Explain the formation of O₂ molecule using molecular orbital theory.

To understand the formation of an O₂ molecule using molecular orbital theory, we need to delve into how atomic orbitals combine to form molecular orbitals. This theory provides a more nuanced view of molecular bonding compared to the simpler valence bond theory, allowing us to explain the properties of molecules like oxygen more effectively.

Atomic Orbitals and Their Combination

Oxygen has an atomic number of 8, meaning it has 8 electrons. The electron configuration of a neutral oxygen atom is 1s² 2s² 2p⁴. When two oxygen atoms approach each other to form an O₂ molecule, their atomic orbitals interact. The relevant orbitals for bonding in this case are the 2s and 2p orbitals.

Molecular Orbitals Formation

In molecular orbital theory, atomic orbitals combine to form molecular orbitals that can be occupied by electrons. These molecular orbitals can be classified as bonding or antibonding:

• Bonding Orbitals: Lower in energy and promote stability when occupied.
• Antibonding Orbitals: Higher in energy and can destabilize the molecule when occupied.

For oxygen, the relevant molecular orbitals formed from the 2s and 2p atomic orbitals are:

• σ(2s) and σ*(2s) from the 2s orbitals
• σ(2p_z) from the 2p orbitals
• π(2p_x) and π(2p_y) from the 2p orbitals
• π*(2p_x) and π*(2p_y) as the corresponding antibonding orbitals

Electron Filling in Molecular Orbitals

When we fill these molecular orbitals with the total of 16 electrons (8 from each oxygen atom), we follow the Aufbau principle, Hund's rule, and the Pauli exclusion principle:

1. First, the two electrons fill the σ(2s) bonding orbital.
2. Next, the two electrons fill the σ*(2s) antibonding orbital.
3. Then, the next two electrons occupy the σ(2p_z) bonding orbital.
4. Finally, the remaining electrons fill the π(2p_x) and π(2p_y) orbitals, with two electrons in each, following Hund's rule.

At this point, the electron configuration in the molecular orbitals for O₂ looks like this:

• σ(2s)²
• σ*(2s)²
• σ(2p_z)²
• π(2p_x)²
• π(2p_y)²
• π*(2p_x)⁰
• π*(2p_y)⁰

Bond Order and Magnetic Properties

The bond order, which indicates the strength and stability of a bond, can be calculated using the formula:

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

For O₂, we have:

Bond Order = (10 - 6) / 2 = 2

This means that O₂ has a double bond, which explains its stability. Additionally, because there are unpaired electrons in the π(2p_x) and π(2p_y) orbitals, O₂ is paramagnetic, meaning it is attracted to magnetic fields.

Summary of O₂ Formation

In summary, the formation of the O₂ molecule through molecular orbital theory illustrates how atomic orbitals combine to create molecular orbitals that dictate the molecule's properties. The double bond and paramagnetic nature of O₂ can be directly attributed to the arrangement and filling of these molecular orbitals. This understanding not only helps explain the behavior of oxygen but also provides a framework for analyzing other diatomic molecules.