Question

In the conversion of \(\mathrm{O}_{2}\) to superoxide ion, the electron is added to (1) \(\sigma\) -orbital (2) \(\sigma^{*}\) -orbital (3) \(\pi\) -orbital (4) \(\pi^{*}\) -orbital

Short answer

The electron is added to the \(\text{pi}^*\) orbital.

Step-by-step solution

Understand the Electron Configuration of \(\text{O}_{2}\)

The molecular orbital (MO) configuration of \(\text{O}_{2}\) in its ground state is \[1s^2 1s^{*2} 2s^2 2s^{*2} 2p^4 2p^{*4} 2p_{\text{orbitals}} (2p_{x}^2 2p_{y}^2 2p_{z}^2 2p_{x}^{*1} 2p_{y}^{*1})\]. In this configuration, all bonding molecular orbitals are fully occupied, and antibonding orbitals (\text{2p}*) are partially occupied.

Identify the Effect of Adding an Electron

When an electron is added to \(\text{O}_{2}\) to form the superoxide ion \(\text{O}_{2}^{-}\), we'll add this electron to the next available molecular orbital. This happens to be an antibonding \(\text{2p}*\) orbital because bonding orbitals are already filled.

Determine Which Specific Antibonding Orbital

In the case of \(\text{O}_{2}\), the antibonding orbitals are split into two types: \(\text{sigma}^*\) and \(\text{pi}^*\). Since the last occupied orbitals in \(\text{O}_{2}\) are \(\text{pi}^*\) orbitals, the electron will enter the \(\text{pi}^*\) orbital upon addition.

Conclude the Correct Option Based on Analysis

Given that the additional electron goes into a \(\text{pi}^*\) orbital, the correct choice is option (4) \(\text{pi}^*}=\) orbital.

Key concepts

Molecular Orbital Theory

Molecular Orbital Theory (MOT) is a method to understand the bonding between atoms in a molecule. According to MOT, atomic orbitals combine to form molecular orbitals. These molecular orbitals spread over the entire molecule and can be occupied by electrons from any of the atoms in the molecule.

There are two main types of molecular orbitals: bonding and antibonding orbitals. Bonding orbitals (represented by \(\text{sigma}\) and \(\text{pi}\)) have lower energy and lead to a stable molecule, while antibonding orbitals (represented by \(\text{sigma}^*\) and \(\text{pi}^*\)) have higher energy and can thereby destabilize the molecule.

Bonding orbitals form when atomic orbitals combine constructively, leading to an increased electron density between the nuclei. On the other hand, antibonding orbitals form due to destructive interference, resulting in a nodal plane where the electron density is low. Each type of orbital plays a crucial role in determining the electronic configuration and properties of a molecule.

MOT can explain phenomena that are difficult to understand using other theories, such as the behavior of paramagnetic and diamagnetic molecules. This theory is particularly useful for explaining the electron configurations of diatomic molecules such as \(\text{O}_{2}\).

Superoxide Ion

The superoxide ion (\(\text{O}_{2}^{-}\)) forms when a molecule of oxygen (\(\text{O}_{2}\)) gains an extra electron. This results in a negatively charged ion due to the extra electron. Understanding the electronic configuration is essential to explain why this happens.

Oxygen in its molecular form has the molecular orbital configuration \( \text{1s}^2 \text{1s}^{*2} \text{2s}^2 \text{2s}^{*2} \text{2p}^4 \text{2p}^{*4} \text{2p}_{\text{orbitals}} (2p_{x}^2 2p_{y}^2 2p_{z}^2 2p_{x}^{*1} 2p_{y}^{*1}) \). When an extra electron is added, it goes into the lowest available energy state, which happens to be an antibonding \(\text{2p}^*\) orbital.

The addition of this electron to the \(\text{2p}^*\) orbital increases the molecular orbital count, making the oxygen molecule a superoxide ion. This process slightly destabilizes the molecule because antibonding orbitals lead to higher energy. However, it does not make the molecule highly unstable. The resulting \(\text{O}_{2}^{-}\) ion has one unpaired electron, making it paramagnetic and highly reactive.

Superoxide ions are involved in various chemical reactions and play essential roles in biological systems such as the immune response, where they are used to kill bacteria. They are also important in materials science for creating certain types of batteries.

Antibonding Orbitals

Antibonding orbitals are critical to the understanding of molecular stability. These orbitals are denoted by the symbols \(\text{sigma}^*\) and \(\text{pi}^*\), and they represent higher energy states compared to their bonding counterparts.

When atomic orbitals combine to form molecular orbitals, they produce both bonding and antibonding orbitals. While bonding orbitals stabilize the molecule through increased electron density between nuclei, antibonding orbitals do the opposite. They create node regions where electron density is minimal, leading to less stability.

To visualize, consider molecular oxygen (\(\text{O}_{2}\)). It has partly filled antibonding \(\text{pi}^*\) orbitals, making it less stable than if all electrons were in bonding orbitals. When an additional electron is added, such as in the formation of a superoxide ion (\(\text{O}_{2}^{-}\)), it's added to one of these antibonding \(\text{pi}^*\) orbitals.

This extra electron increases the electron density in an already less stable region, further increasing the molecule's energy. As a result, molecules with electrons in antibonding orbitals tend to have higher reactivities and different chemical properties compared to when these orbitals are empty.

Antibonding orbitals play a significant role in determining the overall electronic structure and reactivity of molecules. They are essential in many advanced chemical theories and help explain behaviors in inorganic chemistry and materials science.