding this theory is crucial to predicting magnetic properties like diamagnetism or paramagnetism, since the distribution of electrons among these orbitals determines if electrons are paired or unpaired.

Electronic Configuration

Electronic configuration is the arrangement of electrons in the orbitals of an atom or molecule. It provides a map of where each electron resides, influencing the molecule's properties and behaviors. When configuring electrons:

• Electrons fill orbitals starting from the lowest energy level, following the Aufbau principle.
• Each orbital can hold a maximum of two electrons with opposite spins, as stated by the Pauli exclusion principle.
• Hund’s rule suggests that within a subshell, electrons occupy empty orbitals singly before pairing up.

The electronic configuration of a molecule factors significantly into identifying magnetic properties. For instance, if a molecule has electrons that are all paired, such as in the case of the dioxygen ion (0_{2}^{2-} ), it will exhibit diamagnetic behavior, while unpaired electrons, as seen in dioxygen (O₂), indicate paramagnetism.

Paramagnetism

Paramagnetism is a characteristic exhibited by materials with unpaired electrons. These materials are attracted to external magnetic fields because the unpaired electron spins can align with the magnetic field. Key points about paramagnetism include:

• Materials possessing one or more unpaired electrons will experience a net magnetic moment.
• The strength of paramagnetism is proportional to the number of unpaired electrons in the material.
• When the external magnetic field is removed, the alignment of electron spins ceases, resulting in the loss of magnetism.

This property is used to distinguish between different molecules, as seen in molecular orbital analysis. For example, O₂ is a classic example of a paramagnetic molecule due to two unpaired electrons in its molecular orbitals. In contrast, the lack of unpaired electrons in 0_{2}^{2-} results in diamagnetism. Understanding paramagnetism can assist in predicting and explaining the magnetic behaviors of molecular compounds.