Problem 76 - A Complete Resource Book in Chemistry for JEE Main

Question

The paramagnetism of \(\mathrm{O}_{2}^{+}\)is due to the presence of an odd electron in the MO (a) \(\sigma^{*} 2 \mathrm{~s}\) (b) \(\pi 2 \mathrm{py}\) (c) \(\sigma^{*} 2 p x\) (d) \(\pi^{*} 2 \mathrm{py}\)

Step-by-Step Solution

Answer

The paramagnetism of \(\mathrm{O}_2^+\) is due to the unpaired electron in \(\pi^* 2py\), which is option (d).

Step 1: Understanding Molecular Orbital Theory

Molecular Orbital (MO) theory helps to understand the distribution of electrons in molecules. The MO diagram is used to predict the magnetic properties of a molecule by assessing unpaired electrons in its molecular orbitals.

Step 2: Draw the MO Diagram for \(\mathrm{O}_2^+\)

The MO diagram for \(\mathrm{O}_2\) shows how atomic orbitals combine to form molecular orbitals. The removal of an electron in \(\mathrm{O}_2^+\) affects the highest occupied molecular orbital.

Step 3: Identify the Highest Occupied Molecular Orbital

For \(\mathrm{O}_2^+\), the molecular orbital configuration is \((\sigma 2s)^2(\sigma^* 2s)^2(\sigma 2p)^2(\pi 2py)^2(\pi 2pz)^2(\pi^* 2py)^1\). Notice that \(\pi^* 2py\) has an unpaired electron.

Step 4: Determine Paramagnetism

Paramagnetism is due to the presence of unpaired electrons. In \(\mathrm{O}_2^+\), the unpaired electron is in the \(\pi^* 2py\) orbital, causing the molecule to be paramagnetic.

Step 5: Conclusion

The paramagnetic behavior of \(\mathrm{O}_2^+\) is due to the unpaired electron in the \(\pi^* 2py\) orbital, making option (d) the correct answer.

Key Concepts

Paramagnetism

Paramagnetism is a fascinating property seen in certain materials and molecules, like \(\mathrm{O}_2^+\). It occurs due to the presence of unpaired electrons in molecular orbitals. Unpaired electrons have magnetic moments, which means they generate tiny magnetic fields. These fields cause the molecule or material to be attracted to external magnetic fields.
In the context of Molecular Orbital (MO) Theory, when electrons in a molecule are unpaired, they contribute to paramagnetic behavior. In our case, the molecule \(\mathrm{O}_2^+\) is paramagnetic because it has an unpaired electron. This characteristic can be observed experimentally, and such experiments are often simple and demonstrate clear confirmations.
Knowing which molecular orbitals contain unpaired electrons can help predict paramagnetic properties. It is crucial to use molecular orbital diagrams to identify these orbitals and their electron occupancy.

Molecular Orbital Diagram

A molecular orbital (MO) diagram is an essential tool in understanding how electrons are distributed in molecules. This diagram combines atomic orbitals from each atom to form molecular orbitals that spread over the entire molecule. These molecular orbitals are either bonding, antibonding, or non-bonding.
The MO diagram utilizes principles of symmetry and energy conservation to show orbital interactions. In the case of \(\mathrm{O}_2^+\), we follow the arrangement of the molecular orbitals from the lowest to higher energy levels: \(\sigma 2s\), \(\sigma^* 2s\), \(\sigma 2p\), \(\pi 2py\), \(\pi 2pz\), leading up to the higher energy levels like \(\pi^* 2py\).
Understanding the MO diagram is key to identifying which orbitals contain unpaired electrons and whether the molecule is paramagnetic. By observing the MO diagram for \(\mathrm{O}_2^+\), one can spot that the \(\pi^* 2py\) contributes to paramagnetic behavior due to its unpaired electron.

Unpaired Electrons

Unpaired electrons are electrons that occupy an orbital alone, without a partnering electron of opposite spin. These electrons play a crucial role in many chemical and physical properties of molecules, notably determining magnetic behavior such as paramagnetism.
In molecular systems, the occupancy of unpaired electrons is identified through configurations provided by molecular orbital diagrams. For \(\mathrm{O}_2^+\), the molecular orbital configuration reveals that the unpaired electron resides in the \(\pi^* 2py\) orbital. This information is crucial as it directly indicates why \(\mathrm{O}_2^+\) exhibits paramagnetism, aligning with observed experimental magnetism.
Furthermore, understanding unpaired electrons is essential for predicting the reactivity of chemical species, as unpaired electrons often participate more readily in chemical reactions. Their presence is a key consideration in fields ranging from chemical bonding to material science.