Question

Which one of the following species is diamagnetic in nature? (a) \(\mathrm{H}_{2}^{-}\) (b) \(\mathrm{H}_{2}\) (c) \(\mathrm{H}_{2}^{+}\) (d) \(\mathrm{He}_{2}^{+}\)

Short answer

H_{2} is the diamagnetic species.

Step-by-step solution

Understanding Diamagnetism

A species is diamagnetic when all of its electrons are paired. In contrast, paramagnetic species have unpaired electrons.

Molecular Orbital Theory Overview

According to molecular orbital theory, electrons in molecules reside in molecular orbitals rather than atomic orbitals. To determine the electronic configuration, we need to consider how electrons fill in bonding and antibonding molecular orbitals for each species.

Analyzing the Electron Configuration of H_{2}^{-}

- H_{2}^{-} has 3 electrons. - Filling the σ(1s) bonding orbital first, we place 2 electrons in it. - The remaining 1 electron occupies the σ*(1s) antibonding orbital. - This results in unpaired electrons, making H_{2}^{-} paramagnetic.

Analyzing the Electron Configuration of H_{2}

- H_{2} has 2 electrons. - Both electrons fill the σ(1s) bonding orbital, - There is no electron in the antibonding orbitals, thus all electrons are paired. - Therefore, H_{2} is diamagnetic.

Analyzing the Electron Configuration of H_{2}^{+}

- H_{2}^{+} has 1 electron. - The single electron fills the σ(1s) orbital. - The presence of a single electron indicates it is unpaired, making H_{2}^{+} paramagnetic.

Analyzing the Electron Configuration of He_{2}^{+}

- He_{2}^{+} has 3 electrons. - First, 2 electrons fill the σ(1s) bonding orbital. - The remaining 1 electron occupies the σ*(1s) antibonding orbital. - There remains an unpaired electron, making He_{2}^{+} paramagnetic.

Key concepts

Molecular Orbital Theory

Molecular Orbital Theory (MOT) is a fundamental concept in chemistry that helps us understand the behavior of electrons in molecules. Instead of being confined to individual atoms, electrons are delocalized across the molecule in molecular orbitals. These orbitals result from the combination of atomic orbitals when atoms come together to form a molecule.
The key types of molecular orbitals include bonding and antibonding orbitals.

• Bonding Orbitals: When atomic orbitals combine constructively, they form bonding orbitals, which help hold the atoms together.
• Antibonding Orbitals: When atomic orbitals combine destructively, antibonding orbitals are formed. They can weaken or destabilize the bond if filled with electrons.

For a stable molecule, electrons primarily occupy bonding molecular orbitals. To predict the properties of a molecule, it's crucial to understand the order in which these orbitals are filled with electrons and how these electrons are paired in the molecular orbitals.
This theory is central in determining whether a molecule is diamagnetic or paramagnetic.

Electron Configuration

Electron configuration refers to the arrangement of electrons in an atom or molecule. For molecular systems, this involves filling electrons into various molecular orbitals based on their energy levels, from lowest to highest. The electron configuration of a molecule is crucial in predicting its chemical behavior and properties.
In molecular orbital diagrams, we can represent the filling of these orbitals as seen in the step-by-step analysis of species like

• data-mce-fragment="1" data-mce-fragment="1" He_{2}^{+} data-mce-fragment="1" data-mce-fragment="1"

- The electron configuration of molecules follows the Molecular Orbital Theory explained earlier, where electrons fill bonding and antibonding orbitals.

• Filled Bonding Orbital: Electrons first fill the bonding orbital (e.g., "σ(1s)") since it is lower in energy.
• Occupation of Antibonding Orbital: If extra electrons remain, they occupy the antibonding orbital (e.g., "σ*(1s)").

When electrons are added to these orbitals, it is important to check if all are paired. If all electrons are paired, the species is diamagnetic; if there are unpaired electrons, it indicates a paramagnetic nature.

Paramagnetic Species

Species are distinguished as paramagnetic or diamagnetic based on the electron configuration within their molecular orbitals.

• Paramagnetic Species: These have unpaired electrons in their molecular orbitals. The presence of unpaired electrons allows the species to be attracted to a magnetic field.
• Diamagnetic Species: In contrast, all electrons in diamagnetic species are paired, which leads to a slight repulsion from magnetic fields.

This characteristic is determined by examining the molecular orbital diagrams generated by applying the Molecular Orbital Theory to specific species. For example, in the exercise, analyzing the electron configurations of data-mce-fragment="1" H_{2}^{-}, data-mce-fragment="1" H_{2}, data-mce-fragment="1" H_{2}^{+}, and data-mce-fragment="1" He_{2}^{+}, we found that only data-mce-fragment="1" H_{2} has paired electrons, classifying it as diamagnetic. All others are paramagnetic due to having at least one unpaired electron.
Understanding these characteristics can tell us a lot about the electronic and magnetic properties of molecules, which is vital in fields like chemistry and materials science.