a. Draw the MO energy diagram for F2+ ion using the empty MO diagram for period 2 elements below.
The Correct Answer and Explanation is :
Let’s break down how to draw the molecular orbital (MO) diagram for the ( F_2^+ ) ion. The ion is formed by removing one electron from the neutral ( F_2 ) molecule, which has an electron configuration of ( 1s^2 2s^2 2p^5 ) for each fluorine atom. The diagram provided shows the MOs for period 2 elements, and since we are concerned with the valence electrons, we only need to focus on the ( 2s ) and ( 2p ) orbitals.
Step-by-Step Explanation
- Electron Count for ( F_2^+ ):
- In a neutral ( F_2 ) molecule, each fluorine atom has 7 valence electrons, resulting in a total of 14 valence electrons.
- In ( F_2^+ ), one electron is removed, so it has 13 valence electrons.
- Molecular Orbitals:
The molecular orbitals for ( F_2^+ ) will be formed by combining the atomic orbitals of the two fluorine atoms. The atomic orbitals involved are ( 2s ) and ( 2p ). The MO diagram will show the energy levels and how electrons fill these levels.
- The ( 2s ) orbitals combine to form a bonding ( \sigma_{2s} ) orbital and an antibonding ( \sigma_{2s}^* ) orbital.
- The ( 2p ) orbitals combine to form a bonding ( \sigma_{2p_z} ) orbital, antibonding ( \sigma_{2p_z}^* ) orbital, bonding ( \pi_{2p_x} ) and ( \pi_{2p_y} ) orbitals, and antibonding ( \pi_{2p_x}^* ) and ( \pi_{2p_y}^* ) orbitals.
- Electron Distribution:
- Start filling the orbitals with the 13 electrons.
- The electrons will fill the orbitals in order of increasing energy.
- First, the ( \sigma_{2s} ) and ( \sigma_{2s}^* ) orbitals are filled. The bonding ( \sigma_{2s} ) orbital gets 2 electrons, and the antibonding ( \sigma_{2s}^* ) orbital gets 2 electrons.
- Next, the ( \pi_{2p_x} ) and ( \pi_{2p_y} ) orbitals are filled with 4 electrons.
- The ( \sigma_{2p_z} ) orbital gets 2 electrons.
- Finally, there are 3 remaining electrons, and these will fill the antibonding orbitals. The remaining electrons will fill the ( \pi_{2p_x}^* ) and ( \pi_{2p_y}^* ) orbitals.
- MO Energy Diagram for ( F_2^+ ):
- The filled molecular orbitals, from lowest to highest energy, will be: ( \sigma_{2s} ), ( \sigma_{2s}^* ), ( \pi_{2p_x} ), ( \pi_{2p_y} ), ( \sigma_{2p_z} ), ( \pi_{2p_x}^* ), ( \pi_{2p_y}^* ), and the final electron will go into the ( \sigma_{2p_z}^* ) orbital.
Conclusion:
In the ( F_2^+ ) ion, the electron count is 13, and the MO diagram reflects this by placing electrons in the available molecular orbitals, following the energy ordering from the lowest to the highest. The diagram provides insight into the bonding nature of the molecule, with the bond order being determined by the difference between the number of bonding and antibonding electrons.
This approach ensures that the valence electrons are properly accounted for, with the bonding orbitals being filled first, leading to a stable electronic structure.