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Calculate the bond order,the molecular configuration,Number of bonding electron,and Number of anti-bonding electron following molecules

i) Carbon monoxide (CO)
ii) Nitrosonium(NO+)

1 answer

To analyze the bond order, molecular configuration, number of bonding electrons, and number of anti-bonding electrons for the molecules Carbon Monoxide (CO) and Nitrosonium (NO\(^+\)), we will follow the principles of molecular orbital (MO) theory.

i) Carbon Monoxide (CO)

  1. Molecular Configuration: For CO, the electronic configuration based on molecular orbital theory is: \[ \sigma(1s)^2 \sigma^(1s)^2 \sigma(2s)^2 \sigma^(2s)^2 \sigma(2p_z)^2 \pi(2p_x)^2 \pi(2p_y)^2 \pi^(2p_x)^1 \pi^(2p_y)^0 \] This implies:

    • 10 bonding electrons (from \(\sigma\) and \(\pi\) orbitals)
    • 2 anti-bonding electrons (from \(\sigma^*\) in the 1s)

  2. Bond Order Calculation: \[ \text{Bond Order} = \frac{(\text{Number of bonding electrons} - \text{Number of anti-bonding electrons})}{2} = \frac{(10 - 2)}{2} = 4 \]

  3. Number of Bonding Electrons:

    • 10 bonding electrons (including \(\sigma(2p_z)\) and \(\pi(2p_x), \pi(2p_y)\))

  4. Number of Anti-bonding Electrons:

    • 2 anti-bonding electrons (\(\sigma^*(1s)\))

Summary for CO:

  • Bond Order: 3
  • Molecular Configuration: \(\sigma(1s)^2 \sigma^(1s)^2 \sigma(2s)^2 \sigma^(2s)^2 \sigma(2p_z)^2 \pi(2p_x)^2 \pi(2p_y)^2 \pi^*(2p_x)^1\)
  • Number of Bonding Electrons: 10
  • Number of Anti-Bonding Electrons: 2

ii) Nitrosonium (NO\(^+\))

  1. Molecular Configuration: For NO\(^+\) (which has one less electron than NO), the electronic configuration based on molecular orbital theory is: \[ \sigma(1s)^2 \sigma^(1s)^2 \sigma(2s)^2 \sigma^(2s)^2 \sigma(2p_z)^2 \pi(2p_x)^2 \pi(2p_y)^2 \pi^(2p_x)^1 \pi^(2p_y)^0 \] This implies:

    • 9 bonding electrons
    • 2 anti-bonding electrons (contributing from \(\sigma^*(1s)\))

  2. Bond Order Calculation: \[ \text{Bond Order} = \frac{(\text{Number of bonding electrons} - \text{Number of anti-bonding electrons})}{2} = \frac{(9 - 2)}{2} = 3.5 \]

  3. Number of Bonding Electrons:

    • 9 bonding electrons

  4. Number of Anti-bonding Electrons:

    • 2 anti-bonding electrons

Summary for NO\(^+\):

  • Bond Order: 3.5
  • Molecular Configuration: \(\sigma(1s)^2 \sigma^(1s)^2 \sigma(2s)^2 \sigma^(2s)^2 \sigma(2p_z)^2 \pi(2p_x)^2 \pi(2p_y)^2 \pi^*(2p_x)^1\)
  • Number of Bonding Electrons: 9
  • Number of Anti-Bonding Electrons: 2

Final Results:

  • For CO:

    • Bond Order: 3
    • Configuration: \(\sigma(1s)^2 \sigma^(1s)^2 \sigma(2s)^2 \sigma^(2s)^2 \sigma(2p_z)^2 \pi(2p_x)^2 \pi(2p_y)^2 \pi^*(2p_x)^1\)
    • Bonding Electrons: 10
    • Anti-bonding Electrons: 2

  • For NO\(^+\):

    • Bond Order: 3.5
    • Configuration: \(\sigma(1s)^2 \sigma^(1s)^2 \sigma(2s)^2 \sigma^(2s)^2 \sigma(2p_z)^2 \pi(2p_x)^2 \pi(2p_y)^2 \pi^*(2p_x)^1\)
    • Bonding Electrons: 9
    • Anti-bonding Electrons: 2