Question

Explain the molecular orbital structure of \(\mathrm{O}_{2}\). Calculate the bond order.

Short answer

The molecular orbital structure of O₂ is derived by considering the energy levels of atomic orbitals and filling the molecular orbitals according to the aufbau principle. The molecular orbitals are arranged in increasing energy order as σ(2s), σ*(2s), σ(2p), π(2p), π(2p), π*(2p), π*(2p), and σ*(2p). The 12 valence electrons are distributed accordingly, and the bond order is calculated using the formula \(Bond\, Order = \frac{1}{2} (Number\, of\, electrons\, in\, bonding\, orbitals - Number\, of\, electrons\, in\, antibonding\, orbitals)\). The bond order of O₂ is found to be 2, indicating a double bond between the two oxygen atoms.

Step-by-step solution

Identify atomic orbitals of oxygen

Since oxygen has an atomic number of 8, its electronic configuration is given by 1s² 2s² 2p⁴. The valence orbitals are the 2s and 2p orbitals. There are two oxygen atoms in O₂, so we have a total of 2(2s² + 2p⁴) = 12 valence electrons.

Arrange atomic orbitals into molecular orbitals

For the molecular orbitals, we will consider the energy levels of different atomic orbitals and use the aufbau principle to fill them with electrons. The molecular orbitals are arranged in increasing energy order as follows: 1. σ(2s) 2. σ*(2s) 3. σ(2p) 4. π(2p) and π(2p) - these two orbitals are degenerate (having the same energy) 5. π*(2p) and π*(2p) - these two orbitals are degenerate (having the same energy) 6. σ*(2p)

Fill molecular orbitals with electrons

We have a total of 12 valence electrons in O₂. We will now fill the molecular orbitals using the aufbau principle. 1. σ(2s) – 2 electrons 2. σ*(2s) – 2 electrons 3. σ(2p) – 2 electrons 4. π(2p) – 2 electrons (one in each degenerate orbital) 5. π*(2p) – 4 electrons (two in each degenerate orbital) 6. σ*(2p) – 0 electrons

Calculate bond order

Now that we have filled the molecular orbitals with electrons, we can calculate the bond order. Bond order is calculated using the formula: \(Bond\, Order = \frac{1}{2} (Number\, of\, electrons\, in\, bonding\, orbitals - Number\, of\, electrons\, in\, antibonding\, orbitals)\) In our case, Bond order = \(\frac{1}{2}(8 - 4) = \frac{1}{2}(4) = 2\) The molecular orbital structure of O₂ has a bond order of 2, indicating a double bond between the two oxygen atoms.

Key concepts

Bond Order

Bond order is a concept that allows us to understand the strength and type of a bond between two atoms in a molecule. It is derived from molecular orbital theory, which provides a detailed view of which electrons are involved in bonding and which are not. Calculating bond order involves examining the number of electrons in bonding molecular orbitals and antibonding molecular orbitals.
Bond order can be calculated using the formula:

• \(Bond\, Order = \frac{1}{2} (Number\, of\, electrons\, in\, bonding\, orbitals - Number\, of\, electrons\, in\, antibonding\, orbitals)\)

To illustrate, in the oxygen molecule (O₂), which contains a bond order of 2, you first determine the difference between the electrons in bonding orbitals and those in antibonding orbitals. The resulting bond order signifies a double bond in this particular case. Stronger bonds frequently correlate with higher bond orders.

Oxygen Molecule

The oxygen molecule, O₂, is an essential diatomic molecule, notable for its role in various biological and chemical processes. In terms of molecular orbital theory, understanding the structure of O₂ helps explain its magnetic and chemical properties.
O₂ is a homonuclear diatomic molecule, meaning both atoms are the same and belong to the same element, oxygen, having atomic number 8. This makes the molecular orbital configuration somewhat symmetrical. By examining its molecular orbital diagram, we learn where electrons prefer to reside. Notably, in O₂, certain unpaired electrons create paramagnetic properties, allowing it to be attracted to magnetic fields.

Atomic Orbitals

Atomic orbitals are fundamental concepts in molecular orbital theory. They describe the regions around an atom's nucleus where there is a high probability of finding electrons.
For oxygen, the atomic orbitals involved in bonding are primarily the 2s and 2p orbitals. An oxygen atom has electrons filling up the 1s, 2s, and 2p orbitals in sequence, as dictated by the aufbau principle. This principle states that electrons fill orbitals starting from the lowest energy level up to higher ones.
Understanding atomic orbitals is crucial for predicting how atoms will interact and form molecules. For O₂, both oxygen atoms contribute their 2s and 2p orbitals, creating a shared set of molecular orbitals that bond the two atoms together.

Electronic Configuration

The electronic configuration of an atom details how its electrons are distributed among the available atomic orbitals. This configuration is vital for predicting an atom's chemical behavior and how it bonds with other atoms.
In the oxygen molecule, each oxygen atom has an electronic configuration of 1s² 2s² 2p⁴. This configuration reveals that oxygen has six valence electrons, which are the primary electrons involved in bonding. To form O₂, the two oxygen atoms employ their valence electrons to fill molecular orbitals according to the aufbau principle, leading to a stable electron arrangement.
Examining the electronic configuration of each atom before they bond assists in understanding how and why particular molecules form as they do, providing insights into the chemical properties that result from these interactions.