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) \(\sigma^{*} 2 \mathrm{px}\) (d) \(\pi^{*} 2 \mathrm{py}\)

Short answer

The paramagnetism of \(O_2^+\) is due to the unpaired electron in \(\pi^*_{2px}\).

Step-by-step solution

Review Molecular Orbital Theory

Molecular Orbital (MO) theory explains the paramagnetic nature of a molecule when it has unpaired electrons. Paramagnetism is due to these unpaired electrons in molecular orbitals. We need to identify the orbital where this unpaired electron might reside in the particular ion \(O_2^+\).

Determine the Molecular Orbital Configuration of Neutral \(O_2\)

For neutral \(O_2\), the molecular orbital configuration is \((\sigma_{1s})^2 (\sigma^*_{1s})^2 (\sigma_{2s})^2 (\sigma^*_{2s})^2 (\sigma_{2p})^2 (\pi_{2px})^2 (\pi_{2py})^2 (\pi^*_{2px})^1 (\pi^*_{2py})^1\). Notice the two unpaired electrons in the \(\pi^*_{2p}\) orbitals (one each in \(\pi^*_{2px}\) and \(\pi^*_{2py}\)).

Modify the Configuration for \(O_2^+\)

For \(O_2^+\), one electron is removed from \(O_2\). The electron is most likely removed from the highest energy orbital, which is one of the \(\pi^*_{2px}\) or \(\pi^*_{2py}\). Removing one electron makes the configuration: \((\sigma_{1s})^2 (\sigma^*_{1s})^2 (\sigma_{2s})^2 (\sigma^*_{2s})^2 (\sigma_{2p})^2 (\pi_{2px})^2 (\pi_{2py})^2 (\pi^*_{2px})^1 (\pi^*_{2py})^0\).

Identify the Correct MO with Unpaired Electron

With one more electron removed from \(\pi^*_{2py}\), the \(\pi^*_{2px}\) still has one unpaired electron. This is the MO responsible for paramagnetism in \(O_2^+\).

Answer the Question

The paramagnetism of \(O_2^+\) is because one unpaired electron remains in the \(\pi^*_{2px}\) molecular orbital. Therefore, the correct answer is \(\pi^* 2py\).

Key concepts

Molecular Orbital Theory

Molecular Orbital Theory is a fundamental concept in chemistry that explains the formation and behavior of molecules. Unlike other models, it suggests that atomic orbitals combine to form molecular orbitals, which spread across an entire molecule. These molecular orbitals can be bonding, non-bonding, or anti-bonding.
- **Bonding orbitals** result from the constructive interference between atomic orbitals. They have lower energy than the original atomic orbitals.
- **Anti-bonding orbitals** result from destructive interference between atomic orbitals. These have higher energy and are often denoted with an asterisk (e.g., \(\sigma^*\)).
- **Non-bonding orbitals** have energy levels similar to the original atomic orbitals and usually do not significantly affect the stability of the molecule.

Molecular Orbital Theory importantly helps explain properties like magnetism and chemical stability in molecules, offering insights into phenomena like paramagnetism that arises when electrons remain unpaired in their molecular orbitals.

Molecular Orbital Configuration

The molecular orbital configuration of a molecule is simply a representation of how electrons are distributed among the molecular orbitals. It helps to predict the chemical and physical properties of the molecule. For instance, let's consider the neutral oxygen molecule, \(O_2\).
Its configuration is: \((\sigma_{1s})^2 (\sigma^*_{1s})^2 (\sigma_{2s})^2 (\sigma^*_{2s})^2 (\sigma_{2p})^2 (\pi_{2px})^2 (\pi_{2py})^2 (\pi^*_{2px})^1 (\pi^*_{2py})^1\).

This configuration indicates two electrons occupying the anti-bonding \(\pi^*\) orbitals, one each in \(\pi^*_{2px}\) and \(\pi^*_{2py}\).
- **Anti-bonding orbitals**, as noted, have higher energy and possess unpaired electrons contributing to paramagnetism.
- **Bonding orbitals** hold paired electrons, indicating more stability.

The molecular orbital configuration is crucial for understanding why certain molecules have unique properties like magnetism, reactivity, and bond order.

Unpaired Electrons

Unpaired electrons in a molecular orbital are electrons that do not have a second electron with opposite spin occupying the same orbital. These electrons play crucial roles in determining the magnetic properties and reactivity of molecules. In molecular orbital theory, paramagnetism is attributed to the presence of unpaired electrons.

For example, in the oxygen molecule \(O_2\), the presence of unpaired electrons in the \(\pi^*\) orbitals results in paramagnetism. The configuration, \(\pi^*_{2px}^1 \pi^*_{2py}^1\), shows two unpaired electrons.

- **Key Impact**: Unpaired electrons allow molecules to interact with magnetic fields, resulting in paramagnetic behavior.
- **Chemical Reactions**: Molecules with unpaired electrons are often reactive, looking to pair these electrons by forming bonds.

Understanding unpaired electrons aids in predicting how molecules will behave in magnetic fields and chemical environments.

Oxygen Molecule

The oxygen molecule, \(O_2\), is a great example highlighting the application of molecular orbital theory and the importance of unpaired electrons. In its neutral form, \(O_2\) has 16 electrons distributed among its molecular orbitals according to the configuration: \((\sigma_{1s})^2 (\sigma^*_{1s})^2 (\sigma_{2s})^2 (\sigma^*_{2s})^2 (\sigma_{2p})^2 (\pi_{2px})^2 (\pi_{2py})^2 (\pi^*_{2px})^1 (\pi^*_{2py})^1\).

This configuration is significant because the pair of unpaired electrons in the anti-bonding \(\pi^*\) orbitals contributes to its paramagnetic nature, making \(O_2\) attracted to a magnetic field.
- **Reactivity**: As an element, oxygen is highly reactive due to its unpaired electrons and is essential in combustion and respiration processes.
- **Physical Properties**: The paramagnetism of \(O_2\) provides evidence supporting molecular orbital theory over simpler models like valence bond theory.

Understanding the oxygen molecule provides insights into broader chemical behaviors and real-life applications from biology to industrial chemistry.

Ionization

Ionization refers to the process of removing or adding electrons to an atom or molecule, leading to the formation of ions. It is an essential concept when discussing ions like \(O_2^+\), which forms when one electron is removed from neutral \(O_2\).

- **Energy Considerations**: Removing electrons requires energy, described as the ionization energy. This energy is lower when electrons are removed from higher energy orbitals like anti-bonding \(\pi^*\) levels.
- **Changes in Configuration**: For \(O_2^+\), removing an electron from the highest occupied molecular orbital, \(\pi^*_{2py}\), changes the configuration to \((\sigma_{1s})^2 (\sigma^*_{1s})^2 (\sigma_{2s})^2 (\sigma^*_{2s})^2 (\sigma_{2p})^2 (\pi_{2px})^2 (\pi_{2py})^2 (\pi^*_{2px})^1 (\pi^*_{2py})^0\).

Ionization is crucial in chemistry and plays a foundational role in fields ranging from spectroscopy to quantum chemistry. Understanding ionization helps explain changes in chemical and physical properties during reactions.