How to Calculate Bond Order in Chemistry

Bond order is a fundamental concept in chemistry that describes the number of chemical bonds between atoms in a molecule. It provides insight into the strength and stability of the bond, with higher bond orders indicating stronger bonds. This blog post will guide you through the steps to calculate bond order, explain its significance, and include an illustrative example.

What is Bond Order?

Bond order is defined as the number of covalent bonds shared between two atoms in a molecule. It is calculated using molecular orbital theory or Lewis structures. The bond order can be a whole number (e.g., 1 for a single bond, 2 for a double bond) or a fractional number for molecules with resonance structures or delocalized electrons.

The formula for bond order in molecular orbital theory is:

Bond Order = (Number of Bonding Electrons - Number of Antibonding Electrons) / 2

In Lewis structures, bond order is calculated as the average number of bonds between atoms across all resonance structures.

Why is Bond Order Important?

• Bond Strength: Higher bond order indicates a stronger bond, requiring more energy to break.
• Bond Length: Higher bond order corresponds to shorter bond lengths due to increased electron density between atoms.
• Molecular Stability: Molecules with higher bond orders are generally more stable.

Steps to Calculate Bond Order

1. Using Molecular Orbital Theory

Molecular orbital theory considers the combination of atomic orbitals to form bonding and antibonding molecular orbitals. Follow these steps:

1. Determine the Molecular Orbital Diagram: Identify the molecular orbitals for the molecule based on the atoms involved.
2. Count Bonding Electrons: Sum the electrons in bonding molecular orbitals (e.g., σ or π bonding orbitals).
3. Count Antibonding Electrons: Sum the electrons in antibonding molecular orbitals (e.g., σ* or π* orbitals).
4. Apply the Formula: Use the bond order formula:

Bond Order = (Bonding Electrons - Antibonding Electrons) / 2

2. Using Lewis Structures

For molecules with resonance structures, bond order is calculated as follows:

1. Draw All Resonance Structures: Sketch all possible Lewis structures for the molecule.
2. Count Bonds Between Atoms: For each resonance structure, note the number of bonds (single = 1, double = 2, triple = 3) between the atoms of interest.
3. Average the Bonds: Calculate the average bond order by summing the number of bonds across all resonance structures and dividing by the number of resonance structures.

Example: Calculating Bond Order for O₂

Molecular Orbital Theory Approach

Let’s calculate the bond order for the O₂ molecule:

1. Molecular Orbital Diagram: Each oxygen atom contributes 8 electrons, so O₂ has 16 electrons. Fill the molecular orbitals in order of increasing energy (σ2s, σ*2s, σ2p, π2p, π*2p, σ*2p).
2. Bonding Electrons: The bonding orbitals (σ2s, σ2p, π2p) contain 8 electrons.
3. Antibonding Electrons: The antibonding orbitals (σ*2s, π*2p) contain 4 electrons.
4. Bond Order Calculation:
   Bond Order = (8 - 4) / 2 = 2

The bond order of O₂ is 2, indicating a double bond.

Lewis Structure Approach

For O₂, the Lewis structure shows a double bond between the two oxygen atoms:

O=O

Since there are no resonance structures, the bond order is simply 2.

Example: Calculating Bond Order for NO₃⁻ (Nitrate Ion)

The nitrate ion has resonance structures, so we’ll use the Lewis structure method:

1. Draw Resonance Structures: NO₃⁻ has three resonance structures, where the nitrogen atom is bonded to three oxygen atoms. In each structure, one N-O bond is a double bond, and the other two are single bonds.
2. Count Bonds:
   • Structure 1: 1 double bond (2) + 2 single bonds (1 each) = 2 + 1 + 1
   • Structure 2: Same as above
   • Structure 3: Same as above
3. Average Bond Order: For each N-O bond, the bond order is:
   Bond Order = (2 + 1 + 1) / 3 = 4/3 ≈ 1.33

The bond order of each N-O bond in NO₃⁻ is approximately 1.33, reflecting the delocalized bonding.

Illustrated Diagram

Molecular orbital diagram for O₂, showing the distribution of bonding and antibonding electrons, leading to a bond order of 2.

Conclusion

Calculating bond order is a powerful tool for understanding molecular structure and properties. Whether using molecular orbital theory or Lewis structures, the process provides valuable insights into bond strength, length, and molecular stability. Practice with simple molecules like O₂ and ions like NO₃⁻ to master the concept, and use molecular orbital diagrams to visualize electron distribution.