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

Correct statements are (d) 1, 2, and 4.

Step 1: Understanding Bond Order

Bond order is the number of chemical bonds between a pair of atoms. It can be calculated by taking the difference between the number of bonding electrons and antibonding electrons, then dividing by two.

Step 2: Calculating Bond Order for NO

For \(\mathrm{NO}\), the molecular orbital configuration is such that it typically has 10 electrons filling up various molecular orbitals. The bond order is calculated using the formula: \[\text{Bond order} = \frac{\text{Number of bonding electrons} - \text{Number of antibonding electrons}}{2}\] which gives a bond order of 2.5.

Step 3: Calculating Bond Order for NO⁺

For \(\mathrm{NO}^{+}\), there is one less electron compared to \(\mathrm{NO}\) due to the positive charge, making the bond order 3, calculated using the same formula as in Step 2.

Step 4: Calculating Bond Order for O₂

For \(\mathrm{O}_{2}\), the molecular orbital configuration leads to 12 electrons in molecular orbitals, resulting in a bond order of 2 as calculated from traditional methods, but often noted as 1.5 in resonance structures.

Step 5: Calculating Bond Order for CO

For \(\mathrm{CO}\), there are 10 electrons in the molecular orbitals, leading to a calculated bond order of 3, often indicative of a strong triple bond.

Step 6: Comparing Given Statements with Calculations

From the calculations, the bond orders are: \(\mathrm{NO} = 2.5\), \(\mathrm{NO}^{+} = 3\), \(\mathrm{O}_{2} = 2\), \(\mathrm{CO} = 3\). The statement for \(\mathrm{O}_{2}\) is incorrect as it claims the bond order is 1.5 instead of 2. Statements 1, 2, and 4 are correct.

Key Concepts

Molecular Orbital Theory

Molecular orbital theory (MOT) is a fundamental concept in chemistry used to understand the bonding in molecules. Instead of considering each atom's atomic orbitals separately, MOT suggests that when atoms bond, their atomic orbitals combine to form molecular orbitals. These new orbitals belong to the entire molecule rather than any specific atom.

In MOT, electrons are filled into these molecular orbitals following a set of guidelines similar to those used in filling atomic orbitals:

• The Aufbau principle states that electrons will fill the lowest energy molecular orbitals first.
• According to Hund's rule, every orbital in a subshell is singly occupied before any orbital is doubly occupied.
• Pauli's exclusion principle asserts that each orbital can hold a maximum of two electrons with opposite spins.

Understanding how electrons distribute themselves in these molecular orbitals allows chemists to determine the bond order, which is a critical measure of the bond strength and stability.

Chemical Bonding

Chemical bonding refers to the forces that hold atoms together in molecules. It is central to chemistry as it explains how atoms combine to form molecules with new properties. There are three primary types of chemical bonding:

• Ionic Bonding: This occurs when electrons are transferred from one atom to another, resulting in the formation of charged ions. These ions attract each other due to their opposite charges.
• Covalent Bonding: In this type of bonding, atoms share pairs of electrons. It often occurs between non-metal atoms and results in molecules where the shared electrons occupy atomic orbitals belonging to both bonding atoms.
• Metallic Bonding: Metals bond by sharing free electrons that are delocalized over a lattice of atoms, creating a strong bond that accounts for characteristic metallic properties like conductivity.

Chemical bonding determines the molecular structure and is key to understanding the stability and reactivity of different substances. The bond order discussed earlier provides a quantitative measure of the strength and number of bonds between atoms in a molecule.

Molecular Structure

Molecular structure refers to the three-dimensional arrangement of atoms within a molecule. This structure is determined by the chemical bonding of its constituent atoms and the bond order. Understanding molecular structure is vital in chemistry because the shape and geometry of molecules are closely related to their chemical properties and reactivity.

Key concepts associated with molecular structure include:

• Bond Length: This is the distance between the nuclei of two bonded atoms. It usually shortens with increasing bond order, meaning a triple bond is shorter than a double bond.
• Bond Angle: The angle formed between three atoms across at least two bonds. Bond angles help determine the molecular geometry and are essential for predicting molecular shape.
• Resonance Structures: These are different forms of a molecule where the chemical connectivity is the same but the electrons are distributed differently. Resonance contributes to the stability of molecules by allowing electron delocalization.

The molecular structure not only influences basic properties like boiling and melting points but also determines how a molecule will interact with others, playing a crucial role in chemical reactions and interactions.