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

The internuclear distance of \(H_2\) gets smaller when it is ionized to \(H_2^+\) due to decreased electron-electron repulsion. But when ionized further to \(H_2^{2+}\), the internuclear distance becomes effectively infinite, as there are no bonding interactions left.

Step-by-step solution

Understand the Structure of \(H_2\)

The hydrogen molecule, \(H_2\), consists of two hydrogen atoms bonded together. Each hydrogen atom has one electron in their 1s atomic orbital. When they combine to form \(H_2\), these atomic orbitals overlap and form two molecular orbitals: one bonding (more stable) and one antibonding (less stable). The two electrons of \(H_2\) will occupy the lower-energy bonding molecular orbital.

Ionization to \(H_2^+\)

When \(H_2\) is ionized to \(H_2^+\), one electron is removed. So, \(H_2^+\) has only one electron, and this electron occupies the bonding molecular orbital. The removal of one electron reduces the electron-electron repulsion, leading to a stronger bond between the two Hydrogen atoms and decreasing the internuclear distance.

Ionization to \(H_2^{2+}\)

When \(H_2^+\) is ionized further to \(H_2^{2+}\), the remaining electron is also removed. Consequently, there are no electrons in either the bonding or antibonding molecular orbital. This means there is no bonding interaction between the two hydrogen atoms, and hence the internuclear distance increases to effectively infinity, as the hydrogen molecule breaks up into two separate hydrogen ions.

Key concepts

Ionization of Hydrogen Molecule

Ionization of a hydrogen molecule, denoted as \(H_2\), refers to the process of removing one or more electrons from the molecule, resulting in a positively charged ion. When the first electron is removed, \(H_2\) becomes \(H_2^+\), a molecular ion with a single electron. This electron resides in the bonding molecular orbital, which, as the only electron, reduces the mutual repulsion between the nuclei, allowing them to move closer together. Consequently, the internuclear distance decreases.
Continuing the ionization process by removing the second electron forms \(H_2^{2+}\), an ion with no electrons to mediate the attractive forces between the protons in the nuclei. With no electronic bond, the molecule dissociates, and the distance between the two protons becomes infinitely large. In simplified terms, a delicate balance of forces is disrupted upon ionization, altering the distance between the atomic nuclei.

Bonding and Antibonding Orbitals

In molecular orbital theory, bonding and antibonding orbitals are key concepts that describe the behavior of electrons in a molecule. Bonding orbitals are lower in energy and result from the constructive interference of atomic orbitals. Electrons in these orbitals contribute to the attraction between two nuclei, thereby stabilizing the molecule and making it more energetically favorable.
On the other hand, antibonding orbitals form from the destructive interference of atomic orbitals and are higher in energy. Electrons in these orbitals can destabilize the molecule since they contribute to the repulsion between the nuclei. In \(H_2\), the two electrons normally populate the bonding orbital, reinforcing the bond. However, when one or both electrons are removed through ionization, the effects of the bonding and antibonding orbitals on the internuclear distance are directly impacted.

Molecular Structure

The molecular structure of \(H_2\) is the spatial arrangement of the hydrogen atoms and the distribution of electrons within the molecule. Initially, \(H_2\) has a stable structure with their electrons in the bonding orbital, creating a balance of attractive and repulsive forces that determine the optimal internuclear distance. During ionization, the molecular structure undergoes significant changes. The removal of an electron when forming \(H_2^+\) shifts this balance, tightening the bond and shortening the internuclear distance. Complete ionization to \(H_2^{2+}\) results in a lack of electrons for bonding; the molecular structure ceases to exist as the bond dissociates, leading to two isolated hydrogen nuclei (protons).

Internuclear Distance

Internuclear distance is the space between the nuclei of the atoms in a molecule. In \(H_2\), this distance is determined by the forces of attraction between the positively charged nuclei and the negatively charged electrons, as well as the repulsion between the nuclei themselves. When an electron is removed, resulting in \(H_2^+\), the reduction in repulsion leads to a shorter internuclear distance due to a stronger net attractive force. In contrast, further ionization to \(H_2^{2+}\) entirely eliminates the electrons that contribute to the nuclear attraction. As a result, the molecule disintegrates, and the internuclear distance between the protons is no longer defined in the traditional sense; it increases without bound as the molecule ceases to exist.
Understanding these concepts provides insight into the dynamic adjustments that occur within the molecular structure as a response to changes in electron configuration, evident by the varying internuclear distances.