Question

Which of the following are predicted by the molecular orbital model to be stable diatomic species? a. \(\mathrm{N}_{2}{ }^{2-}, \mathrm{O}_{2}{ }^{2-}, \mathrm{F}_{2}{ }^{2-}\) b. \(\mathrm{Be}_{2}, \mathrm{~B}_{2}, \mathrm{Ne}_{2}\)

Short answer

The stable diatomic species predicted by the molecular orbital model are N₂²⁻ and B₂, as their bond orders calculated are greater than 0. O₂²⁻, F₂²⁻, Be₂, and Ne₂ are not stable diatomic species according to this model.

Step-by-step solution

Determine the electronic configuration for each molecule

For each element in the given list, determine its electron configuration based on its atomic number and the aufbau principle. Recall that for diatomic molecules, the electrons are shared between the two atoms, and the given oxidation states need to be considered: a. \(\mathrm{N}_{2}{ }^{2-}\): N has 7 electrons; N₂ will have 14 electrons; N₂²⁻ will have 14 + 2 = 16 electrons \(\mathrm{O}_{2}{ }^{2-}\): O has 8 electrons; O₂ will have 16 electrons; O₂²⁻ will have 16 + 2 = 18 electrons \(\mathrm{F}_{2}{ }^{2-}\): F has 9 electrons; F₂ will have 18 electrons; F₂²⁻ will have 18 + 2 = 20 electrons b. \(\mathrm{Be}_{2}\): Be has 4 electrons, so Be₂ will have 4 + 4 = 8 electrons \(\mathrm{B}_{2}\): B has 5 electrons, so B₂ will have 5 + 5 = 10 electrons \(\mathrm{Ne}_{2}\): Ne has 10 electrons, so Ne₂ will have 10 + 10 = 20 electrons

Analyze the molecular orbital diagrams

Analyze the molecular orbital diagrams for each element, considering the number of bonding and antibonding electrons. a. For N₂²⁻, we have 16 electrons. The molecular orbital diagram for nitrogen shows that it fills the 1σ bonding, 2σ bonding, 1π bonding, and 3σ antibonding orbitals completely, leaving two extra electrons to occupy the 1π antibonding orbitals. This overall combination yields a bond order of 3 - 1 = 2. For O₂²⁻, we have 18 electrons. The molecular orbital diagram for oxygen shows that it fills the 1σ bonding, 2σ bonding, 1π bonding, and 4σ antibonding orbitals completely, leaving two extra electrons to occupy the 1π antibonding orbitals. This overall combination results in a bond order of 2 - 2 = 0. For F₂²⁻, we have 20 electrons. The molecular orbital diagram for fluorine shows that it fills the 1σ bonding, 2σ bonding, 1π bonding, 4σ antibonding, and 1π antibonding orbitals completely. This overall combination results in a bond order of 1 - 3 = -2. b. For Be₂, we have 8 electrons. The molecular orbital diagram for beryllium indicates that it fills the 1σ bonding, 2σ bonding, and 1σ antibonding orbitals completely. This overall combination results in a bond order of 1 - 1 = 0. For B₂, we have 10 electrons. The molecular orbital diagram for boron shows that it fills the 1σ bonding, 2σ bonding, 1π bonding, and 1σ antibonding orbitals completely. This overall combination results in a bond order of 2 - 1 = 1. For Ne₂, we have 20 electrons. The molecular orbital diagram for neon does not offer any stable diatomic configuration as Ne atoms have filled orbitals and any added bonding electrons would be canceled out by antibonding ones.

Determine the stability of diatomic species

Based on the calculated bond orders in step 2, determine the stability of the diatomic species. If the bond order > 0, the diatomic species is stable; if the bond order ≤ 0, the diatomic species is not stable: a. N₂²⁻: Bond order = 2, stable O₂²⁻: Bond order = 0, not stable F₂²⁻: Bond order = -2, not stable b. Be₂: Bond order = 0, not stable B₂: Bond order = 1, stable Ne₂: No stable diatomic configuration Hence, the stable diatomic species are N₂²⁻ and B₂.

Key concepts

Diatomic Molecules

Diatomic molecules are molecules made up of only two atoms. These atoms can either be the same, like in oxygen (O₂), or different, like in carbon monoxide (CO). In the context of molecular orbital theory, these molecules are particularly interesting because their stability and properties can be analyzed by examining the combination of atomic orbitals. Each atom's atomic orbitals overlap to form molecular orbitals, which can either be bonding or antibonding.

• Bonding molecular orbitals are lower in energy and stabilize the molecule when filled with electrons.
• Antibonding molecular orbitals are higher in energy and destabilize the molecule when filled.

Understanding how these molecular orbitals interact in diatomic molecules allows chemists to predict whether a molecule will be stable. This prediction is crucial in many practical applications, such as developing new materials and understanding chemical reactions.

Bond Order

Bond order is a concept that helps us determine the stability of a molecule. It is calculated using the difference between the number of electrons in bonding and antibonding orbitals. The formula for bond order is:\[\text{Bond Order} = \frac{{\text{Number of bonding electrons} - \text{Number of antibonding electrons}}}{2}\]If the bond order is greater than zero, the molecule is likely to be stable. Conversely, a bond order of zero or less indicates that the molecule may not exist or is highly unstable.
For example, in the case of - \(\text{N}_2^{2-}\), with 16 electrons, the bond order is 2, indicating a stable molecule.- In \(\text{O}_2^{2-}\), with 18 electrons, the bond order is zero, signifying a lack of stability.- Similarly, for \(\text{F}_2^{2-}\), with 20 electrons, a negative bond order of -2 suggests instability.
Understanding bond order helps chemists predict not only the existence but also the strength and length of the bonds between atoms in a molecule.

Electronic Configuration

The electronic configuration of a molecule provides insight into the arrangement of electrons within its molecular orbitals. For diatomic molecules, electronic configuration is crucial as it determines how electrons are distributed in bonding and antibonding orbitals.
For any given diatomic molecule, we consider:

• The number of total electrons, which is the sum of electrons from the individual atoms plus or minus any given charge.
• The Aufbau principle, which is used to fill molecular orbitals from lowest to highest energy.

For instance, consider different electronic configurations:
- In N₂²⁻, there are 16 electrons to be arranged in molecular orbitals leading to a stable configuration. - In O₂²⁻, with 18 total electrons, the filling does not lead to a stable molecule. - Similarly, Ne₂, with 20 electrons, results in filled, but non-stabilizing, orbitals.
The concept of electronic configuration allows chemists to predict and visualize how molecules form bonds and what chemical and physical properties they might exhibit.