Problem 4 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

If the magnetic moment of a dioxygen species is \(1.73\) B.M, it may be: [Main Jan. 09, 2020 (I)] (a) \(\mathrm{O}_{2}^{-}\)or \(\mathrm{O}_{2}^{+}\) (b) \(\mathrm{O}_{2}\) or \(\mathrm{O}_{2}^{+}\) (c) \(\mathrm{O}_{2}\) or \(\mathrm{O}_{2}^{-}\) (d) \(\mathrm{O}_{2}, \mathrm{O}_{2}^{-}\)or \(\mathrm{O}_{2}^{+}\)

Step-by-Step Solution

Answer

(a) \(\mathrm{O}_{2}^{-}\) or \(\mathrm{O}_{2}^{+}\).

Step 1: Understanding Magnetic Moment

The magnetic moment of a species in Bohr Magneton (B.M.) is a measure of its unpaired electrons. A magnetic moment of \(1.73\) B.M. is characteristic of one unpaired electron, as calculated by the formula \(\mu = \sqrt{n(n+2)}\) where \(n\) is the number of unpaired electrons.

Step 2: Calculate for One Unpaired Electron

For one unpaired electron, the magnetic moment is calculated as follows: \(\mu = \sqrt{1(1+2)} = \sqrt{3} \approx 1.73\, \text{B.M.}\). This confirms that \(1.73\, \text{B.M.}\) corresponds to one unpaired electron.

Step 3: Determine Electron Configurations of Dioxygen Species

Examine each potential dioxygen species: \(\mathrm{O}_{2}\), \(\mathrm{O}_{2}^{-}\), \(\mathrm{O}_{2}^{+}\). \(\mathrm{O}_{2}\) has two unpaired electrons in its \(\pi^*\) antibonding molecular orbitals according to molecular orbital theory, \(\mathrm{O}_{2}^{-}\) (superoxide) has one unpaired electron, and \(\mathrm{O}_{2}^{+}\) (dioxygenyl) has also one unpaired electron.

Step 4: Identify the Correct Options

Given that a magnetic moment of \(1.73\, \text{B.M.}\) corresponds to one unpaired electron, the species \(\mathrm{O}_{2}^{-}\) and \(\mathrm{O}_{2}^{+}\) can both display this moment. Therefore, the correct answer is the option that includes these species.

Key Concepts

Unpaired Electrons

Unpaired electrons play a crucial role in determining the magnetic properties of a molecule. If an electron is unpaired, it means that there is no other electron in the molecule with the same spin, leading to magnetic characteristics. In magnetic terms, the presence of unpaired electrons facilitates a net magnetic moment. This concept is pivotal in understanding why certain molecules exhibit magnetism while others do not.

Some key points to remember about unpaired electrons:

• Unpaired electrons create a magnetic field, leading to paramagnetism.
• The more unpaired electrons a molecule has, the stronger its magnetic field.
• The magnetic moment (\(\mu\)) of a molecule increases with the number of unpaired electrons, calculated using the formula \(\mu = \sqrt{n(n+2)}\), where \(n\) is the number of unpaired electrons.

The dioxygen molecule (\(\mathrm{O}_{2}\)) is an example of a molecule with unpaired electrons, showcasing why it is paramagnetic and exhibits distinctive magnetic properties.

Bohr Magneton

The Bohr Magneton (B.M.) is a physical constant that specifies the natural unit of the magnetic moment. It's fundamentally important in expressing the magnetic moment of atoms, ions, or molecules. Named after Niels Bohr, the Bohr Magneton is especially relevant in quantum physics and chemistry when calculating the magnetic properties at an atomic scale.

Here are some highlights about the Bohr Magneton:

• It represents the magnetic moment quantum of an electron due to its orbital or spin motion.
• Measured in units of magnetic dipole moment, a typical value for electrons is approximately \(9.274 \times 10^{-24}\) A⋅m².
• The Bohr Magneton is a reference for comparing the magnetic moments of molecules, facilitating the quantification of magnetism in paramagnetic species.

In the scenario of the problem, the magnetic moment of \(1.73\) B.M indicates a specific number of unpaired electrons, helping to narrow down the possible dioxygen species.

Molecular Orbital Theory

Molecular Orbital (MO) Theory explains the formation, nature, and properties of molecules by combining atomic orbitals to form molecular orbitals. The theory provides a model that can predict the electronic structure of molecules.

According to MO Theory:

• Electrons are not assigned to individual bonds between atoms. Instead, they are considered to be delocalized throughout the molecule.
• Molecular orbitals are formed by the linear combination of atomic orbitals.
• These molecular orbitals are classified as bonding or antibonding, which determine the stability and magnetic properties of the molecule.

In the case of dioxygen (\(\mathrm{O}_{2}\)), MO Theory helps explain why it has two unpaired electrons, occupying the \(\pi^*\) antibonding orbitals, which results in its paramagnetic behavior. For species like \(\mathrm{O}_{2}^{-}\) and \(\mathrm{O}_{2}^{+}\), understanding their molecular orbital configuration reveals which of them have one unpaired electron, aligning with the given magnetic moment.