Problem 125 - A Complete Resource Book in Chemistry for JEE Main

Question

Consider the following statements: 1\. the bond order of \(\mathrm{NO}\) is \(2.5\) 2\. the bond order of \(\mathrm{NO}^{+}\)is 3 3\. the bond order of \(\mathrm{O}_{2}\) is \(1.5\) 4\. the bond order of \(\mathrm{CO}\) is 3 Which of these statements are correct? (a) 1,2 and 3 (b) 2,3 and 4 (c) 1,3 and 4 (d) 1,2 and 4

Step-by-Step Solution

Answer

The correct answer is (d) 1, 2 and 4.

Step 1: Understanding Bond Order

Bond order refers to the number of chemical bonds between a pair of atoms. It can be calculated using molecular orbital theory, where bond order = (number of bonding electrons - number of antibonding electrons) / 2.

Step 2: Calculate Bond Order of NO

The molecular orbital configuration for NO can be written as: \[\sigma(2s)^2, \sigma^*(2s)^2, \pi(2p)^4, \sigma(2p)^2, \pi^*(2p)^1\]Using the formula, Bond Order = (number of bonding electrons - number of antibonding electrons)/2:Bond Order for NO = (8 - 3)/2 = 2.5.

Step 3: Calculate Bond Order of NO+

For NO⁺, remove one electron from the antibonding orbital:\[\sigma(2s)^2, \sigma^*(2s)^2, \pi(2p)^4, \sigma(2p)^2\]Bond Order = (number of bonding electrons - number of antibonding electrons) / 2:Bond Order for NO⁺ = (8 - 2)/2 = 3.

Step 4: Calculate Bond Order of O2

The configuration for O₂ can be given by:\[\sigma(2s)^2, \sigma^*(2s)^2, \sigma(2p)^2, \pi(2p)^4, \pi^*(2p)^2\]Bond Order for O₂ = (number of bonding electrons - number of antibonding electrons) / 2:Bond Order = (10 - 6) / 2 = 2.

Step 5: Calculate Bond Order of CO

For CO, the electron configuration can be approximated by:\[\sigma(2s)^2, \sigma^*(2s)^2, \pi(2p)^4, \sigma(2p)^2\]Bond Order for CO = (number of bonding electrons - number of antibonding electrons) / 2:Bond Order = (10 - 4) / 2 = 3.

Step 6: Compare Results with Statements

1. Bond order of NO is 2.5 (Correct) 2. Bond order of NO⁺ is 3 (Correct) 3. Bond order of O₂ is 1.5 (Incorrect, correct order is 2) 4. Bond order of CO is 3 (Correct) The correct statements are 1, 2, and 4.

Key Concepts

Molecular Orbital Theory

Molecular Orbital (MO) Theory is a fundamental concept that helps us understand the behavior of electrons in molecules. Instead of thinking about individual atoms forming bonds, MO Theory considers molecules as whole entities in which atomic orbitals combine to form molecular orbitals. These molecular orbitals are spread over the entire molecule and can hold electrons that influence molecular stability. Molecular orbitals are categorized into two types: bonding and antibonding orbitals. Bonding orbitals are lower in energy and contribute to the stability of a molecule, while antibonding orbitals are higher in energy and can destabilize a molecule if occupied. Electrons fill these orbitals starting from the lowest energy levels, following principles similar to atomic orbitals like the Aufbau Principle, Pauli Exclusion Principle, and Hund’s Rule. MO Theory is particularly powerful in explaining magnetic and spectroscopic properties of molecules. It also enables us to calculate the bond order, which gives insights into the strength, length, and stability of chemical bonds.

Chemical Bonding

Chemical bonding is the force that holds atoms together in a molecule. It involves the attraction between atoms or ions and can occur in various forms such as ionic, covalent, and metallic bonds. Understanding the nature of chemical bonds is essential for explaining how molecules are structured and how they interact with one another. The Key Types of Bonds:

• Ionic Bonds: These are formed when electrons are transferred from one atom to another, resulting in oppositely charged ions that attract each other.
• Covalent Bonds: Occur when atoms share pairs of electrons. The strength and number of shared pairs determine the bond order.
• Metallic Bonds: Involve a "sea of electrons" that are free to move around, which allows metals their characteristic conductivity and malleability.

Bonding determines the physical and chemical properties of substances and is crucial in the molecule formation from atoms.

NO Bond Order

Nitric oxide (NO) is an interesting molecule with mixed properties. Determining its bond order involves using the concepts from Molecular Orbital Theory. The bond order tells us how strong and stable the bond is between the nitrogen and oxygen in the molecule.For NO, the molecular orbital configuration is as follows: \[\sigma(2s)^2, \sigma^*(2s)^2, \pi(2p)^4, \sigma(2p)^2, \pi^*(2p)^1\].To calculate bond order, use the formula:\[\text{Bond Order} = \frac{\text{number of bonding electrons} - \text{number of antibonding electrons}}{2}\]In NO, there are 8 bonding electrons and 3 antibonding electrons, which gives a bond order of:\[\text{Bond Order for NO} = \frac{8 - 3}{2} = 2.5\]This fractional bond order indicates a partial bond character and reflects the strength and reactivity of the NO molecule.

NO⁺ Bond Order

The molecule NO⁺ or nitrosonium ion is a cation formed by removing an electron from NO. This change affects the molecular orbital configuration and consequently the bond order.For NO⁺, the molecular configuration becomes simpler:\[\sigma(2s)^2, \sigma^*(2s)^2, \pi(2p)^4, \sigma(2p)^2\].Using the bond order formula again:\[\text{Bond Order for NO⁺} = \frac{8 - 2}{2} = 3\]This bond order of 3 indicates a stronger bond compared to NO. The removal of the antibonding electron enhances the bond's stability, showing how changing the electron count can significantly impact molecular properties.

O₂ Bond Order

Oxygen molecule (O₂) demonstrates another application of bond order within the framework of Molecular Orbital Theory. The calculation involves understanding how electrons are distributed across molecular orbitals.For O₂, the molecular orbital configuration is:\[\sigma(2s)^2, \sigma^*(2s)^2, \sigma(2p)^2, \pi(2p)^4, \pi^*(2p)^2\].Using the bond order formula:\[\text{Bond Order for O₂} = \frac{10 - 6}{2} = 2\]The bond order of 2 reflects a double bond character in the O₂ molecule, explaining its relative stability as a diatomic element in nature. This calculation contrasts with other exercises where the incorrect bond order of 1.5 might be mistakenly used, highlighting the need for careful consideration of electron distributions.

CO Bond Order

Carbon monoxide (CO) is a small but chemically significant molecule with a notable bond order that contributes to its properties.The molecular orbital configuration for CO is:\[\sigma(2s)^2, \sigma^*(2s)^2, \pi(2p)^4, \sigma(2p)^2\].For calculating bond order:\[\text{Bond Order for CO} = \frac{10 - 4}{2} = 3\]This bond order of 3 signifies a triple bond between carbon and oxygen, one of the strongest types of bonds. This strength accounts for CO's stability, reactivity, and the observed toxicity, as the bond strength makes it challenging for organisms to process the compound efficiently. Understanding CO's bond order underscores its role in chemistry and biology as a molecule worth handling cautiously.