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) \(\pi^{*} 2 \mathrm{py}\)

Short answer

The paramagnetism is due to the electron in the ^* 2p_y orbital (option d).

Step-by-step solution

Understand the Molecular Orbital Theory

Molecular Orbital (MO) theory describes how atomic orbitals combine to form molecular orbitals that are spread over the molecule. For diatomic oxygen ( ), the important orbitals in the valence shell are the  2s,  2p, ^* 2s, and ^* 2p orbitals. The asterisk (*) denotes antibonding orbitals.

Write the Molecular Orbital Configuration of  ^+

The   molecule usually has the electron configuration of  2s^2, ^* 2s^2,  2p_x^2,  2p_y^2,  2p_z^2, ^* 2p_x^1, and ^* 2p_y^1. When one electron is removed (for  ^+), it's from the highest occupied molecular orbital, which is typically the ^* 2p orbital.

Identify the Paramagnetism Source

Paramagnetism is due to the presence of unpaired electrons. In the case of  ^+, the single unpaired electron is located in the ^* 2p orbital. The ^* 2p orbitals correspond to the ^* 2p_x and ^* 2p_y molecular orbitals because these are where the odd electron will be found.

Match the MO to the Given Options

Among the given options, ^* 2p_y is listed as option (d) ^* 2 _y. This matches our determination of where the odd electron resides, as the ^* 2p orbitals include both ^* 2p_x and ^* 2p_y and one of them is where the unpaired electron will be.

Key concepts

Paramagnetism

Paramagnetism is a fascinating phenomenon observed in some molecules, and it originates from the presence of unpaired electrons. Essentially, when a molecule has one or more unpaired electrons in its molecular orbitals, it exhibits paramagnetism. This is because these unpaired electrons have magnetic moments that can align with an external magnetic field, leading to a magnetic attraction.

In the context of molecular orbital theory, paramagnetism is a key concept used to explain why certain molecules are attracted to magnets. If all electrons in a molecule are paired, the magnetic moments cancel each other out, leading to a diamagnetic property, which is a weak repulsion from a magnetic field. However, if even one electron remains unpaired, this gives rise to paramagnetic properties of the molecule.

In the case of  ^+, the removal of an electron results in an unpaired electron in its antibonding molecular orbitals, specifically in one of the ^* 2p orbitals, which contributes to its paramagnetism.

Molecular Orbital Configuration

Molecular orbital configuration is crucial to understanding the behavior of molecules according to molecular orbital theory. This theory describes how individual atomic orbitals combine to form new orbitals called molecular orbitals, which are spread over the entire molecule. These molecular orbitals can be bonding or antibonding, with bonding orbitals being lower in energy and thus more stable.

The molecular orbital configuration represents the arrangement of electrons within these molecular orbitals. For the molecule  , and subsequently  ^+, the configuration is initially:  2s^2, ^* 2s^2,  2p_x^2,  2p_y^2,  2p_z^2, ^* 2p_x^1, and ^* 2p_y^1.

• Bonding orbitals ( 2s,  2p_x,  2p_y,  2p_z) stabilize the molecule.
• Antibonding orbitals (^* 2s, ^* 2p_x, ^* 2p_y) destabilize it, having higher energy.

This configuration means that, when an electron is removed to form  ^+, it is typically taken from the highest energy orbital, which is the ^* 2p orbital. This leaves an unpaired electron, leading to the molecule's paramagnetic nature.

Antibonding Orbitals

Antibonding orbitals are a type of molecular orbital that plays a key role in the molecular orbital theory. These orbitals occur when the combination of atomic orbitals results in orbitals that have higher energy than the original atomic orbitals.

Antibonding orbitals are characterized by a region of zero electron probability, known as a node, between the nuclei of the bonded atoms. This node results in a repulsive interaction, leading to a destabilization of the molecule.

• They are denoted with an asterisk (*), such as ^* 2s or ^* 2p.
• Electrons in these orbitals increase the energy of the molecule.
• Any unpaired electrons in these orbitals contribute to the molecule's magnetic properties, such as paramagnetism.

For example, in  ^+, the unpaired electron resides in an antibonding orbital (^* 2p), contributing to its paramagnetic character. Understanding antibonding orbitals helps elucidate why the stability of a molecule might be reduced when these orbitals are occupied.