Problem 112 - Chemistry: An Atoms-Focused Approach

Question

Do any of the anions of the homonuclear diatomic molecules formed by \(\mathrm{B}, \mathrm{C}, \mathrm{N}, \mathrm{O},\) and \(\mathrm{F}\) have shorter bond lengths than those of the corresponding neutral molecules? Consider only the \(1-\) and \(2-\) anions.

Step-by-Step Solution

Answer

Short Answer: No, none of the anions of the homonuclear diatomic molecules formed by B, C, N, O, and F have shorter bond lengths compared to their neutral states. This is because the anionic states experience increased electron repulsion and the formation of additional antibonding orbitals, which increase bond lengths.

Step 1: Understanding Molecular Orbitals and Bond Length

Molecular orbitals (MO) are formed from the combination of atomic orbitals. Bond length is the distance between the nuclei of two atoms in a molecule. A shorter bond length often indicates stronger bonding between the atoms. Comparing the stability of the anions and their neutral counterparts can help us draw conclusions about their bond lengths.

Step 2: B₂ Molecule

For the B₂ molecule, the electrons fill the molecular orbitals in the order \(\sigma_{1s}^2, \sigma_{1s}^{*2}, \sigma_{2s}^2, \sigma_{2s}^{*2}, \pi_{2px}^1, \pi_{2py}^1\). The anionic molecules are: 1. B₂⁻: \(\sigma_{1s}^2, \sigma_{1s}^{*2}, \sigma_{2s}^2, \sigma_{2s}^{*2}, \pi_{2px}^2, \pi_{2py}^1\) 2. B₂²⁻: \(\sigma_{1s}^2, \sigma_{1s}^{*2}, \sigma_{2s}^2, \sigma_{2s}^{*2}, \pi_{2px}^2, \pi_{2py}^2\) Since electron filling remains the same, there is no significant change in bond lengths.

Step 3: C₂ Molecule

For the C₂ molecule, the electrons fill the molecular orbitals in the order \(\sigma_{1s}^2, \sigma_{1s}^{*2}, \sigma_{2s}^2, \sigma_{2s}^{*2}, \pi_{2px}^2, \pi_{2py}^2\). The anionic molecules are: 1. C₂⁻: \(\sigma_{1s}^2, \sigma_{1s}^{*2}, \sigma_{2s}^2, \sigma_{2s}^{*2}, \pi_{2px}^2, \pi_{2py}^2, \pi_{2pz}^1\) 2. C₂²⁻: \(\sigma_{1s}^2, \sigma_{1s}^{*2}, \sigma_{2s}^2, \sigma_{2s}^{*2}, \pi_{2px}^2, \pi_{2py}^2, \pi_{2pz}^2\) The increasing electron repulsion in the anions would result in increased bond lengths, so the anions have longer bond lengths than the neutral molecule.

Step 4: N₂ Molecule

For the N₂ molecule, the electrons fill the molecular orbitals in the order \(\sigma_{1s}^2, \sigma_{1s}^{*2}, \sigma_{2s}^2, \sigma_{2s}^{*2}, \pi_{2px}^2, \pi_{2py}^2, \sigma_{2pz}^2\). The anionic molecules are: 1. N₂⁻: \(\sigma_{1s}^2, \sigma_{1s}^{*2}, \sigma_{2s}^2, \sigma_{2s}^{*2}, \pi_{2px}^2, \pi_{2py}^2, \sigma_{2pz}^2, \pi_{2pz}^1\) 2. N₂²⁻: \(\sigma_{1s}^2, \sigma_{1s}^{*2}, \sigma_{2s}^2, \sigma_{2s}^{*2}, \pi_{2px}^2, \pi_{2py}^2, \sigma_{2pz}^2, \pi_{2pz}^2\) The formation of additional antibonding orbitals and increasing electron repulsion will cause an increase in bond length, so both anions will have longer bond lengths than the neutral molecule.

Step 5: O₂ Molecule

For the O₂ molecule, the electrons fill the molecular orbitals in the order \(\sigma_{1s}^2, \sigma_{1s}^{*2}, \sigma_{2s}^2, \sigma_{2s}^{*2}, \pi_{2px}^2, \pi_{2py}^2, \sigma_{2pz}^{*1}, \pi_{2pz}^1\). The anionic molecules are: 1. O₂⁻: \(\sigma_{1s}^2, \sigma_{1s}^{*2}, \sigma_{2s}^2, \sigma_{2s}^{*2}, \pi_{2px}^2, \pi_{2py}^2, \sigma_{2pz}^{*1}, \pi_{2pz}^2\) 2. O₂²⁻: \(\sigma_{1s}^2, \sigma_{1s}^{*2}, \sigma_{2s}^2, \sigma_{2s}^{*2}, \pi_{2px}^2, \pi_{2px}^2, \sigma_{2pz}^{*1}, \pi_{2pz}^2, \sigma_{2pz}^{*2}\) The bond length increases in both anions due to the formation of additional antibonding orbitals and increasing electron repulsion.

