Question

Use the valence molecular orbital configuration to determine which of the following species is expected to have the lowest ionization energy: (a) \(\mathrm{C}_{2}^{+} ;\) (b) \(\mathrm{C}_{2}\) (c) \(\mathrm{C}_{2}^{-}\)

Short answer

The species \(C_{2}^{-}\) is expected to have the lowest ionization energy.

Step-by-step solution

Understand the Molecular Ion Notations

The notation of a molecule in the form \(C_{2}^{+}\) or \(C_{2}^{-}\) represents a molecular ion where \(C_{2}^{+}\) has lost an electron and \(C_{2}^{-}\) has gained an electron. ⁠Subsequently, \(C_{2}\) is a neutral molecule with no charge.

Determine the Valence Molecular Orbital Configuration for Each Species

The valence molecular orbital configuration for each species is as follows: For \(C_{2}^{+}\), the highest energy electron resides in the \(\pi\) antibonding orbital; For \(C_{2}\), the highest energy electron is in the \(\pi\) orbital;For \(C_{2}^{-}\), the highest energy electron is in the \(\pi^{*}\) antibonding orbital. The asterisk indicates a higher energy antibonding orbital.

Compare Ionization Energies Based on Valence Molecular Orbital Configurations

Ionization energy increases with the energy of the most loosely bound electron. Hence, \(C_{2}^{-}\) has the lowest ionization energy because the highest energy electron lies in the \(\pi^{*}\) antibonding orbital, which is a higher energy level compared to the \(\pi\) orbital or \(\pi\) antibonding level. Removing an electron from the \(\pi^{*}\) antibonding orbital would require less energy than removing one from the \(\pi\) or \(\pi\) antibonding orbital.

Key concepts

Ionization Energy

Ionization energy is the energy required to remove an electron from a gaseous atom or an ion. It is a crucial property that reflects how strongly an atom holds onto its electrons. The higher the ionization energy, the more difficult it is to remove an electron. This property is influenced by several factors:

• Atomic Size: Smaller atoms have higher ionization energies because their electrons are closer to the nucleus.
• Charge of the Ion: Positive ions (cations) generally have higher ionization energies compared to their neutral counterparts.
• Electron Configuration: Electrons that are in lower energy orbitals or in stable configurations are harder to remove.

In the context of molecular orbitals, understanding ionization energy involves analyzing where the highest-energy electron resides. Electrons in higher energy orbitals are less tightly bound and thus require less energy to be removed. This is why the ionization energy of \( \mathrm{C}_{2}^{-} \) is lower compared to \( \mathrm{C}_{2} \) and \( \mathrm{C}_{2}^{+} \). Its highest energy electron is in an antibonding orbital, which is a higher energy state.

Molecular Ions

Molecular ions are molecules that have gained or lost electrons, resulting in a net charge. They are denoted with a superscript indicating the charge, such as \( \mathrm{C}_{2}^{-} \) for a negative charge or \( \mathrm{C}_{2}^{+} \) for a positive charge. The process of ionization can affect the stability and energy of the molecular orbitals within the ion.

• Formation: Ionization occurs due to electron loss or gain, often through chemical reactions or external energy like electromagnetic radiation.
• Properties: Molecular ions can have different properties from their neutral forms, including variations in reactivity and electromagnetic interactions.
• Stability: Ion stability is partly dictated by the electron configuration, with ions often settling into lower energy, more stable configurations if possible.

In a molecular ion like \( \mathrm{C}_{2}^{+} \), the electron is removed from what is usually a higher energy state, which influences properties like ionization energy and chemical reactivity. Understanding these differences is essential to predict the behavior of ions in different environments.

Antibonding Orbitals

Antibonding orbitals are types of molecular orbitals that weaken the bond between atoms when occupied by electrons. They are designated with an asterisk (\( ^* \)), as seen in the \( \pi^{*} \) antibonding orbitals. These orbitals are crucial in determining the molecular stability and the ease with which a molecule can be ionized.

• Formation: Antibonding orbitals are formed when atomic orbitals overlap out of phase, leading to a reduction in electron density between the nuclei.
• Energy Levels: They have higher energy than bonding orbitals, making them less stable when they contain electrons.
• Impact on Stability: Electrons in antibonding orbitals counteract the stabilizing effect of electrons in bonding orbitals, making certain molecules less stable.

In molecular ions, such as \( \mathrm{C}_{2}^{-} \), the presence of electrons in the \( \pi^{*} \) antibonding orbital results in lower overall stability and a lower ionization energy. This is because removing an electron from an antibonding orbital can increase stability, requiring less energy compared to removing an electron from a bonding or non-antibonding orbital. Understanding how antibonding orbitals influence molecular properties helps in predicting reactivity and ionization potential.