Problem 14 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

Which of the following is paramagnetic ? [Main Online April 8, 2017] (a) \(\mathrm{NO}^{+}\) (b) \(\mathrm{CO}\) (c) \(\mathrm{O}_{2}^{2-}\) (d) \(\mathrm{B}_{2}\)

Step-by-Step Solution

Answer

B\(_2\) is paramagnetic due to unpaired electrons.

Step 1: Understand Paramagnetic Substances

Paramagnetic substances have one or more unpaired electrons, which means they are attracted to magnetic fields. We will check the electronic configurations of each molecule to find unpaired electrons.

Step 2: Examine \\( \mathrm{NO}^{+} \\)

The neutral molecule, NO, has 15 electrons. Removing one electron for NO\(^{+}\) gives 14 electrons. The molecular orbital configuration of NO\(^{+}\) is: \\( \sigma(1s)^{2} \sigma^{*}(1s)^{2} \sigma(2s)^{2} \sigma^{*}(2s)^{2} \sigma(2p_z)^{2} \pi(2p_x)^{2} = \pi(2p_y)^{2} \sigma^{*}(2p_z)^{2} \). All electrons are paired, making NO\(^{+}\) diamagnetic.

Step 3: Examine \\( \mathrm{CO} \\)

Carbon monoxide has 14 electrons. The molecular orbital configuration is: \\( \sigma(1s)^{2} \sigma^{*}(1s)^{2} \sigma(2s)^{2} \sigma^{*}(2s)^{2} \pi(2p_x)^{2} \pi(2p_y)^{2} \sigma(2p_z)^{2} \). All electrons are paired, so CO is diamagnetic.

Step 4: Examine \\( \mathrm{O}_{2}^{2-} \\)

The neutral O\( _2 \) molecule has 16 electrons, so O\( _2^{2-} \) has 18 electrons. The molecular orbital configuration is: \\( \sigma(1s)^{2} \sigma^{*}(1s)^{2} \sigma(2s)^{2} \sigma^{*}(2s)^{2} \sigma(2p_z)^{2} \pi(2p_x)^{2} \pi(2p_y)^{2} \pi^{*}(2p_x)^{2} \pi^{*}(2p_y)^{2} \). All the electrons are paired, so O\( _2^{2-} \) is diamagnetic.

Step 5: Examine \\( \mathrm{B}_{2} \\)

Diatomic boron (B\( _2 \)) has 10 electrons. The molecular orbital configuration is: \\( \sigma(1s)^{2} \sigma^{*}(1s)^{2} \sigma(2s)^{2} \sigma^{*}(2s)^{2} \pi(2p_x)^{1} \pi(2p_y)^{1} \). There are two unpaired electrons, which makes B\( _2 \) paramagnetic.

Key Concepts

Molecular Orbital Theory

Molecular Orbital (MO) Theory is a fundamental concept that helps us understand how atoms combine to form molecules. According to this theory, atomic orbitals combine to create new orbitals called molecular orbitals. These molecular orbitals belong to the entire molecule rather than a single atom.

There are two main types of molecular orbitals: bonding and antibonding. Bonding orbitals are lower in energy and help to hold the molecule together. In contrast, antibonding orbitals are higher in energy and can destabilize the molecule if occupied.

• Bonding Orbitals: These arise from the constructive interference of atomic orbitals, which lead to electron sharing.
• Antibonding Orbitals (designated by *): These result from destructive interference, causing increased electron repulsion.

Understanding which electrons fill which molecular orbitals is key to predicting whether a substance is paramagnetic or diamagnetic.

Electronic Configuration

The electronic configuration of a molecule tells us how the electrons are distributed among the various molecular orbitals. This configuration plays a crucial role in determining the magnetic properties of a substance. In Molecular Orbital Theory, electronic configurations are written by listing the occupied molecular orbitals and their electron counts.

For example, when examining the electronic configurations of molecules like CO, NO\(^{+}\), O\(_2^{2-}\), and B\(_2\), as shown in the Original Solution, understanding these configurations helps us determine their magnetism.

• In CO, the electrons are fully paired, leading to a diamagnetic property.
• NO\(^{+}\) also has paired electrons in its molecular orbitals, making it diamagnetic.
• O\(_2^{2-}\) has 18 electrons, all paired, resulting in a diamagnetic nature.
• B\(_2\), however, has unpaired electrons in its \(\pi(2p_x)\) and \(\pi(2p_y)\) orbitals, making it paramagnetic.

Unpaired Electrons

Unpaired electrons are electrons that occupy an orbital alone, without a second electron of opposite spin. The presence of unpaired electrons in a substance is what causes paramagnetism. When electrons are unpaired, the substance can be attracted to magnetic fields due to the magnetic moment created by these electrons.

The population of these electrons in molecular orbitals can be decisive for their magnetic properties.

• In B\(_2\), each \(\pi(2p_x)\) and \(\pi(2p_y)\) orbital contains one unpaired electron, which is responsible for its paramagnetic nature.
• Molecules like CO, NO\(^{+}\), and O\(_2^{2-}\) do not have unpaired electrons in their ground state electronic configurations, which is why they are diamagnetic.

Identifying unpaired electrons through electronic configuration helps in understanding whether a molecule is paramagnetic or diamagnetic.