Problem 106 - A Complete Resource Book in Chemistry for JEE Main

Question

Bond order of nitric oxide is (a) 1 (b) \(2.5\) (c) 2 (d) \(1.5\)

Step-by-Step Solution

Answer

The bond order of nitric oxide is 2.5, which is option (b).

Step 1: Write the electronic configuration of NO

Nitric oxide (NO) consists of nitrogen and oxygen atoms. Begin by writing the electronic configuration for the molecular orbitals of NO. Nitrogen has 7 electrons, and oxygen has 8 electrons, totaling 15 electrons for NO.

Step 2: Fill the molecular orbitals

Based on the molecular orbital theory, fill the molecular orbitals with the 15 electrons. The order is as follows: - \(\sigma_{1s}\) and \(\sigma_{1s}^*\): full- \(\sigma_{2s}\) and \(\sigma_{2s}^*\): full- \ (\pi_{2p_x}=\pi_{2p_y}) \: 4 electrons- \(\sigma_{2p_z}\): 2 electrons Electrons fill following Hund's rule and Hund's rule of maximum multiplicity.

Step 3: Calculate the bond order

Use the formula for bond order: \[ \text{Bond Order} = \frac{1}{2} \times (\text{Number of bonding electrons} - \text{Number of antibonding electrons}) \]For NO, the number of bonding electrons is 10, and the number of antibonding electrons is 5. Thus, the bond order is:\[ \text{Bond Order} = \frac{1}{2} \times (10 - 5) = \frac{5}{2} = 2.5 \]

Step 4: Compare bond order with options

Compare the calculated bond order of 2.5 with the given options. The correct option corresponds to the bond order we've calculated.

Key Concepts

Molecular Orbital Theory

Molecular Orbital Theory is like a bridge that helps us connect atoms to form molecules. It explains how we can imagine electrons in molecules in a similar way to how we imagine them around a single atom. Instead of thinking of electrons belonging to individual atoms, we imagine them spread out over the entire molecule. These electrons occupy molecular orbitals, which can extend over several atoms within a molecule.
Molecular orbitals are formed from the combination of atomic orbitals. Just like atomic orbitals, they have different energy levels. The theory states that when atomic orbitals combine, they form new orbitals: bonding and antibonding orbitals. Bonding orbitals have lower energy and result in more stability, meaning they're like a cozy spot for electrons. Antibonding orbitals, on the other hand, are higher in energy and less stable.
This theory helps us predict the behavior of electrons in molecules and thereby understand a molecule's structure, stability, and magnetic properties. For example, in the case of nitric oxide (NO), we use the molecular orbital theory to calculate properties like bond order, which tells us how strong a bond is.

Nitric Oxide

Nitric Oxide, often referred to as NO, is a molecule composed of one nitrogen atom and one oxygen atom. You could think of it as a small, yet important molecule in the world of chemistry and biology. Despite its simplicity, NO plays a crucial role in many biological processes and is even used medically.

• In our bodies, nitric oxide acts as a signaling molecule. It helps vessels expand, so it affects blood pressure regulation.
• It's also involved in immune responses where it can help kill invading pathogens.

For chemists, studying NO involves understanding its electronic structure. Knowing the number of electrons and how they're arranged in molecular orbitals gives us insights into the molecule's behavior. In the case of NO, the electrons total to 15, derived from its nitrogen and oxygen components. This arrangement and the distribution of electrons across bonding and antibonding orbitals help determine NO’s bond order. The bond order offers a glimpse into how tightly the nitrogen and oxygen atoms are bound together.

Bonding and Antibonding Electrons

When atomic orbitals combine to form molecular orbitals, we classify them as either bonding or antibonding. Bonding orbitals are like safe havens where electrons feel most comfortable, and their presence here makes the molecule more stable. Antibonding orbitals are the opposite; they make the molecule feel uneasy or quite unstable.

• Bonding electrons decrease the energy of the molecule, leading to stronger bonds.
• Antibonding electrons increase the molecule's energy, making bonds weaker if populated.

In mathematical terms, we calculate the bond order to understand this dynamic. The formula is a simple one - it takes the difference in number between bonding and antibonding electrons:\[ \text{Bond Order} = \frac{1}{2} \times (\text{Number of bonding electrons} - \text{Number of antibonding electrons}) \]This formula acts as an indicator of the molecule’s stability. For nitric oxide (NO), we find 10 bonding electrons and 5 antibonding electrons, leading to a bond order of 2.5. This value tells us there's a relatively strong bond between nitrogen and oxygen, balancing both stability and unsteadiness due to the presence of antibonding electrons.