Determine the bond orders of S2, Cl2, and NO2 from their molecular orbital configurations and compare the values with the bond orders determined from Lewis Structures
The Correct Answer and Explanation is :
To determine the bond orders of ( S_2 ), ( Cl_2 ), and ( NO_2 ) from their molecular orbital configurations and compare them to those derived from Lewis structures, we first need to understand the concept of bond order. Bond order is a measure of the number of chemical bonds between a pair of atoms. In molecular orbital theory, it is calculated as ( \frac{(number\ of\ bonding\ electrons – number\ of\ antibonding\ electrons)}{2} ).
Molecular Orbital Configurations
- ( S_2 ):
- Electron Configuration: ( \sigma_{2s}^2 \sigma_{2s}^{2} \sigma_{2p}^2 \pi_{2p}^4 \pi_{2p}^{2} )
- Bond Order: ( \frac{(2 + 4 – 2 – 2)}{2} = 1 )
- ( Cl_2 ):
- Electron Configuration: ( \sigma_{2s}^2 \sigma_{2s}^{2} \sigma_{2p}^2 \pi_{2p}^4 \pi_{2p}^{4} \sigma_{2p}^2 )
- Bond Order: ( \frac{(2 + 4 + 2 – 4)}{2} = 2 )
- ( NO_2 ):
- Note: ( NO_2 ) is a radical, and we usually consider ( NO_2^+ ) for simplicity.
- Electron Configuration for ( NO_2^+ ): ( \sigma_{2s}^2 \sigma_{2s}^{*2} \sigma_{2p}^2 \pi_{2p}^3 )
- Bond Order: ( \frac{(2 + 3 – 2)}{2} = 1.5 )
Lewis Structures
- ( S_2 ):
- Typically depicted as ( S=S ) with a double bond.
- Bond Order from Lewis: 2
- ( Cl_2 ):
- Represented as ( Cl-Cl ) with a single bond.
- Bond Order from Lewis: 1
- ( NO_2 ):
- ( NO_2 ) usually involves one single bond and one double bond in resonance with a lone electron.
- Bond Order from Lewis: 1.5
Comparison and Conclusion
The molecular orbital theory gives slightly different results compared to Lewis structures. For ( S_2 ) and ( Cl_2 ), the bond orders vary due to the difference in treatment of electron pairing and antibonding orbitals. For ( NO_2 ), both approaches agree because of the radical nature and resonance structures.
Molecular orbital theory provides a more detailed representation by considering the distribution of all electrons in bonding and antibonding orbitals, which often gives more insight, especially for molecules with unpaired electrons or radicals like ( NO_2 ).
Let’s now generate an image that visually summarizes this comparison.
Here is an illustration that compares the molecular orbital configurations and Lewis structures for ( S_2 ), ( Cl_2 ), and ( NO_2 ). The image includes diagrams of molecular orbitals with electrons in bonding and antibonding positions, alongside their respective Lewis structures showing the different types of bonds. It also features text labels indicating each molecule’s bond order calculated by both molecular orbital theory and Lewis structure methods, providing a clear comparison between the two approaches.