Use Molecular Orbital Theory to Determine Whether F2 2 Plus is Paramagnetic or Diamagnetic and Calculate the Bond Order

To analyze whether F₂²⁺ is paramagnetic or diamagnetic, we first need to construct its molecular orbital configuration using the molecular orbital theory.

Fluorine (F) has an atomic number of 9, which means each F atom has 9 electrons. In the diatomic molecule F₂, we have a total of 18 electrons. However, since we’re examining F₂²⁺, we need to subtract 2 electrons from this total, resulting in 16 electrons.

The molecular orbital filling order for diatomic molecules like F₂ is as follows:

• σ_1s (2 electrons)
• σ_1s^* (2 electrons)
• σ_2s (2 electrons)
• σ_2s^* (2 electrons)
• σ_2pz (2 electrons)
• π_2px (2 electrons)
• π_2py (2 electrons)
• π_2px^* (2 electrons)
• π_2py^* (0 electrons)

Now, let’s fill the molecular orbitals for F₂²⁺:

• σ_1s: 2
• σ_1s^*: 2
• σ_2s: 2
• σ_2s^*: 2
• σ_2pz: 2
• π_2px: 2
• π_2py: 2
• π_2px^*: 0
• π_2py^*: 0

In total, we have filled 16 electrons in the available molecular orbitals. Now, to check if F₂²⁺ is paramagnetic or diamagnetic, we look for unpaired electrons. In this case, all electrons are paired, which means F₂²⁺ is diamagnetic.

Now, to calculate the bond order, we use the following formula:

Bond Order = (Number of bonding electrons – Number of antibonding electrons) / 2

From our molecular orbital configuration:

• Bonding electrons: 10 (σ_1s + σ_2s + σ_2pz + 2x π_2px)
• Antibonding electrons: 2 (σ_1s^* + σ_2s^*)

Plugging these into the formula gives:

Bond Order = (10 – 2) / 2 = 8 / 2 = 4

Thus, the bond order for F₂²⁺ is 4.