Use molecular orbital theory to predict if each molecule or ion exists in a relatively stable form. a. H₂^2- b. Ne₂ c. He₂²⁺ d. F₂^2-

Verified step by step guidance

1. Identify the total number of electrons in the molecule or ion. For \( \text{H}_2^{2-} \), each hydrogen atom contributes 1 electron, and the 2- charge adds 2 more electrons, giving a total of 4 electrons.
2. Write the molecular orbital (MO) configuration for the molecule. For \( \text{H}_2^{2-} \), the electrons will fill the molecular orbitals in the order: \( \sigma_{1s} \), \( \sigma_{1s}^* \).
3. Fill the molecular orbitals with the 4 electrons: \( \sigma_{1s}^2 \sigma_{1s}^*^2 \).
4. Calculate the bond order using the formula: \( \text{Bond Order} = \frac{(\text{Number of electrons in bonding MOs} - \text{Number of electrons in antibonding MOs})}{2} \).
5. Determine the stability of the molecule based on the bond order. A positive bond order indicates a stable molecule, while a bond order of zero or negative suggests instability.

Key Concepts

Molecular Orbital Theory

Molecular Orbital Theory (MOT) describes the behavior of electrons in molecules by combining atomic orbitals to form molecular orbitals. These orbitals can be bonding, antibonding, or non-bonding, and the distribution of electrons among them determines the stability and properties of the molecule. In this theory, the stability of a molecule is assessed by the number of electrons in bonding versus antibonding orbitals.

Bonding and Antibonding Orbitals

Bonding orbitals are formed when atomic orbitals combine constructively, leading to increased electron density between nuclei and a stabilizing effect. Conversely, antibonding orbitals arise from destructive interference, resulting in decreased electron density between nuclei and instability. The relative occupancy of these orbitals is crucial for predicting the stability of a molecule or ion, as a higher number of electrons in bonding orbitals typically indicates greater stability.

Electron Configuration in Ions

The electron configuration of ions reflects the distribution of electrons in molecular orbitals after accounting for the charge. For the H22- ion, two additional electrons must be considered, which will occupy the available molecular orbitals. Analyzing the resulting electron configuration helps determine whether the ion is stable, based on the balance between bonding and antibonding electrons.