Draw the molecular orbital (MO) electron diagram for the B2 molecular ion. Be sure vour diagram contains all of the electrons in the ion, including ay core electrons_ Energy
The Correct Answer and Explanation is:
Here is the completed molecular orbital (MO) diagram for the B₂²⁺ molecular ion.
Explanation of the MO Diagram
To construct the molecular orbital (MO) diagram for the B₂²⁺ ion, we first determine the total number of electrons. A neutral boron atom (B) has an atomic number of 5, meaning it has 5 electrons. A neutral diatomic boron molecule (B₂) would therefore have 10 electrons. The B₂²⁺ ion has a +2 charge, indicating it has lost two electrons, leaving a total of 8 electrons to place in the MO diagram.
The diagram is built from the atomic orbitals (AOs) of the two boron atoms, which are the 1s, 2s, and 2p orbitals. These are shown on the left and right sides. When these AOs combine, they form an equal number of molecular orbitals (MOs), shown in the center, arranged by increasing energy. For elements in the second period up to and including nitrogen, significant s-p mixing occurs, which causes the π₂p orbitals to be lower in energy than the σ₂p orbital. The energy order for B₂ is therefore:
σ₁s < σ₁s < σ₂s < σ₂s < π₂p < σ₂p < π₂p < σ₂p
The 8 electrons of the B₂²⁺ ion are then filled into these molecular orbitals according to the Aufbau principle (lowest energy first), the Pauli exclusion principle (two electrons per orbital with opposite spins), and Hund’s rule.
- Two electrons fill the σ₁s bonding orbital.
- Two electrons fill the σ*₁s antibonding orbital.
- Two electrons fill the σ₂s bonding orbital.
- The final two electrons fill the σ*₂s antibonding orbital.
The resulting electron configuration for B₂²⁺ is (σ₁s)²(σ₁s)²(σ₂s)²(σ₂s)².
From this diagram, we can calculate the bond order, which is a measure of the number of chemical bonds between the two atoms. The formula is:
Bond Order = ½ (Number of bonding electrons – Number of antibonding electrons)
Bond Order = ½ (4 – 4) = 0
A bond order of zero indicates that there is no net chemical bond between the two boron ions. Therefore, the B₂²⁺ ion is predicted to be unstable and unlikely to exist. Since all electrons in the MO diagram are paired, the ion is diamagnetic.
