Problem 201 - A Complete Resource Book in Chemistry for JEE Main

Question

Which of the following molecules/ions does not contain unpaired electrons? (a) \(\mathrm{O}_{2}^{2}\) (b) \(\mathrm{B}_{2}\) (c) \(\mathrm{N}_{2}\) (d) \(\mathrm{O}_{2}\)

Step-by-Step Solution

Answer

 extrm{O}_{2}^{2-} and  extrm{N}_{2} do not contain unpaired electrons.

Step 1: Understand the problem

We need to find which molecule or ion among the given options does not have unpaired electrons. Unpaired electrons in a molecule's molecular orbitals are a key factor in its magnetic properties. Molecules with all electrons paired are diamagnetic, while those with unpaired electrons are paramagnetic.

Step 2: Analyzing oxygen ion  extrm{O}_{2}^{2-}

For  extrm{O}_{2}^{2-} (the peroxide ion), let's apply molecular orbital theory. The addition of two electrons to  extrm{O}_{2} fills its  extrm{* extrm{2p}} antibonding orbitals. As a result, the  extrm{O}_{2}^{2-} ion has all its electrons paired, making it diamagnetic.

Step 3: Analyzing boron molecule  extrm{B}_{2}

For  extrm{B}_{2}, the molecular orbital theory shows that it has two  extrm{* extrm{2p}} orbitals occupied with unpaired electrons. Hence,  extrm{B}_{2} is paramagnetic.

Step 4: Analyzing nitrogen molecule  extrm{N}_{2}

For  extrm{N}_{2}, all electrons fill bonding orbitals up to  extrm{ extrm{2p}}, leaving none unpaired. This makes nitrogen very stable and diamagnetic.

Step 5: Analyzing oxygen molecule  extrm{O}_{2}

For  extrm{O}_{2}, there are two unpaired electrons in the  extrm{* extrm{2p}} antibonding orbitals. This results in paramagnetism for molecular oxygen.

Key Concepts

Diamagnetism

Diamagnetism is a term used to describe materials that show no attraction to a magnetic field and, in fact, may be slightly repelled by it. This phenomenon occurs in molecules where all electrons are paired. Understanding diamagnetism involves grasping why electron pairing is so vital. Electrons are negatively-charged particles that exist in atomic or molecular orbitals, and they come with a property called "spin." The spin can be likened to tiny magnetic fields. When two electrons occupy the same orbital, they pair up with opposite spins. This opposite orientation cancels out their respective magnetic fields, leading to a situation where the molecule does not have any net magnetic moment. In the context of chemical structures, such as the peroxide ion

• The addition of electrons fills the antibonding orbitals.
• When these orbitals are filled, all electrons achieve paired status.
• This results in a diamagnetic molecule, which is unaffected by external magnetic fields.

This concept is crucial when predicting the behavior of different ions and molecules in magnetic fields.

Paramagnetism

Paramagnetism describes substances that are attracted into a magnetic field. It occurs in materials where there are one or more unpaired electrons. These unpaired electrons contribute to a net magnetic moment, making the substance responsive to magnetic fields. Unlike diamagnetic materials, paramagnetic molecules have a permanent magnetic moment due to the presence of these unpaired electrons. Let’s explore why

• Unpaired electrons mean their individual tiny magnetic dipoles are not canceled.
• As a result, the cumulative magnetic moment is non-zero.
• When placed within a magnetic field, these materials align according to the field orientation, indicating attraction to the field.

For example, molecular oxygen (

• Has two unpaired electrons in its antibonding orbitals.
• This trait aligns its magnetic dipoles with external fields.
• Thus, it exhibits paramagnetism.

Understanding paramagnetism helps in recognizing materials that will demonstrate noticeable magnetic behavior in response to external fields.

Electron Pairing

Electron pairing is a fundamental concept used to predict the magnetic behavior of molecules. Electrons, behaving as spinning charges, create local magnetic moments. When evaluating electron pairing, it is essential to consider how these electrons occupy molecular orbitals. Pairing happens when electrons share the same orbital by residing with opposing spins, effectively canceling out each other’s magnetic effects. This electronic arrangement results in no net magnetic moment for the molecule, hence affecting its magnetic properties. Key points to understand electron pairing include:

• Molecules with all electrons paired exhibit no net magnetic moment and are typically diamagnetic.
• Unpaired electrons contribute to a net magnetic moment, causing paramagnetism.
• In the atomic or molecular orbital scheme, if electrons can occupy all lower energy levels fully, the stability is maximized, and electron unpairing is minimized.

In practical applications, electron pairing is used to predict how molecules and ions interact with magnetic fields and to understand their stability and reactivity in chemical reactions.