Step 6: F₂ Molecule

For the F₂ molecule, the electrons fill the molecular orbitals in the order \(\sigma_{1s}^2, \sigma_{1s}^{*2}, \sigma_{2s}^2, \sigma_{2s}^{*2}, \pi_{2px}^2, \pi_{2py}^2, \sigma_{2pz}^{*2}, \pi_{2pz}^2\). The anionic molecules are: 1. F₂⁻: \(\sigma_{1s}^2, \sigma_{1s}^{*2}, \sigma_{2s}^2, \sigma_{2s}^{*2}, \pi_{2px}^2, \pi_{2py}^2, \sigma_{2pz}^{*2}, \pi_{2pz}^2, \sigma_{3s}^1\) 2. F₂²⁻: \(\sigma_{1s}^2, \sigma_{1s}^{*2}, \sigma_{2s}^2, \sigma_{2s}^{*2}, \pi_{2px}^2, \pi_{2py}^2, \sigma_{2pz}^{*2}, \pi_{2pz}^2, \sigma_{3s}^2\) The electron filling in anions leads to an increase in bond length due to increased electron repulsion.

Step 7: Conclusion

None of the anions of the homonuclear diatomic molecules formed by B, C, N, O, and F have shorter bond lengths than those of the corresponding neutral molecules. In all cases, the bond length increases in the anionic states (1- and 2-) due to the increasing electron repulsion and the formation of additional antibonding orbitals.

Key Concepts

Bond Length

Bond length refers to the distance between two nuclei in a molecule. It's a crucial parameter that can tell us a lot about the nature of the chemical bond.
A shorter bond length indicates a stronger attraction between the bonded atoms, while longer bond lengths suggest weaker bonds.
In general, several factors affect bond length:

• Number of Bonding Electrons: More electrons in bonding orbitals often lead to shorter bond lengths.
• Orbital Hybridization: Different hybridizations can affect bond lengths due to varying proportions of s and p orbital character.
• Electronegativity: Differences in electronegativity can pull electron density towards one atom, modifying bond length.
• Electron Repulsion: Increased electron repulsion between electron clouds or in antibonding orbitals can lengthen bonds.

For homonuclear diatomic molecules formed from elements like B, C, N, O, and F, bond length changes when they form anions (extra electrons), which could potentially increase due to added electron-electron repulsion.

Homonuclear Diatomic Molecules

Homonuclear diatomic molecules are made of two identical atoms, such as \( ext{B}_2, ext{C}_2, ext{N}_2, ext{O}_2, ext{F}_2 \). These types of molecules help us explore concepts of symmetry in molecular orbitals and bonding.In these molecules, the shared electron cloud is symmetrically distributed, owing to the identical nature of the atoms involved. This symmetry affects how molecular orbitals form and interact. The principle of molecular orbital theory states that

• Atomic orbitals combine to form bonding and antibonding molecular orbitals.
• Electrons prefer to occupy these orbitals in a way that lowers energy, favoring bonding orbitals over antibonding ones.
• When additional electrons are added as in the case of anion formation, they prefer to occupy the next available orbital which is often antibonding.

Concerning the inquiry into bond lengths, the addition of electrons typically fills these antibonding orbitals, leading to increased internuclear repulsion and hence longer bond lengths.

Electron Repulsion

Electron repulsion occurs because electrons, which carry negative charges, will naturally repel each other. This fundamental principle directly affects the structure and properties of molecules.Consider homonuclear diatomic molecules turning into anions by adding electrons (\(-1\) or \(-2\) charges). When electrons are added to an occupied or higher-energy orbital:

• Increased Electron Density: Added electrons increase electron density in key regions, leading to greater electron-electron repulsion.
• Antibonding Orbitals: Electrons often enter antibonding orbitals, which are higher in energy and less stable.

Both these factors cause an expansion of bond lengths compared to the neutral molecule. In essence, because the electron clouds are attempting to maintain as much distance as possible from one another, greater repulsion results in the elongation of the bond within the molecule.
Thus, understanding electron repulsion is crucial for explaining why anions of homonuclear diatomic molecules have longer bond lengths compared to their neutral counterparts.