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

According to the molecular orbital model, the stable diatomic species among the given options are: a. \(\mathrm{N}_{2}{ }^{2-}\) and \(\mathrm{F}_{2}^{2-}\) b. \(\mathrm{B}_{2}\)

Step-by-step solution

Find the atomic electron configuration

First, we need to find the atomic electron configuration for each atom involved in the diatomic species. 1. N (7): 1s², 2s², 2p³ 2. O (8): 1s², 2s², 2p⁴ 3. F (9): 1s², 2s², 2p⁵ 4. Be (4): 1s², 2s² 5. B (5): 1s², 2s², 2p¹ 6. Ne (10): 1s², 2s², 2p⁶

Draw molecular orbital diagrams

Use the atomic electron configuration and knowledge of molecular orbitals to draw the molecular orbital diagrams for each diatomic species. a. For \(\mathrm{N}_{2}{ }^{2-}, \mathrm{O}_{2}^{2-}, \mathrm{F}_{2}^{2-}\), we need to fill in the electrons and consider the extra two electrons due to the negative charge: 1. \(\mathrm{N}_{2}{ }^{2-}\): N has 7 electrons + 2 from the charge = 9 electrons per atom in the molecule 2. \(\mathrm{O}_{2}^{2-}\): O has 8 electrons + 2 from the charge = 10 electrons per atom in the molecule 3. \(\mathrm{F}_{2}^{2-}\): F has 9 electrons + 2 from the charge = 11 electrons per atom in the molecule b. For \(\mathrm{Be}_{2}, \mathrm{~B}_{2}, \mathrm{Ne}_{2}\), we need to fill in the electrons as they are in their neutral state: 1. \(\mathrm{Be}_{2}\): Be has 4 electrons per atom in the molecule 2. \(\mathrm{B}_{2}\): B has 5 electrons per atom in the molecule 3. \(\mathrm{Ne}_{2}\): Ne has 10 electrons per atom in the molecule

Analyze molecular orbital diagrams

Compare the number of bonding and antibonding electrons for each diatomic species to determine their stability: a. 1. \(\mathrm{N}_{2}{ }^{2-}\): 10 bonding electrons - 8 antibonding electrons = 2 (Stable) 2. \(\mathrm{O}_{2}^{2-}\): 10 bonding electrons - 10 antibonding electrons = 0 (Unstable) 3. \(\mathrm{F}_{2}^{2-}\): 12 bonding electrons - 10 antibonding electrons = 2 (Stable) b. 1. \(\mathrm{Be}_{2}\): 4 bonding electrons - 4 antibonding electrons = 0 (Unstable) 2. \(\mathrm{B}_{2}\): 6 bonding electrons - 4 antibonding electrons = 2 (Stable) 3. \(\mathrm{Ne}_{2}\): 10 bonding electrons - 10 antibonding electrons = 0 (Unstable)

Conclusion

According to the molecular orbital model, the stable diatomic species among the given options are: a. \(\mathrm{N}_{2}{ }^{2-}\) and \(\mathrm{F}_{2}^{2-}\) b. \(\mathrm{B}_{2}\)

Key concepts

Diatomic Molecules

Diatomic molecules are a fascinating type of molecule composed of only two atoms. In the context of molecular orbital theory, these molecules can consist of identical atoms—like those found in the diatomic gases such as hydrogen (H₂), nitrogen (N₂), and oxygen (O₂)—or different atoms. The molecular orbital theory provides a comprehensive way to predict the stability and properties of diatomic molecules. To understand molecular orbital theory, it is crucial to grasp how atoms combine their atomic orbitals to form molecular orbitals.
The stability of a diatomic molecule depends on the balance between bonding and antibonding interactions. Molecular orbitals are classified into bonding, which stabilize the molecule, and antibonding, which destabilize it. The greater the number of electrons in the bonding orbitals compared to the antibonding, the more stable the molecule tends to be. By using molecular orbital diagrams and counting electrons, scientists can predict with accuracy whether a diatomic molecule will be stable.

Electron Configuration

The electron configuration of an atom is a description of how electrons are distributed among the different atomic orbitals. Understanding electron configurations is key when predicting diatomic molecular behavior and stability using molecular orbital theory. For example, let's consider the electron configurations for some key elements:

• Nitrogen ( (N): 1s^2 2s^2 2p^3 )
• Oxygen ( (O): 1s^2 2s^2 2p^4 )
• Fluorine ( (F): 1s^2 2s^2 2p^5 )

The electronic structure offers insight into which and how many orbitals will overlap when atoms form molecules. When these atoms come together to form diatomic species, their electrons occupy shared molecular orbitals rather than remaining localized on a single atom. This transformation from atomic to molecular orbitals is the heart of molecular orbital theory.

Bonding and Antibonding Electrons

Bonding and antibonding electrons play a fundamental role in determining the stability of a diatomic molecule in molecular orbital theory. When atoms approach each other, their atomic orbitals combine to form molecular orbitals. These orbitals are classified as either bonding or antibonding based on their energy and the constructive or destructive overlap of atomic orbitals.

• Bonding orbitals form when the combination of atomic orbitals results in electron density being amassed between the nuclei of the bonded atoms. This space-filling increases attraction and lowers the overall energy of the molecule, contributing to its stability.
• Antibonding orbitals, marked by an asterisk (*), represent combinations where electron density is located outside the region between the nuclei. These higher-energy orbitals actually decrease the stability of a molecule since they contribute positive energy.

To predict if a diatomic molecule is stable, the number of electrons in bonding orbitals is compared to those in antibonding orbitals. A greater number of electrons in bonding orbitals compared to antibonding signifies a stable molecule, while an equal or greater number of antibonding electrons implies instability. By evaluating this balance, the molecular orbital model provides an effective way to understand and anticipate molecular properties.