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

Question

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

Step-by-Step Solution

Answer

The paramagnetism is due to the presence of an odd electron in \( \pi^{*} 2 \mathrm{py} \).

Step 1: Understanding Paramagnetism

Paramagnetism occurs in molecules due to the presence of unpaired electrons. Therefore, to determine the paramagnetism in \( \mathrm{O}_{2}^{+} \), we need to identify which molecular orbital has an unpaired electron.

Step 2: Writing the Electron Configuration

\( \mathrm{O}_{2} \) has the molecular orbital configuration of: \( \sigma_{1s}^{2} \sigma^{*}_{1s}^{2} \sigma_{2s}^{2} \sigma^{*}_{2s}^{2} \sigma_{2p}^{2} \pi_{2p}^{4} \pi^{*}_{2p}^{2} \). \( \mathrm{O}_{2}^{+} \) means removing one electron from \( \pi^{*}_{2p} \) orbitals because they have the highest energy.

Step 3: Identify the Orbital with the Odd Electron

After removing one electron from \( \pi^{*}_{2p} \) orbitals, \( \mathrm{O}_{2}^{+} \) will be left with one unpaired electron in \( \pi^{*}_{2p} \) orbitals. The unpaired electron in \( \pi^{*}_{2p} \) orbital is responsible for paramagnetism.

Step 4: Conclusion

The odd electron in \( \mathrm{O}_{2}^{+} \) resides in the \( \pi^{*}_{2p} \) orbital, specifically in the \( \pi^{*} 2 \mathrm{py} \) or \( \pi^{*} 2 \mathrm{px} \) depending on notation.

Key Concepts

Molecular Orbital Theory

Molecular Orbital Theory is a fundamental concept in chemistry that describes the behavior of electrons in a molecule. Unlike atomic orbital theory, which focuses on individual atoms, molecular orbital (MO) theory considers the molecule as a whole.
It assumes that atomic orbitals combine to form molecular orbitals when atoms bond together. This allows electrons to be more delocalized across the molecule rather than being confined to a particular atom.
Molecular orbitals are divided into bonding and antibonding orbitals:

• Bonding orbitals result from the constructive combination of atomic orbitals. They have lower energy and contribute to the stability of a molecule.
• Antibonding orbitals occur when atomic orbitals combine destructively. They have higher energy and, if occupied by electrons, can destabilize a molecule.

Molecular orbitals are filled with electrons in accordance with the Pauli exclusion principle and Hund's rule. These principles help determine the magnetic properties and stability of molecules, such as paramagnetism in oxygen molecules.

Electron Configuration

Electron configuration is the arrangement of electrons in the orbitals of an atom or molecule. It's important because it affects how an element or compound behaves chemically.
To write the electron configuration for a molecule like \( \mathrm{O}_2 \), we follow the order of increasing energy of the molecular orbitals:

• \(\sigma_{1s}^2\sigma^{*}_{1s}^2\) indicates the inner core electrons.
• \(\sigma_{2s}^2\sigma^{*}_{2s}^2\) represents the next level, including the non-bonding electrons.
• The \(\sigma_{2p}^2\pi_{2p}^4\pi^{*}_{2p}^2\) shows the configuration of electrons in the bonding and antibonding orbitals.

When ionizing oxygen to form \( \mathrm{O}_2^{+} \), you typically remove an electron from the highest energy level, which is the \(\pi^{*}_{2p}\) level. This change results in an unpaired electron that has significant consequences for the molecule's magnetic properties.

Unpaired Electrons

Unpaired electrons are essential when discussing the magnetic properties of a molecule. They occur when there's an electron in an orbital without a partner with opposite spin.
In the context of \(\mathrm{O}_2^{+}\), when one electron is removed from the \(\pi^{*}_{2p}\) molecular orbitals, it results in one unpaired electron.
These unpaired electrons cause the molecule to be paramagnetic. Paramagnetic materials have at least one unpaired electron and are attracted to magnetic fields.

• In contrast, diamagnetic substances have no unpaired electrons and repel magnetic fields.

Understanding unpaired electrons helps explain why \(\mathrm{O}_2^{+}\) exhibits paramagnetism and more broadly, how electrons influence the physical properties of a molecule.