Question

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

Ionizing H_2 to H_2^+ increases the internuclear distance; H_2^{2+} typically dissociates due to the lack of a bond.

Step-by-step solution

Understanding the Initial Molecule ( H_2 )

The hydrogen molecule ( H_2 ) is composed of two hydrogen atoms, each contributing one electron, resulting in a total of two electrons. These electrons fill the σ_{1s} bonding molecular orbital, leading to a stable bond with an internuclear distance that is optimal for electron sharing.

Ionization to H_2^+

When H_2 is ionized to form H_2^+ , one electron is removed from the σ_{1s} bonding molecular orbital. This results in only one electron remaining in the bonding orbital. Although there is still attraction that holds the two atoms together, the bond is weakened compared to H_2 due to the loss of a bonding electron. Consequently, the internuclear distance typically increases because there is less electron density to hold the hydrogen nuclei together closely.

Ionization to H_2^{2+}

Further ionization to H_2^{2+} results in the removal of the second electron from the σ_{1s} bonding orbital. With no electrons left to maintain a bond in the σ_{1s} orbital, any bonding interaction is lost. As a result, the cohesive force between the two hydrogen nuclei is greatly reduced, causing a significant increase in the internuclear distance or resulting in dissociation of the molecule.

Key concepts

H-H Internuclear Distance

The internuclear distance in molecular chemistry refers to the space between the nuclei of two atoms bonded together. In the case of the hydrogen molecule, \( \text{H}_2 \), two hydrogen atoms share electrons, which allows them to stay bonded. The optimal distance, or the H-H internuclear distance, is achieved when the energy is minimized: it’s close enough for electron sharing without causing repulsion between the positively charged nuclei. Here, the electrons in the \( \sigma_{1s} \) bonding molecular orbital help maintain this bond, keeping the H-H internuclear distance at an equilibrium level.

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

The ionization process involves removing electrons from an atom or molecule, which can significantly alter chemical properties. For molecular \( \text{H}_2 \), ionization occurs in stages. Firstly, when \( \text{H}_2 \) loses one electron due to the input of energy, it becomes \( \text{H}_2^+ \). This is the first ionization stage. Since one bonding electron is removed from the \( \sigma_{1s} \) orbital, the molecule's stability decreases, and the internuclear distance increases.

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

In molecular orbital theory, electrons are not confined to individual atoms but are viewed as occupying "molecular orbitals" spread over a molecule. Specifically, for \( \text{H}_2 \), the bonding molecular orbital \( \sigma_{1s} \) plays a critical role in the molecule's structure. This orbital is formed when atomic orbitals overlap constructively, allowing the sharing of electrons between hydrogen atoms.

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

Removing electrons from a molecule like \( \text{H}_2 \) impacts its structure and the bonding between atoms. Each electron in the \( \sigma_{1s} \) bonding orbital plays a crucial role in maintaining the molecular bond. When an electron is removed during ionization, the attractive force that holds the two hydrogen nuclei together diminishes.

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