1. Using Molecular Orbital Theory

Question

(a) Calculate the bond order, the molecular configuration, Number of bonding electrons and Number of anti-bonding electrons for the following molecules.

1. Carbon monoxide (CO)

Answer 1

To analyze the molecular orbital (MO) configuration for carbon monoxide (CO), we need to follow these steps:

1. Determine the number of valence electrons:

   • Carbon (C) has 4 valence electrons.
   • Oxygen (O) has 6 valence electrons.
   • Therefore, CO has a total of 4 + 6 = 10 valence electrons.

2. Molecular orbital configuration: The molecular orbitals for CO can be filled based on the standard order of orbitals. For diatomic molecules like CO, the general order is:

   \[\sigma(1s) < \sigma^(1s) < \sigma(2s) < \sigma^(2s) < \sigma(2p_z) < \pi(2p_x) = \pi(2p_y) < \pi^(2p_x) = \pi^(2p_y) < \sigma^*(2p_z)\]

   For CO, we fill the molecular orbitals as follows (each box represents a molecular orbital, and we'll fill them with electrons):

   • (1s) orbitals:
     • 2 electrons in \(\sigma(1s)\)
     • 2 electrons in \(\sigma^*(1s)\)
   • (2s) orbitals:
     • 2 electrons in \(\sigma(2s)\)
     • 0 electrons in \(\sigma^*(2s)\)
   • (2p) orbitals:
     • 2 electrons in \(\sigma(2p_z)\)
     • 2 electrons in \(\pi(2p_x)\) and \(\pi(2p_y)\) (1 electron each)

   Thus, the filling of the molecular orbitals for CO is (in the relevant orbitals for carbon and oxygen):

   \[\sigma(1s)^2 \sigma^(1s)^2 \sigma(2s)^2 \sigma^(2s)^0 \sigma(2p_z)^2 \pi(2p_x)^1 \pi(2p_y)^1\]

   The MO configuration for CO is thus: \[\sigma(1s)^2 \sigma^(1s)^2 \sigma(2s)^2 \sigma^(2s)^0 \sigma(2p_z)^2 \pi(2p_x)^1 \pi(2p_y)^1\]

3. Count bonding and antibonding electrons:

   • Bonding electrons:

     • \(\sigma(1s)\): 2
     • \(\sigma(2s)\): 2
     • \(\sigma(2p_z)\): 2
     • \(\pi(2p_x)\): 1
     • \(\pi(2p_y)\): 1
     • Total bonding electrons = 2 + 2 + 2 + 1 + 1 = 8

   • Antibonding electrons:

     • \(\sigma^*(1s)\): 2
     • \(\sigma^*(2s)\): 0
     • \(\pi^*(2p_x)\): 0
     • \(\pi^*(2p_y)\): 0
     • \(\sigma^*(2p_z)\): 0
     • Total antibonding electrons = 2 + 0 + 0 + 0 + 0 = 2

4. Calculate the bond order: The bond order is calculated using the formula: \[ \text{Bond Order} = \frac{\text{(Number of bonding electrons) - (Number of antibonding electrons)}}{2} \] Substituting the values: \[ \text{Bond Order} = \frac{8 - 2}{2} = \frac{6}{2} = 3 \]

Summary for CO:

• Molecular Configuration: \(\sigma(1s)^2 \sigma^(1s)^2 \sigma(2s)^2 \sigma^(2s)^0 \sigma(2p_z)^2 \pi(2p_x)^1 \pi(2p_y)^1\)
• Bond order: 3
• Number of bonding electrons: 8
• Number of antibonding electrons: 2