How to Calculate Bond Order of Polyatomic Molecules?

To calculate the bond order of polyatomic molecules, determine the average number of bonds between a specific pair of atoms within the molecule. This is often best approached by considering resonance structures.

Here's a breakdown of the process:

1. Draw the Lewis Structure(s):

• Begin by drawing the most stable Lewis structure for the polyatomic molecule or ion. If resonance is possible, draw all significant resonance structures.

2. Identify the Atoms of Interest:

• Determine which two atoms you want to calculate the bond order between.

3. Count the Number of Bonds:

• For a single Lewis structure: Count the number of bonds (single, double, or triple) between the two identified atoms. The bond order is simply this number.
• For multiple resonance structures: Count the number of bonds between the two identified atoms in each resonance structure.

4. Count the Number of Resonance Structures or Groups of Equivalent Atoms:

• Resonance structures: Count the total number of resonance structures you drew.
• Equivalent atom groups: If you're looking for the average bond order across multiple identical atom pairs, count the number of these equivalent pairs. For instance, in benzene, all C-C bonds are equivalent.

5. Calculate the Bond Order:

• Bond Order = (Total number of bonds between the two atoms across all resonance structures) / (Number of resonance structures)
• Bond Order = (Total number of bonds between the two atoms) / (Number of equivalent atom pairs)

Example: Ozone (O₃)

1. Lewis Structures: Ozone has two resonance structures: O=O-O and O-O=O

2. Atoms of Interest: We want to calculate the bond order between any two adjacent oxygen atoms.

3. Count Bonds:

   • In the first structure (O=O-O), there are 2 bonds between the first two oxygens and 1 bond between the last two oxygens.
   • In the second structure (O-O=O), there is 1 bond between the first two oxygens and 2 bonds between the last two oxygens.
   • Across both resonance structures, there is a total of (2 + 1 + 1 + 2) = 6 "bonds" between oxygens.

4. Count Resonance Structures: There are 2 resonance structures. There are also 2 identical O-O bond lengths.

5. Calculate Bond Order:

   • Bond Order = (3 bonds) / (2 resonance structures) = 1.5
   • (Alternatively using equivalence) Bond Order = (1 double bond + 1 single bond) / (2 bond sites) = 3/2 = 1.5

Therefore, the bond order between the oxygen atoms in ozone is 1.5. This indicates a bond strength and length intermediate between a single and double bond.

Example: Carbonate Ion (CO₃^2-)

1. Lewis Structures: Carbonate has three resonance structures, each with one C=O double bond and two C-O single bonds.

2. Atoms of Interest: The bond between Carbon and Oxygen.

3. Count Bonds: There are a total of 4 bonds (one double, two single) spread across three C-O links.

4. Count Resonance Structures: There are 3 resonance structures. All three C-O bonds are equivalent.

5. Calculate Bond Order:
   Bond Order = (4 bonds) / (3 resonance structures) = 1.33

The carbon-oxygen bond order in the carbonate ion is 1.33.

In summary, calculating the bond order of polyatomic molecules involves analyzing Lewis structures, considering resonance, and determining the average number of bonds between specific atoms. This provides insights into the bond strength and length.