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 that of atomic fluorine. This is because the highest occupied molecular orbital (HOMO) in \(\mathrm{F}_{2}\) is the nonbonding π*(2p) orbital, which has a higher energy level than the 2p orbital in atomic fluorine. It is easier to remove an electron from the lower-energy 2p orbital in atomic fluorine, resulting in a lower ionization energy compared to \(\mathrm{F}_{2}\).

Step-by-step solution

Understand Molecular Orbital Theory and Ionization Energy

To solve this problem, we need to understand the Molecular Orbital Theory, which explains the formation of bonds between atoms in a molecule. In this theory, atomic orbitals combine to form molecular orbitals that belong to the entire molecule. Electrons in these orbitals help determine the bond order and stability of the molecule. The ionization energy is the energy required to remove an electron from an atom or molecule—higher ionization energy means that it is harder to remove an electron.

Construct the MO energy-level diagram for F₂

To create the MO energy-level diagram for \(\mathrm{F}_{2}\), we need to know the atomic orbitals of F and how they combine to form molecular orbitals. For fluorine, the valence shell electron configuration is 2s²2p⁵. When two F atoms bond, the 2s and 2p orbitals combine to form molecular orbitals. In the MO diagram, the 2s orbitals combine to form σ and σ* molecular orbitals, while the 2p orbitals form following molecular orbitals: σ, π, π*, and σ*. The 2s orbitals are lower in energy than the 2p orbitals. Electrons will fill the molecular orbitals from lowest to highest energy according to the Aufbau principle.

Determine the electron configuration of F₂

Each F atom has 7 valence electrons, which means \(\mathrm{F}_{2}\) has a total of 14 valence electrons. Following the Aufbau principle, electrons fill the molecular orbitals from lowest to highest energy level: - 2 electrons in σ(2s) - 2 electrons in σ*(2s) - 2 electrons in σ(2p) - 4 electrons in π(2p) (2 in each degenerate orbital) - 4 electrons in π*(2p) (2inedegenerate orbital) Now we have filled all 14 valence electrons in the MO diagram.

Comparing the first ionization energy of F₂ and F

From the MO diagram, the highest occupied molecular orbital (HOMO) in \(\mathrm{F}_{2}\) is the nonbonding π*(2p) orbital. In atomic fluorine, the outermost electron is found in the 2p orbital. To remove an electron from \(\mathrm{F}_{2}\), we need to remove one of the electrons from the nonbonding π*(2p) orbital, which has a higher energy level than the bonding orbitals. In atomic fluorine, electrons are in the 2p orbital which is lower in energy than the nonbonding orbitals of \(\mathrm{F}_{2}\), making it easier to remove an electron from atomic fluorine. Therefore, the first ionization energy of atomic fluorine is lower than that of \(\mathrm{F}_{2}\).

Key concepts

MO energy-level diagram

Molecular Orbital (MO) energy-level diagrams are graphical representations that help us understand how molecular orbitals are formed when atomic orbitals combine. These diagrams illustrate how electrons are distributed in a molecule, helping scientists predict properties like bond strength and reactivity.
For F_{2}, the valence shell electron configuration reflects the combination of 2s and 2p atomic orbitals from two fluorine atoms. When these orbitals combine:

• The 2s orbitals form two molecular orbitals: the \( \sigma (2s)\) bonding orbital and the \(\sigma^{*} (2s)\) antibonding orbital.
• The 2p orbitals merge to create: \(\sigma (2p)\), \(\pi (2p)\), \(\pi^{*} (2p)\), and \(\sigma^{*} (2p)\) molecular orbitals.

The energy of these orbitals increases in the order they are listed. Electrons fill these orbitals following the Aufbau principle, ensuring that lower energy orbitals fill first. This systematic filling pattern gives us insight into the bond strengths and the magnetic properties of the molecule.

first ionization energy

Ionization energy refers to the energy needed to remove an electron from an atom or molecule. It's a measure of how tightly an electron is held within an atom or molecule. The higher the ionization energy, the more difficult it is to remove an electron.
Comparing the ionization energy of atomic fluorine to that of the F_{2} molecule involves examining where the electrons reside in their respective energy diagrams. In atomic fluorine, the outermost electron occupies the 2p orbital. In contrast, for F_{2}, the highest electron energy is in the nonbonding \(\pi^{*} (2p)\) molecular orbital, indicating a higher energy level than the 2p orbital of atomic fluorine.
This means that removing an electron from F_{2} requires more energy, as the electron is less tightly held in atomic fluorine due to its location in a lower energy orbital. Thus, F_{2} has a higher first ionization energy compared to atomic fluorine.

bond order

Bond order is a concept in chemistry used to describe the stability of a bond in a molecule. It is calculated as the difference between the number of bonding and antibonding electrons, divided by two. The bond order provides insight into the bond strength and length:- A higher bond order implies a stronger and shorter bond.In F_{2}, the bond order can be calculated using its electron configuration from the MO diagram:

• There are 8 bonding electrons (in \(\sigma(2s)\) and \(\sigma(2p)\), \(\pi(2p)\)) and 6 antibonding electrons (in \(\sigma^{*}(2s)\) and \(\pi^{*}(2p)\)).

The bond order for F_{2} is \(\frac{1}{2}(8 - 6) = 1\), indicating a stable single bond between the two fluorine atoms. Bond order affects not just the length and strength of a bond, but also the molecule's stability, making it a crucial factor in predicting how a molecule behaves.

electron configuration

Electron configuration refers to the distribution of electrons among orbitals in a molecule. In molecular orbital theory, this configuration is important for understanding molecular properties and behavior.
For F_{2}, with a total of 14 electrons shared between the two fluorine atoms, the MO electron configuration illustrates how these electrons are arranged:- 2 electrons fill the \(\sigma(2s)\) orbital.- 2 electrons fill the \(\sigma^{*}(2s)\) orbital, which is antibonding.- 2 electrons fill the \(\sigma(2p)\) bonding orbital.- 4 electronseach fill the degenerate \(\pi(2p)\) orbitals, and \(\pi^{*}(2p)\) orbitals, which are antibonding.This configuration results in a stable F_{2} molecule with a bond order of 1. By looking at the electron configuration, we can predict the molecule's properties such as reactivity, stability, and even color, if applicable. Understanding this distribution is key to mastering molecular interactions and the predictions of molecular behavior.