Chapter 9: Problem 48
Explain in molecular orbital terms the changes in \(\mathrm{H}-\mathrm{H}\) internuclear distance that occur as the molecular \(\mathrm{H}_{2}\) is ionized first to \(\mathrm{H}_{2}^{+}\) and then to \(\mathrm{H}_{2}^{2+}\).
Short Answer
Step by step solution
Key Concepts
These are the key concepts you need to understand to accurately answer the question.
H-H Internuclear Distance
The equilibrium distance is essential for the molecule's stability. If this distance is too short, the nuclei repel each other. If it's too long, the bond weakens because the shared electrons fail to effectively bridge the hydrogen atoms. Therefore, a balance is achieved at an ideal internuclear distance.
- Maintains balanced interaction
- Optimizes energy conservation
- Facilitates stable bonding
Ionization Process
Further ionizing \( \text{H}_2^+ \) by removing another electron results in \( \text{H}_2^{2+} \). At this stage, all electrons are stripped away from the bonding molecular orbital. This complete removal means there are no bonding electrons left to keep the two hydrogen atoms together, making them likely to separate completely.
- Initial removal makes molecule \( \text{H}_2^+ \)
- Further removal leads to \( \text{H}_2^{2+} \)
- Electron removal weakens or severs bonds
Bonding Molecular Orbital
The \( \sigma_{1s} \) orbital leads to a lower energy state compared to individual hydrogen atoms, making \( \text{H}_2 \) more stable. The shared electrons in this bonding molecular orbital create an attractive force, pulling the two hydrogen nuclei closer, which helps maintain the optimal H-H internuclear distance. The molecular bonding holds the nuclei together, ensuring a stable molecular structure.
- Overlap of atomic orbitals
- Provides electron-sharing mechanism
- Establishes molecular stability
Electron Removal Effects
For \( \text{H}_2 \), the removal of a single electron, creating \( \text{H}_2^+ \), weakens the bond. The internuclear distance extends because less electron density exists between the nuclei, weakening the attraction. If the second electron is removed, forming \( \text{H}_2^{2+} \), no electrons remain to sustain the bond, potentially leading to a complete dissociation of the hydrogen atoms.
- Reduces electron density in bonding region
- Leads to increased internuclear distance
- Potential for complete dissociation without bonding electrons