Sure, let's determine the bond order of the carbonate ion ([tex]$\text{CO}_3^{2-}$[/tex]).
1. Understanding the Structure of [tex]$\text{CO}_3^{2-}$[/tex]:
The carbonate ion ([tex]$\text{CO}_3^{2-}$[/tex]) has three equivalent resonance structures. In each resonance structure, the carbon atom is bonded to three oxygen atoms. However, the nature of these bonds (single or double) changes in each resonance structure.
2. Resonance Structures:
Each of the three resonance structures contributes to the overall structure of the carbonate ion. In every structure:
- One of the carbon-oxygen bonds is a double bond.
- The other two carbon-oxygen bonds are single bonds.
3. Average Bonding:
Because all three resonance structures are equivalent, the actual structure of the ion is an average of these resonance structures. This averaging results in bonds that are intermediate between single and double bonds.
4. Total Number of Bonds:
Across all three resonance structures, the total number of C-O bonds can be counted. Each resonance form has:
- 1 double bond
- 2 single bonds
Summing for all three resonance structures, we get:
- Total double bonds: [tex]$1 + 1 + 1 = 3$[/tex]
- Total single bonds: [tex]$2 + 2 + 2 = 6$[/tex]
5. Effective Bonds Per Resonance Structure:
Since each double bond can be considered as two single bonds, we can convert the total bond count into an equivalent number of single bonds:
- Total bonds from double bonds: [tex]$3 \times 2 = 6$[/tex]
- Total single bonds: 6
- Total effective bonds: [tex]$6 + 6 = 12$[/tex]
6. Number of Bond Groups:
In the carbonate ion, there are 3 C-O bonds.
7. Bond Order Calculation:
Bond order is defined as the number of bonds divided by the number of bond groups. Thus, for the carbonate ion:
[tex]\[
\text{Bond Order} = \frac{\text{Total number of bonds}}{\text{Number of bond groups}} = \frac{4}{3} \approx 1.33
\][/tex]
Therefore, the bond order of the carbonate ion ([tex]$\text{CO}_3^{2-}$[/tex]) is approximately 1.33.
