Question

Use molecular orbital theory to account for the paramagnetism of \(\mathrm{O}_{2}\) and its \(\mathrm{O}=\mathrm{O}\) double bond.

Short answer

O2 is paramagnetic due to unpaired electrons in antibonding MOs and has a double bond with bond order 2.

Step-by-step solution

Understand the Molecular Orbital Theory

Molecular orbital (MO) theory explains the bonding and properties of molecules by combining the atomic orbitals of the bonding atoms into molecular orbitals. These molecular orbitals can be occupied by the molecular electrons, and they are spread out over the entire molecule rather than being localized between atoms.

Construct the MO Diagram for O2

To construct the molecular orbital (MO) diagram for \( ext{O}_2\), start by considering the combination of atomic orbitals (AOs) from two oxygen atoms. The AO energy levels for each O atom are: \(1s, 2s,\) and \(2p\) orbitals. In \( ext{O}_2\), the relevant orbitals for bonding are the \(2s\) and the \(2p\) orbitals. The bond order is derived from the occupied bonding and antibonding molecular orbitals.

Fill the Molecular Orbitals with Electrons

When filling the MO diagram for \(\text{O}_2\), 12 valence electrons need to be accounted for: 8 from the \(2p\) orbitals and 4 from the \(2s\) orbitals of both oxygen atoms. Start filling the bonding orbitals: \(\sigma_{2s}, \, \sigma_{2s}^*\) and then the bonding \(\sigma_{2p_z}\) and antibonding \(\pi_{2p_x}, \, \pi_{2p_y}\) followed by their antibonding counterparts \(\pi_{2p_x}^*, \, \pi_{2p_y}^*\). For \(\text{O}_2\), the last two electrons will occupy the \(\pi_{2p_x}^*\) and \(\pi_{2p_y}^*\) orbitals.

Count the Bonding and Antibonding Electrons

In the \(\text{O}_2\) molecule, the MO diagram reveals that there are 8 electrons in bonding orbitals and 4 electrons in antibonding orbitals. The bond order is calculated using the formula: \[ \text{Bond Order} = \frac{(\text{Number of bonding electrons} - \text{Number of antibonding electrons})}{2} \] For \(\text{O}_2\), this results in a bond order of \[ \frac{8 - 4}{2} = 2 \,\] confirming the \(\text{O} = \text{O}\) double bond.

Determine the Magnetic Properties

Since the last two electrons in the \(\pi_{2p_x}^*, \, \pi_{2p_y}^*\) orbitals are unpaired, \(\text{O}_2\) has unpaired electrons, causing it to be paramagnetic. Paramagnetism arises when there are one or more unpaired electrons in a molecule's molecular orbitals, as observed in \(\text{O}_2\).

Key concepts

Paramagnetism

When you hear about paramagnetism, it refers to certain materials that are attracted by an external magnetic field. This intriguing property occurs due to the presence of unpaired electrons in the material's molecular orbitals. Each unpaired electron has a magnetic moment, which means it behaves like a tiny magnet. An important aspect of paramagnetism is that it only arises when there are unpaired electrons.
For molecules, like the oxygen molecule \(\text{O}_2\), this is precisely what's happening. In the case of \(\text{O}_2\), the last two electrons reside in separate \(\pi_{2p_x}^*\) and \(\pi_{2p_y}^*\) molecular orbitals and remain unpaired.

• This creates two individual magnetic moments.
• Hence, \(\text{O}_2\) is attracted to a magnetic field.

This characteristic distinguishes paramagnetic substances from diamagnetic substances, where all electrons are paired and there is no net magnetic moment.

Oxygen Molecule

The oxygen molecule (\(\text{O}_2\)) is an essential diatomic molecule that plays a crucial role in supporting life on Earth. But what makes its structure so unique? Using Molecular Orbital (MO) theory helps us understand its structure and properties more deeply. In the context of \(\text{O}_2\), we start by constructing the MO diagram to visualize its electron configuration.
The molecular orbital diagram for \(\text{O}_2\) is built by combining the atomic orbitals of the two oxygen atoms.
The focus is on the valence shell orbitals, which include the \(2s\) and \(2p\) orbitals.

• These orbitals combine to form
  **bonding molecular orbitals** like \(\sigma_{2s}\), \(\sigma_{2p_z}\)
• and
  **antibonding orbitals** such as \(\sigma_{2s}^*\), \(\pi_{2p_x}^*\), \(\pi_{2p_y}^*\).

Completing the electron filling in the MO diagram ensures we have 8 electrons in bonding orbitals and 4 in antibonding ones, an arrangement unique to \(\text{O}_2\). This electronic setup gives oxygen its distinctive characteristics, like paramagnetism.

Bond Order

Bond order is a fundamental concept in understanding the stability of a molecule. It tells us how strong or stable a bond is between two atoms. The concept springs from Molecular Orbital Theory and measures the difference between the number of bonding and antibonding electrons. To calculate bond order, use the formula: \[\text{Bond Order} = \frac{(\text{Number of Bonding Electrons} - \text{Number of Antibonding Electrons})}{2}\]For the oxygen molecule \(\text{O}_2\), we observe that there are 8 electrons filling the bonding molecular orbitals and 4 electrons in the antibonding molecular orbitals from our MO diagram. When plugged into the formula:

• Bond order comes out to be \(\frac{8 - 4}{2} = 2\).

A bond order of 2 indicates a double bond between the oxygen atoms, signifying that \(\text{O}_2\) is stable and possesses a pronounced \(\text{O}=\text{O}\) double bond.
Bond order is not just about stability; it is also instrumental in predicting other properties like bond length and bond energy. A higher bond order corresponds to a shorter and stronger bond, making it essential in molecular chemistry.