Problem 42 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

The molecule having one unpaired electron is: (a) NO (b) \(\mathrm{CO}\) (c) \(\mathrm{CN}^{-}\) (d) \(\mathrm{O}_{2}\)

Step-by-Step Solution

Answer

NO is the molecule with one unpaired electron.

Step 1: Understanding the Molecular Orbital (MO) Theory

First, we need to determine the number of unpaired electrons in each molecule. Understanding MO theory helps in this assessment. MO theory explains the bonding in molecules in terms of molecular orbitals which are formed by the linear combination of atomic orbitals.

Step 2: Determine the Electron Configuration for NO

NO has a total of 15 electrons (7 from N and 8 from O). Filling the molecular orbitals according to MO theory: \[ (\sigma_{1s})^2 (\sigma^{*}_{1s})^2 (\sigma_{2s})^2 (\sigma^{*}_{2s})^2 (\sigma_{2p_z})^2 (\pi_{2p_x})^2 (\pi_{2p_y})^2 (\pi^{*}_{2p_x})^1. \]This leaves one unpaired electron in one of the \(\pi^{*}_{2p}\) orbitals.

Step 3: Analyze Electron Configuration for CO

CO has a total of 14 electrons (6 from C and 8 from O). Filling according to MO theory gives:\[ (\sigma_{1s})^2 (\sigma^{*}_{1s})^2 (\sigma_{2s})^2 (\sigma^{*}_{2s})^2 (\sigma_{2p_z})^2 (\pi_{2p_x})^2 (\pi_{2p_y})^2. \]All electrons are paired in CO.

Step 4: Analyze Electron Configuration for CN⁻

CN⁻ has a total of 14 electrons (6 from C, 7 from N, and 1 added for the negative charge). Its 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 in CN⁻.

Step 5: Analyze Electron Configuration for O₂

O₂ has a total of 16 electrons (8 from each O). Its configuration according to MO theory is:\[ (\sigma_{1s})^2 (\sigma^{*}_{1s})^2 (\sigma_{2s})^2 (\sigma^{*}_{2s})^2 (\sigma_{2p_z})^2 (\pi_{2p_x})^2 (\pi_{2p_y})^2 (\pi^{*}_{2p_x})^1 (\pi^{*}_{2p_y})^1. \]There are two unpaired electrons in two different \(\pi^{*}_{2p}\) orbitals.

Step 6: Conclusion: Identify the Molecule with One Unpaired Electron

From the above steps, the molecule with one unpaired electron is NO. CO and CN⁻ have no unpaired electrons, while O₂ has two unpaired electrons.

Key Concepts

Unpaired Electrons

When we talk about unpaired electrons, we're focusing on electrons in an atom or molecule that do not have a partner with opposite spin in the same orbital. These unpaired electrons often play a crucial role in determining the chemical and magnetic properties of a molecule. For example, unpaired electrons are responsible for the paramagnetic nature of a substance. Knowing whether a molecule has unpaired electrons is important:

• Unpaired electrons can cause substances to be attracted to magnetic fields.
• They often participate actively in chemical reactions.

According to Molecular Orbital (MO) Theory, when electrons fill into molecular orbitals, they do so in a way that minimizes energy (similar to the Aufbau principle used in atomic chemistry). By assessing the electron configuration using MO theory, we can determine if unpaired electrons are present in a molecule. In our exercise, only nitrogen monoxide (NO) and oxygen (O₂) had unpaired electrons present.

Electron Configuration

Electron configuration describes how electrons are distributed amongst the orbital shells and subshells of a molecule according to the Molecular Orbital Theory. By understanding the electron configuration, one can deduce the chemical characteristics and reactivity of a molecule. To determine the electron configuration of a molecule, follow these steps:

• Count the total number of electrons in the molecule by summing the atomic numbers of all atoms involved.
• Use MO diagrams to arrange these electrons in increasing energy levels.
• Ensure compliance with the Pauli exclusion principle and Hund’s rule during electron filling.

For NO in the given exercise, the electron configuration is \[ (\sigma_{1s})^2 (\sigma^{*}_{1s})^2 (\sigma_{2s})^2 (\sigma^{*}_{2s})^2 (\sigma_{2p_z})^2 (\pi_{2p_x})^2 (\pi_{2p_y})^2 (\pi^{*}_{2p_x})^1 \]This shows one unpaired electron, indicating the molecule's paramagnetic nature.

Molecular Bonding

Molecular bonding refers to the interactions that hold molecules together. In the context of Molecular Orbital Theory, bonds between atoms form when atomic orbitals overlap to create molecular orbitals, which can accommodate electrons from both participating atoms. The type and number of bonds can greatly influence the physical and chemical properties of a molecule.Key points about molecular bonding include:

• Bonds are classified as either bonding or antibonding. Electrons in bonding orbitals stabilize a molecule, whereas electrons in antibonding orbitals can destabilize it.
• The bond order, calculated as \( (\text{number of electrons in bonding orbitals} - \text{number of electrons in antibonding orbitals}) / 2 \), helps predict the stability of the molecule.
• Molecular bonding gives insight into the magnetic properties of molecules. If there are unpaired electrons in molecular orbitals, the substance may exhibit paramagnetism.

In our exercise, although NO and O₂ have unpaired electrons, their bond orders, determined through MO configurations, are indicators of their specific molecular stabilities and characteristics.