Question

Using an MO energy-level diagram, would you expect \(\mathrm{F}_{2}\) to have a lower or higher first ionization energy than atomic fluorine? Why?

Short answer

The first ionization energy of \(\mathrm{F}_{2}\) is higher than the first ionization energy of atomic fluorine, because the highest occupied molecular orbital in \(\mathrm{F}_{2}\) is the \(\sigma_{2p}\) orbital, which is lower in energy than the 2p atomic orbital in atomic fluorine. This makes it more difficult to remove an electron from \(\mathrm{F}_{2}\), thus requiring more energy.

Step-by-step solution

Understanding the MO energy-level diagram

An MO energy-level diagram shows the energy levels of atomic and molecular orbitals as well as their order. Electrons fill up these orbitals based on their energy, starting from the lowest. The first ionization energy refers to the energy needed to remove one electron from the species.

Determine the electron configuration of atomic fluorine

The electron configuration of atomic fluorine is \(1s^{2}2s^{2}2p^{5}\). It has 9 electrons, with the outermost electron in the 2p orbital.

Determine the electron configuration of \(\mathrm{F}_{2}\)

The electron configuration of \(\mathrm{F}_{2}\) is found by filling the molecular orbitals in the energy-level diagram with a total of 18 electrons (9 from each fluorine atom). The electron configuration for \(\mathrm{F}_{2}\) is \(\sigma_{1s}^{2}\sigma_{1s^{*}}^{2}\sigma_{2s}^{2}\sigma_{2s^{*}}^{2}\pi_{2p}^{4}\pi_{2p^{*}}^{4}\sigma_{2p}^{2}\).

Identify the highest occupied molecular orbital in \(\mathrm{F}_{2}\)

The highest occupied molecular orbital in \(\mathrm{F}_{2}\) is the \(\sigma_{2p}\) orbital.

Compare ionization energies

The first ionization energy of atomic fluorine corresponds to the energy required to remove an electron from the 2p atomic orbital, while the first ionization energy of \(\mathrm{F}_{2}\) corresponds to the energy required to remove an electron from the \(\sigma_{2p}\) molecular orbital. Since \(\sigma_{2p}\) is lower in energy than the 2p atomic orbital, the first ionization energy of \(\mathrm{F}_{2}\) will be higher than the first ionization energy of the atomic fluorine. In conclusion, the first ionization energy of \(\mathrm{F}_{2}\) is higher than the first ionization energy of atomic fluorine, as the electrons are found in a lower-energy molecular orbital.

Key concepts

First Ionization Energy

First ionization energy can be thought of as the 'membership fee' required to remove the most loosely bound electron from an atom or a molecule in its gaseous state. It is a reflection of an element's reluctance to part with one of its electrons. The higher the first ionization energy, the more energy is needed to remove the electron, indicating a stronger attraction between the nucleus and the electron.

When we compare \textbf{atomic fluorine} and \textbf{molecular fluorine (\texorpdfstring{\(\boldsymbol{F}_2\)}{F2})}, the variance in first ionization energy stems from the different environments the electron is leaving. In atomic fluorine, the electron is ejected from an individual fluorine atom, whereas in \texorpdfstring{\(F_2\)}{F2}, the electron leaves from a molecular orbital that is shared between two atoms. This shared arrangement often results in a lower energy level for the departing electron, which translates to a higher first ionization energy for the molecule compared to the individual atom.

Molecular Orbitals

The concept of molecular orbitals (MOs) revolutionizes the way we visualize electrons in molecules as opposed to single atoms. Molecular orbitals are formed when atomic orbitals, the regions in an atom where electrons are most likely to be found, overlap as atoms bond together to form a molecule.

In a simplistic view, when two atomic orbitals combine, they create two molecular orbitals — one bonding orbital that has lower energy (promotes stability) and one antibonding orbital with higher energy (disrupts stability). Electrons tend to fill the bonding orbitals before the antibonding ones. This is elegantly captured in \textbf{MO energy-level diagrams}, which visually layout the relative energies of the MOs. For \texorpdfstring{\(F_2\)}{F2}, we see that the last electrons enter the \texorpdfstring{\(\boldsymbol{\text{sigma}}_{2p}\)}{sigma2p} MO, a bonding orbital, which is of crucial importance when discussing ionization energy.

Electron Configuration

Electron configuration serves as a map that guides us through the complex neighborhoods of an atom's electrons. It lets us know where electrons reside and helps predict chemical behavior such as ionization energy. For \textbf{atoms}, like fluorine, the electron configuration is a straightforward list of occupied orbitals. Fluorine, with its configuration of \texorpdfstring{\(1s^2 2s^2 2p^5\)}{1s^2 2s^2 2p^5}, succinctly tells us that its most energetic electron is in a 2p orbital.

However, when atoms marry into the unified entity of a \textbf{molecule} like \texorpdfstring{\(F_2\)}{F2}, the electron configuration becomes a reflection of the molecular orbitals. The notation for molecular fluorine, \texorpdfstring{\(\boldsymbol{\text{sigma}}_{1s}^2 \boldsymbol{\text{sigma}}_{1s^*}^2 \boldsymbol{\text{sigma}}_{2s}^2 \boldsymbol{\text{sigma}}_{2s^*}^2 \boldsymbol{\text{pi}}_{2p}^4 \boldsymbol{\text{pi}}_{2p^*}^4 \boldsymbol{\text{sigma}}_{2p}^2\)}{sigma1s2 sigma1s*2 sigma2s2 sigma2s*2 pi2p4 pi2p*4 sigma2p2}, provides a roadmap of where electrons are distributed in the molecule, with the last two electrons comfortably seated in the sigma2p bonding orbital – a detail that underpins their effect on ionization energy.