Question

Which of the following would you expect to be more favorable energetically? Explain. a. an \(\mathrm{H}_{2}\) molecule in which enough energy is added to excite one electron from the bonding to the antibonding \(\mathrm{MO}\) b. two separate \(\mathrm{H}\) atoms

Short answer

The more energetically favorable scenario is b. two separate \(\mathrm{H}\) atoms. This is because they have lower energy levels and are stable in their ground state, whereas the \(\mathrm{H}_{2}\) molecule with the excited electron has a higher energy level and decreased stability due to the presence of the electron in the antibonding MO.

Step-by-step solution

Examine the H2 molecule with an excited electron

In the first scenario, we have an \(\mathrm{H}_{2}\) molecule with enough energy added to excite one electron from the bonding molecular orbital to the antibonding molecular orbital. The bonding MO is formed by the constructive overlap of atomic orbitals, leading to an overall lower energy state and stabilization of the molecule. The antibonding MO is formed by destructive overlap of atomic orbitals, which leads to an overall higher energy state and destabilization of the molecule. When the electron is excited to the antibonding MO, it effectively cancels out the stabilization provided by the bonding MO and increases the overall energy of the molecule. This can make the molecule less stable and more reactive.

Examine the two separate H atoms

In the second scenario, we have two separate \(\mathrm{H}\) atoms. These atoms do not interact with each other, so there is no bonding or antibonding MO involved. Each hydrogen atom has one electron in its 1s atomic orbital, which is the ground state for hydrogen. In this state, the hydrogen atoms have relatively low energy and are stable.

Compare the energy and stability of both scenarios

Now that we have examined both scenarios, we can compare their energetic favorability. In the first scenario, the \(\mathrm{H}_{2}\) molecule with an excited electron has an increased energy level and decreased stability due to the presence of the electron in the antibonding MO. In the second scenario, the two separate \(\mathrm{H}\) atoms have lower energy levels and are stable in their ground state.

Determine the more energetically favorable scenario

Based on the analysis above, we can conclude that the more energetically favorable scenario is: b. two separate \(\mathrm{H}\) atoms This is because they have lower energy levels and are stable in their ground state, whereas the \(\mathrm{H}_{2}\) molecule with the excited electron has a higher energy level and decreased stability due to the presence of the electron in the antibonding MO.

Key concepts

Antibonding Orbitals

Antibonding orbitals are a fascinating concept in molecular chemistry. These orbitals arise when two atomic orbitals combine in such a way that their overlap is destructive. This means that instead of creating a strong connection between the atoms, they weaken or even negate it. The resulting molecular orbital has a higher energy than the original atomic orbitals.

To visualize this, imagine waves on water: when the peaks of two waves coincide, they amplify each other in a constructive way; when a peak and a trough coincide, they cancel each other out, which is destructive. Similarly, antibonding orbitals lead to less stability in a molecule.

In terms of notation, these orbitals are typically denoted with an asterisk (\(*\)). For instance, the antibonding orbital of diatomic hydrogen is written as \(\sigma^{*}\). When electrons occupy these orbitals, the molecule becomes less stable and more energetic, essentially less favorable energetically.

Bonding Molecular Orbital

Bonding molecular orbitals are fundamental to the formation of stable molecules. When atomic orbitals overlap constructively, they form a bonding molecular orbital. This results in a lower energy state compared to the original atomic orbitals.

The bonding molecular orbital is like the sweet spot where the atomic orbitals merge positively, leading to a strong attraction between the nuclei of the combining atoms. You can think of it as a snug handshake that brings two hydrogen atoms together to form an \(\mathrm{H}_{2}\) molecule.

Mathematically, the bonding orbital can be represented as \(\sigma\). Electrons in this orbital experience a lower energy environment, which essentially glues the atoms together more firmly and prevents them from easily breaking apart. That's why these orbital types are key to stability and lower energy configurations in molecules.

Hydrogen Atom Stability

The stability of a hydrogen atom, or any atom, fundamentally relates to its energy state. A single hydrogen atom contains one electron orbiting its nucleus, which is situated in the 1s atomic orbital. This is considered the ground state—an atom's lowest energy state—and it naturally features high stability.

In terms of molecular physics, hydrogen atoms possess a unique stability when isolated. Without external forces such as bonding interactions or elevated energy, this stability remains intact. When two hydrogen atoms approach, if they do not bond, they remain in this stable state without any shared electrons or molecular interactions.

Separately, hydrogen atoms are in a low-energy, stable configuration because each one maintains its electron without interference. This contrasts with scenarios in which atoms interact, such as in the creation of \(\mathrm{H}_{2}\) molecules, where the electrons move into bonding or antibonding orbitals. While bonding brings the atoms together, isolated hydrogen atoms conserve a stable, low-energy environment, which is energetically favorable compared to any excited state where instability might arise.