Problem 4 - A Complete Resource Book in Chemistry for JEE Main

Question

Which one of the following is not paramagnetic? (a) \(\mathrm{NO}\) (b) \(\mathrm{N}^{+}{\underline{\phantom{xx}}}_{2}\) (c) \(\mathrm{CO}\) (d) \(\mathrm{O}_{2}^{-}\)

Step-by-Step Solution

Answer

CO is not paramagnetic; it is diamagnetic.

Step 1: Understanding Paramagnetism

Paramagnetism occurs when a molecule or ion has one or more unpaired electrons. Molecules with unpaired electrons are attracted to magnetic fields, while those with paired electrons are not (diamagnetic). To determine if a molecule is paramagnetic, we need to look at its electronic configuration.

Step 2: Analyzing NO

The molecule \( \text{NO} \) has 15 electrons. Filling in the molecular orbitals, the configuration is \( (\sigma_{1s})^2(\sigma^*_{1s})^2(\sigma_{2s})^2(\sigma^*_{2s})^2(\sigma_{2p_z})^2(\pi_{2p_x, 2p_y})^4(\pi^*_{2p_x,2p_y})^1 \). This configuration shows one unpaired electron, making NO paramagnetic.

Step 3: Analyzing \(\mathrm{N}_2^+\)

The ion \(\mathrm{N}_2^+\) has 13 electrons. Its molecular orbital configuration is \( (\sigma_{1s})^2(\sigma^*_{1s})^2(\sigma_{2s})^2(\sigma^*_{2s})^2(\sigma_{2p_z})^2(\pi_{2p_x, 2p_y})^4(\pi^*_{2p_x, 2p_y})^1 \). This configuration has one unpaired electron, hence \(\mathrm{N}_2^+\) is paramagnetic.

Step 4: Analyzing CO

The molecule \(\mathrm{CO}\) has 14 electrons. Its molecular orbital configuration is \( (\sigma_{1s})^2(\sigma^*_{1s})^2(\sigma_{2s})^2(\sigma^*_{2s})^2(\sigma_{2p_z})^2(\pi_{2p_x, 2p_y})^4 \). All electrons are paired, which makes CO diamagnetic.

Step 5: Analyzing \(\mathrm{O}_2^-\)

The ion \(\mathrm{O}_2^-\) has 17 electrons. Its molecular orbital configuration is \( (\sigma_{1s})^2(\sigma^*_{1s})^2(\sigma_{2s})^2(\sigma^*_{2s})^2(\sigma_{2p_z})^2(\pi_{2p_x, 2p_y})^4(\pi^*_{2p_x, 2p_y})^4(\sigma^*_{2p_z})^1 \). The presence of unpaired electrons means \(\mathrm{O}_2^-\) is paramagnetic.

Key Concepts

Molecular Orbitals

Molecular orbitals (MOs) are a crucial concept for understanding chemical bonding and electron behavior in molecules. Unlike atomic orbitals that apply to single atoms, molecular orbitals describe regions in a molecule where electrons are most likely to be found. This theory allows us to visualize how electrons are distributed across an entire molecule rather than being limited to individual atoms.

• Electrons in bonding molecular orbitals lead to attractive forces holding the atoms together.
• Anti-bonding orbitals have higher energy and can weaken the bond if occupied.
• Non-bonding orbitals do not influence bond strength and are typically localized on one atom.

Molecular orbitals are constructed from combinations of atomic orbitals, and their formations can result in different electron configurations, affecting the molecule's magnetic properties. By analyzing these orbitals, scientists can determine if a molecule is paramagnetic or diamagnetic based on the presence of unpaired electrons.

Electronic Configuration

Electronic configuration provides insight into how electrons are distributed among the molecular orbitals of an atom or molecule. This concept helps us predict the chemical and physical properties of molecules, including their reactivity and magnetic properties.

For instance, in the case of \( \mathrm{NO} \), the molecular electron configuration reveals an unpaired electron due to the presence of a half-filled \( \pi^* \) molecular orbital. This specific arrangement leads to paramagnetism as the molecule is attracted to a magnetic field.

• The filling order follows the Aufbau principle, prioritizing lower energy orbitals first.
• Hund's rule ensures electrons occupy degenerate orbitals singly before pairing up.
• Pauli's exclusion principle means no two electrons in a molecule can have identical quantum numbers.

Understanding these configuration rules allows for precise predictions about molecule features, such as magnetic behavior as seen with \( \text{CO} \), which has paired electrons and shows diamagnetism.

Diamagnetism

Diamagnetism is a property observed in molecules or ions that do not have unpaired electrons in their electron configuration. When external magnetic fields are applied, diamagnetic substances create a weak repulsive effect because their electron pairs generate small internal magnetic fields that oppose the external field.

• All electrons are paired in a diamagnetic substance.
• Diamagnetism occurs in both common materials and complex molecules.
• It is considered a universal property, as even in atoms with unpaired electrons, their paired electron response remains invariably diamagnetic.

Taking \( \text{CO} \) as an example of a diamagnetic molecule, we find that all its electrons are paired, leading to a lack of attraction to magnetic fields. This distinct characteristic differentiates diamagnetic substances from paramagnetic ones, which have unpaired electrons and are attracted to magnetic fields.