Using the MO diagram of NO, calculate the bond order. Compare it to _N^O+

To calculate the bond order of nitric oxide (NO) using its molecular orbital (MO) diagram, we first need to understand the arrangement of electrons in its molecular orbitals. The bond order can be determined using the formula: Bond Order = (Number of bonding electrons - Number of antibonding electrons) / 2. Let's break this down step by step.

Understanding the Electron Configuration of NO

Nitric oxide consists of one nitrogen atom and one oxygen atom. The atomic numbers of nitrogen and oxygen are 7 and 8, respectively. Therefore, the total number of electrons in NO is:

• 7 (from N) + 8 (from O) = 15 electrons

Filling the Molecular Orbitals

The molecular orbitals for diatomic molecules like NO can be filled according to the Aufbau principle, Hund's rule, and the Pauli exclusion principle. The order of filling for NO is as follows:

• σ(1s)
• σ*(1s)
• σ(2s)
• σ*(2s)
• σ(2p_z)
• π(2p_x) = π(2p_y)
• π*(2p_x) = π*(2p_y)
• σ*(2p_z)

For NO, the filling of the molecular orbitals would look like this:

• σ(1s): 2 electrons
• σ*(1s): 2 electrons
• σ(2s): 2 electrons
• σ*(2s): 2 electrons
• σ(2p_z): 2 electrons
• π(2p_x): 2 electrons
• π(2p_y): 1 electron

In total, we have filled 15 electrons, with the last electron going into one of the π(2p) orbitals.

Calculating Bond Order for NO

Now, let's identify the bonding and antibonding electrons:

• Bonding electrons: 10 (2 from σ(1s), 2 from σ(2s), 2 from σ(2p_z), and 2 from π(2p_x) + 1 from π(2p_y))
• Antibonding electrons: 5 (2 from σ*(1s) and 2 from σ*(2s) + 1 from π*(2p_x) or π*(2p_y))

Now we can apply the bond order formula:

Bond Order = (10 - 5) / 2 = 2.5

Comparing with N O +

Now, let's look at the molecular ion NO⁺. This ion has one less electron than neutral NO, giving it a total of 14 electrons. The filling of the molecular orbitals would be similar, but we would remove one electron from the highest energy orbital, which is one of the π(2p) orbitals.

• Bonding electrons: 10 (same as NO)
• Antibonding electrons: 4 (2 from σ*(1s), 2 from σ*(2s), and 0 from π*(2p))

Now, applying the bond order formula again:

Bond Order for NO⁺ = (10 - 4) / 2 = 3

Summary of Findings

In summary, the bond order of nitric oxide (NO) is 2.5, indicating a bond that is stronger than a double bond but weaker than a triple bond. In contrast, the bond order of the NO⁺ ion is 3, suggesting a stronger bond due to the removal of an electron from an antibonding orbital. This comparison highlights how the presence or absence of electrons in bonding and antibonding orbitals can significantly affect the stability and strength of molecular bonds.