Question

The bond order of a molecule is given by (1) Half the difference between number of bonding electrons and anti-bonding electrons. (2) The difference between the number of bonding electrons and anti-bonding electrons. (3) Twice the difference between the number of bonding electrons and anti- bonding electrons. (4) The total number of bonding electrons.

Short answer

Option (1) is correct.

Step-by-step solution

Identify the key concept

The bond order of a molecule is typically calculated using molecular orbital theory, which involves bonding and anti-bonding electrons.

Recall the bond order formula

The bond order can be calculated using the formula: \[ \text{Bond Order} = \frac{1}{2} (\text{Number of Bonding Electrons} - \text{Number of Anti-bonding Electrons}) \]

Analyze the options

Given the formula, the answer choices need to be evaluated. Let's look at them: 1. Half the difference between number of bonding electrons and anti-bonding electrons.2. The difference between the number of bonding electrons and anti-bonding electrons.3. Twice the difference between the number of bonding electrons and anti-bonding electrons.4. The total number of bonding electrons.

Match the correct formula

Compare each option to the bond order formula: \[ \text{Bond Order} = \frac{1}{2} (\text{Number of Bonding Electrons} - \text{Number of Anti-bonding Electrons}) \]. Option (1) matches this formula precisely.

Key concepts

molecular orbital theory

Molecular Orbital Theory (MOT) is a fascinating approach in chemistry that helps us understand the behavior of electrons in molecules. Instead of thinking of electrons as being located between pairs of atoms, MOT considers electrons to be in 'molecular orbitals' that extend over the entire molecule.
According to this theory, when atoms combine to form a molecule, their atomic orbitals combine to form molecular orbitals. These molecular orbitals can be either bonding or anti-bonding.
Bonding orbitals are lower in energy and help hold the atoms together, while anti-bonding orbitals are higher in energy and can actually weaken the bond if they are occupied by electrons.

bonding electrons

Bonding electrons are those found in molecular orbitals that contribute to the bond between atoms. These electrons are located in orbitals that are lower in energy compared to the original atomic orbitals.
They work to 'glue' the atoms together, providing stability to the molecule. In the context of calculating bond order, the number of bonding electrons plays a crucial role because it is used in the formula that determines the bond order.
For example, in the molecule of nitrogen gas (N₂), there are 10 bonding electrons that contribute to the triple bond between the two nitrogen atoms.

anti-bonding electrons

Anti-bonding electrons reside in molecular orbitals that have higher energy levels compared to the atomic orbitals. They work against bond formation and can destabilize the molecule if they are present in large numbers.
These electrons occupy what we call anti-bonding orbitals, usually denoted with a star (*) symbol. The fewer the number of anti-bonding electrons, the stronger the bond between the atoms in a molecule.
When calculating bond order, the number of anti-bonding electrons is subtracted from the number of bonding electrons, and this difference is then divided by two. This helps to determine the overall stability and bond strength of the molecule.
For instance, in the oxygen molecule (O₂), there are 2 anti-bonding electrons present.