Use the Molecular Orbital Theory to Determine the Bond Order of CN Ion: Is It Paramagnetic or Diamagnetic?

The bond order of the CN^– ion can be determined using molecular orbital theory, which provides insight into the bonding between atoms based on the combination of their atomic orbitals.

First, we need to construct the molecular orbital diagram for the CN^– ion. Carbon (C) has 4 valence electrons, and nitrogen (N) has 5. Therefore, the neutral CN molecule has a total of 9 electrons. Since the CN^– ion has one extra electron, we will consider a total of 10 electrons:

1. The order of molecular orbitals for CN is:
   • 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)
2. Filling these orbitals with the 10 electrons, we get:
   • σ(1s) – 2 electrons
   • σ*(1s) – 2 electrons
   • σ(2s) – 2 electrons
   • σ*(2s) – 2 electrons
   • σ(2p_z) – 2 electrons
   • π(2p_x) – 1 electron
   • π(2p_y) – 1 electron

Now, we can calculate the bond order using the formula:

Bond Order = (N_b – N_a) / 2,

where N_b is the number of electrons in bonding orbitals and N_a is the number of electrons in antibonding orbitals.

From our filling, we have:

• N_b = 2 (σ(2p_z)) + 2 (π(2p_x) + π(2p_y)
• N_a = 0

Substituting these values into the bond order formula:

Bond Order = (6 – 0) / 2 = 3

The bond order of the CN^– ion is 3, indicating a strong triple bond between carbon and nitrogen.

Next, to determine whether CN^– is paramagnetic or diamagnetic, we look at the presence of unpaired electrons. In our case:

• Bonding orbitals: 6 electrons (all paired)
• Antibonding orbitals: 0 electrons

All electrons in the CN^– ion are paired; therefore, the CN^– ion is diamagnetic.

In summary, the bond order of the CN^– ion is 3, and it is diamagnetic due to the absence of unpaired electrons.