Question

Draw molecular orbital energy level diagrams for \(\mathrm{O}_{2}\) \(\mathrm{O}_{2}^{-},\) and \(\mathrm{O}_{2}^{2-}\)

Short answer

For O_2, O_2^-, and O_2^{2-}, fill MOs with 12, 13, and 14 electrons respectively.

Step-by-step solution

Understand Diatomic Molecular Orbitals

Molecular orbitals (MOs) are formed by the linear combination of atomic orbitals (AOs). For diatomic molecules like O_2, the MOs are sigma (σ) and pi (π) types, derived from atomic s and p orbitals.

Construct the MO Diagram for O_2

For O_2 (12 valence electrons total), fill the MOs from lowest to highest energy: 1. σ_{1s} - fully filled 2. σ^*_{1s} - fully filled 3. σ_{2s} - fully filled 4. σ^*_{2s} - fully filled 5. σ_{2p_z} - filled 6. π_{2p_x} , π_{2p_y} - degenerate, each has one electron pair 7. π^*_{2p_x} , π^*_{2p_y} - degenerate, each has one unpaired electron with opposite spins (accounting for the 12th electron).

Construct the MO Diagram for O_2^-

Add one extra electron to O_2, giving O_2^- 13 valence electrons. Add this electron to the lowest energy unfilled orbital: - Add it into either π^*_{2p_x} or π^*_{2p_y} , making now one of them fully filled.

Construct the MO Diagram for O_2^{2-}

Add two extra electrons to O_2 to form O_2^{2-}, giving it 14 valence electrons. Add these electrons to the lowest energy unfilled orbitals: - Completely fill both π^*_{2p_x} and π^*_{2p_y} .

Key concepts

Molecular Orbital Diagrams

When studying molecular orbital diagrams, it's crucial to understand how atoms in a molecule share electrons in molecular orbitals. These diagrams visually represent how atomic orbitals combine to form molecular orbitals, illustrating both the bonding and anti-bonding interactions between atoms. The key energy levels in a molecular orbital diagram indicate the respective energies of different molecular orbitals. To construct a molecular orbital diagram for a diatomic molecule like \(O_2\) or its ions (\(O_2^{-}\), \(O_2^{2-}\)), you fill the available molecular orbitals with electrons \(-\) starting from the lowest energy levels and moving upwards.
This progression from lower energy bonding orbitals to higher energy anti-bonding orbitals helps determine the molecule's stability, bonding order, and magnetic properties. Understanding this concept is fundamental when predicting how changes in electron counts affect molecular properties such as bond length and strength.

Diatomic Molecules

Diatomic molecules comprise only two atoms, which can be either the same element or different elements. In cases like the oxygen molecule \((O_2)\), it consists of two oxygen atoms. These molecules serve as excellent examples for studying molecular orbital theory due to their simplicity and symmetry.
When analyzing diatomic molecules, understand that their behavior and properties are significantly influenced by such factors as

• The types of orbitals involved
• The number of available electrons
• The energy levels of their molecular orbitals

These factors, when plotted in a molecular orbital diagram, help depict interactions between atoms, providing insight into the resultant molecular characteristics.
The simplest diatomic molecules, such as hydrogen (H₂) or oxygen \((O_2)\), often serve as a foundation for understanding more complex molecular structures.

Oxygen Molecule

The oxygen molecule \((O_2)\) is a well-known example of a diatomic molecule studied using molecular orbital theory. Oxygen consists of 12 valence electrons shared between its two atoms, arranged in specific molecular orbitals - \(σ_{1s}\), \(σ^*_{1s}\), \(σ_{2s}\), \(σ^*_{2s}\), \(σ_{2p_z}\), \(π_{2p_x}\), and \(π_{2p_y}\).
In the ground state, these orbitals fill in a way that contains non-bonding, bonding, and anti-bonding electrons, resulting in the molecule's paramagnetic character due to the two unpaired electrons found in the \(π^*\) orbitals.
When extra electrons are added, as in the \(O_2^{-}\) or \(O_2^{2-}\) ions, they occupy the \(π^*\) orbitals, altering molecular properties like magnetism and bond order. Understanding the electron distribution in \(O_2\) through an MO diagram clarifies several unique features of oxygen, including its ability to form various oxidation states and its role in combustion and respiration.

Electron Configuration

Electron configuration refers to the arrangement of electrons within an atom or molecule. In molecular orbital theory, knowing the electron configuration is vital as it influences chemical bonding and molecular stability. For diatomic oxygen \((O_2)\), the configuration shifts depending on the molecule's charge state:

• Neutral \(O_2\) has a configuration of \(σ_{1s}^2 σ^*_{1s}^2 σ_{2s}^2 σ^*_{2s}^2 σ_{2p_z}^2 π_{2p_x}^2 π_{2p_y}^2 π^*_{2p_x}^1 π^*_{2p_y}^1\)
• For \(O_2^{-}\), one additional electron means one of the \(π^*\) orbitals gains another electron, changing the electron distribution.
• In \(O_2^{2-}\), the extra two electrons fully pair up in the \(π^*\) orbitals, rendering the molecule diamagnetic.

Understanding how electrons are distributed in various molecular states offers insights into molecular reactivity and bonding patterns, aiding in predicting molecule behavior in chemical processes.