Explain the formation of O 2 ​ molecule using molecular orbital theory.

The formation of the O₂ molecule can be understood using Molecular Orbital (MO) Theory, which provides a more sophisticated approach than the older valence bond theory. MO theory takes into account the quantum mechanical nature of the electrons and describes how atomic orbitals combine to form molecular orbitals. Let's go step-by-step to explain the formation of the O₂ molecule.

Step 1: Atomic Orbitals of Oxygen Atoms

Each oxygen atom has an electron configuration of 1s² 2s² 2p⁴. When two oxygen atoms approach each other to form the O₂ molecule, their atomic orbitals combine to form molecular orbitals. Since oxygen has electrons in the 2p orbitals, we focus on the combination of these 2p orbitals.

For each oxygen atom, the 2p orbitals (px, py, and pz) combine to form molecular orbitals. These molecular orbitals can be bonding or antibonding, depending on how the atomic orbitals interact:

• Bonding molecular orbitals: Formed when atomic orbitals overlap in phase, reinforcing each other.
• Antibonding molecular orbitals: Formed when atomic orbitals overlap out of phase, canceling each other out.

Step 2: Molecular Orbitals in O₂

When two oxygen atoms approach each other, their 2p orbitals combine in a way that forms bonding and antibonding molecular orbitals. For two O atoms, the combination of their 2p orbitals results in the following molecular orbitals:

• Two bonding molecular orbitals: σ₂p (bonding) and π₂p (bonding).
• Two antibonding molecular orbitals: σ*₂p (antibonding) and π*₂p (antibonding).

Step 3: Electron Configuration in Molecular Orbitals

Each oxygen atom has 8 electrons, so for the O₂ molecule, we have a total of 16 electrons. These electrons fill the molecular orbitals in order of increasing energy, following the Pauli exclusion principle (no more than two electrons in each orbital, and they must have opposite spins) and Hund's rule (degenerate orbitals are filled singly before pairing). The order of filling the molecular orbitals is:

• σ₂s (bonding) - 2 electrons
• σ*₂s (antibonding) - 2 electrons
• σ₂p (bonding) - 2 electrons
• π₂p (bonding) - 4 electrons
• π*₂p (antibonding) - 4 electrons
• σ*₂p (antibonding) - 2 electrons

Thus, the molecular orbital diagram for the O₂ molecule has the following filling (with the electrons in each molecular orbital indicated in the order of filling):

• σ₂s (2 electrons), σ*₂s (2 electrons), σ₂p (2 electrons), π₂p (4 electrons), π*₂p (4 electrons), and σ*₂p (2 electrons).

Step 4: Bond Order Calculation

The bond order of a molecule is given by the formula:

For the O₂ molecule:

• Bonding electrons = 2 (σ₂s) + 2 (σ₂p) + 4 (π₂p) = 8 electrons
• Antibonding electrons = 2 (σ*₂s) + 4 (π*₂p) + 2 (σ*₂p) = 8 electrons

The bond order for the O₂ molecule is 0, indicating that there is no bonding in the O₂ molecule.

Step 5: Magnetic Properties and Oxygen Molecule

The O₂ molecule is paramagnetic, meaning it has unpaired electrons. This is because after filling the bonding orbitals, there are still electrons in the antibonding orbitals (π*₂p), which results in two unpaired electrons. This gives the O₂ molecule its characteristic magnetic behavior.

Conclusion

According to molecular orbital theory, the O₂ molecule is formed by the combination of atomic orbitals from two oxygen atoms. The result is a molecule with a bond order of 2, indicating a stable bond between the two oxygen atoms. The magnetic properties of O₂ are also explained by the presence of unpaired electrons in antibonding orbitals.