Question

Which of the following species exhibits the diamagnetic behaviour? (a) \(\mathrm{O}_{2}^{+}\) (b) \(\mathrm{O}_{2}\) (c) NO (d) \(\mathrm{O}_{2}^{2-}\)

Short answer

The species \\(\mathrm{O}_{2}^{2-}\\) exhibits diamagnetic behavior.

Step-by-step solution

Understand Diamagnetic and Paramagnetic

A species is diamagnetic if all of its electrons are paired, and it is not attracted by a magnetic field. Conversely, paramagnetic species have unpaired electrons and are attracted by a magnetic field.

Determine Electron Configuration for Each Species

Calculate the electron configuration of each species and count the unpaired electrons. Start by determining the total number of electrons. Use molecular orbital theory to help with electron arrangement:- For diatomic oxygen molecules: - \(\mathrm{O}_{2}\) has 16 electrons. - \(\mathrm{O}_{2}^{+}\) has 15 electrons (losing one electron). - \(\mathrm{O}_{2}^{2-}\) has 18 electrons (gaining two electrons).- For nitric oxide: - \( ext{NO}\) has 15 electrons (11 from nitrogen and 4 from oxygen).

Write Molecular Orbital Configuration for Each Species

Based on molecular orbital theory:- \(\mathrm{O}_{2}\): \(\sigma_{1s}^{2}\sigma^*_{1s}^{2}\sigma_{2s}^{2}\sigma^*_{2s}^{2}\sigma_{2pz}^{2}\pi_{2px}^2=\pi_{2py}^{2}\pi^*_{2px}^{1}=\pi^*_{2py}^{1}\) \(\rightarrow\) Two unpaired electrons.- \(\mathrm{O}_{2}^{+}\): \(\sigma_{1s}^{2}\sigma^*_{1s}^{2}\sigma_{2s}^{2}\sigma^*_{2s}^{2}\sigma_{2pz}^{2}\pi_{2px}^2=\pi_{2py}^{2}\pi^*_{2px}^{1}\) \(\rightarrow\) One unpaired electron.- \(\mathrm{O}_{2}^{2-}\): \(\sigma_{1s}^{2}\sigma^*_{1s}^{2}\sigma_{2s}^{2}\sigma^*_{2s}^{2}\sigma_{2pz}^{2}\pi_{2px}^2=\pi_{2py}^{2}\pi^*_{2px}^{2}\pi^*_{2py}^{2}\) \(\rightarrow\) No unpaired electrons.- \(\text{NO}\): \(\sigma_{1s}^{2}\sigma^*_{1s}^{2}\sigma_{2s}^{2}\sigma^*_{2s}^{2}\sigma_{2pz}^{2}\pi_{2px}^2=\pi_{2py}^{2}\pi^*_{2px}^{1}\) \(\rightarrow\) One unpaired electron.

Identify Diamagnetic Species

From the molecular orbital configurations, \(\mathrm{O}_{2}^{2-}\) is the only species with all electrons paired and hence exhibits diamagnetic behavior.

Key concepts

Molecular Orbital Theory

Molecular Orbital Theory is fundamental to understanding how electrons are arranged in molecules. Unlike the simpler view of individual atoms, molecular orbital theory considers that electrons in a molecule are not localized to one atom but spread out over the entire molecule. In this model, when atoms combine, their atomic orbitals mix to form molecular orbitals. - **Bonding Orbitals**: These are lower in energy and result when orbitals constructively combine, allowing the molecule to be more stable. - **Antibonding Orbitals**: Higher in energy and formed when orbitals combine destructively, resulting in decreased stability. - **Nonbonding Orbitals**: Orbitals that do not contribute to bonding or antibonding. Molecular Orbitals are filled with electrons in a similar manner to atomic orbitals, following Hund’s rule and the Pauli exclusion principle. This theory is used to explain the arrangement and properties of molecules beyond what simpler models, like Lewis structures, can provide.

Electron Configuration

Electron configuration helps predict how an atom or molecule will interact with others, based on the distribution of its electrons across different orbitals. In molecules, especially diatomic ones, this configuration can be complex as seen in molecular orbital theory. - **Process for Molecular Electron Configuration**: - Identify the total number of electrons present. - Fill molecular orbitals starting from the lowest energy level, adhering to principles such as Hund's rule. - Assign electrons to bonding or antibonding orbitals as per the energy diagram of the molecule.For example, in For diatomic molecules like \(\) O2\(\), this would involve filling the various sigma \(\sigma\) and pi \(\pi\) orbitals. The specific arrangements determine the molecule's properties, including its magnetic behavior. This structure will dictate whether a molecule faces a magnetic field with paired or unpaired electrons.

Magnetic Properties of Molecules

Magnetic properties of molecules arise from the arrangement of their electrons. When molecules contain only paired electrons, they do not generate a magnetic field in the presence of an external magnet, and are termed "diamagnetic." Conversely, molecules with unpaired electrons are "paramagnetic," as they are attracted to magnetic fields.- **Diamagnetic**: - All electrons are paired. - Example: \(\mathrm{O}_{2}^{2-}\) - Not attracted to magnetic fields.- **Paramagnetic**: - Possess one or more unpaired electrons. - Example: \(\mathrm{O}_{2}\), NO, and \(\mathrm{O}_{2}^{+}\) - Attracted to magnetic fields.Understanding and predicting these properties can clarify how substances behave in different environments, playing a crucial role in fields like materials science and chemistry.