Problem 70 - A Complete Resource Book in Chemistry for JEE Main

Question

Which of the following is diamagnetic? (a) \(\mathrm{H}_{2}^{+}\) (b) \(\mathrm{O}_{2}\) (c) \(\mathrm{Li}_{2}\) (d) \(\mathrm{He}_{2}^{+}\)

Step-by-Step Solution

Answer

\\(\mathrm{Li}_{2}\\) is diamagnetic because all its electrons are paired.

Step 1: Understanding Diamagnetism

Diamagnetism is a property of materials that have all their electrons paired. Such substances are weakly repelled by a magnetic field. To determine which molecule is diamagnetic, identify which one has all paired electrons in its molecular orbitals.

Step 2: Examine \\(\mathrm{H}_{2}^{+}\\)

The \(\mathrm{H}_{2}^{+}\) ion has one electron, so it has an unpaired electron. Thus, it is paramagnetic.

Step 3: Examine \\(\mathrm{O}_{2}\\)

Oxygen (\(\mathrm{O}_{2}\)) has 12 electrons in its molecular orbital configuration. The outermost molecular orbitals are \(\pi^*_{2p}\), each with one unpaired electron, making it paramagnetic.

Step 4: Examine \\(\mathrm{Li}_{2}\\)

\(\mathrm{Li}_{2}\) has a total of 6 electrons. In its molecular orbital diagram, all electrons are paired, making \(\mathrm{Li}_{2}\) a diamagnetic molecule.

Step 5: Examine \\(\mathrm{He}_{2}^{+}\\)

\(\mathrm{He}_{2}^{+}\) has 3 electrons. The molecular orbital configuration results in one unpaired electron in a \(\sigma_{1s}\) molecular orbital, indicating paramagnetism.

Key Concepts

Molecular Orbital Theory

Molecular Orbital (MO) Theory is a fundamental concept used to describe the electronic structure of molecules. It helps us understand how the atomic orbitals of bonding atoms combine to form molecular orbitals, which are spread over the entire molecule.
In essence, molecular orbitals can be thought of as the wave-like solutions to the Schrödinger equation for a molecule, similar to how atomic orbitals describe electrons in isolated atoms. These orbitals can be bonding, antibonding, or non-bonding:

• Bonding Orbitals: These are lower in energy than the atomic orbitals that combined to form them, and they help stabilize the molecule.
• Antibonding Orbitals: These are higher in energy and can destabilize a molecule if occupied by electrons.
• Non-bonding Orbitals: These have energy equivalent to the atomic orbitals and do not contribute directly to bonding.

Understanding a molecule's MO configuration helps us predict its bonding behavior, magnetic properties, and more. For example, in the exercise, we determine whether molecules like \(\mathrm{Li}_2\) or \(\mathrm{O}_2\) are diamagnetic by examining their MO diagrams for paired and unpaired electrons.

Paramagnetism

Paramagnetism occurs in substances with unpaired electrons. Unlike diamagnetic materials, which are repelled by magnetic fields, paramagnetic materials are attracted to magnetic fields.
This attraction is due to the unpaired electrons being able to align their spins with an external magnetic field. Here's what happens:

• Unpaired Electrons: Electrons that are alone in an orbital contribute to magnetic properties due to their spin.
• Magnetic Alignment: These spins can line up with a magnetic field, enhancing the magnetic effect.
• Temporary Magnetization: The magnetism disappears once the external field is removed since the electron spins can return to random orientations.

For instance, in the original exercise, \(\mathrm{H}_2^+\), \(\mathrm{O}_2\), and \(\mathrm{He}_2^+\) each have unpaired electrons, and hence, demonstrate paramagnetic behavior. The presence of these unpaired electrons in molecular orbitals can be inferred from the MO theory.

Electron Pairing

Electron pairing is a foundational concept in chemistry that helps to explain the stability and reactivity of molecules. Electrons in atoms and molecules organize themselves to minimize energy, often pairing up in accordance with the Pauli Exclusion Principle.
In a given molecular orbital or atomic orbital, electrons prefer to pair their spins in opposite directions:

• Spin Pairing: Each pair consists of one electron with a spin of +1/2 and another with a spin of -1/2. This pairing minimizes magnetic interactions.
• Increased Stability: Paired electrons contribute to a more stable energy state and can lead to diamagnetic properties when all electrons are paired in a molecule.

Electrons prefer to occupy orbitals individually if possible (Hund's Rule), but when forced to pair due to space constraints or energy levels, they do so in a way that lowers the system’s overall energy. In our initial exercise, \(\mathrm{Li}_2\) is diamagnetic due to all electrons being paired in its molecular orbitals.