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

Two separate H atoms (scenario b) are more energetically favorable than an H₂ molecule with one electron excited to the antibonding MO (scenario a). This is because exciting an electron to the antibonding orbital increases the overall energy of the system, making it less energetically stable than two separate H atoms in their ground state.

Step-by-step solution

Understanding Molecular Orbitals

When two atomic orbitals combine, they form molecular orbitals. In the case of H₂, two 1s orbitals from two H atoms interact and form a bonding molecular orbital (σ) and an antibonding molecular orbital (σ*). In an H₂ molecule, there are two electrons, which fill the lower energy bonding orbital (σ).

Exciting an electron in the H₂ molecule

In scenario (a), we add enough energy to excite one electron from the bonding (σ) to the antibonding (σ*) molecular orbital. By promoting this electron to the higher energy antibonding orbital, the energy of the entire system increases, making it less energetically favorable.

Comparing with two separate H atoms

In scenario (b), we have two separate H atoms. Each H atom contains one electron, which occupies the 1s atomic orbital. The energy of each H atom in this state is relatively low compared to that of the H₂ molecule in scenario (a), where one electron has been excited to the antibonding orbital.

Evaluating the most energetically favorable scenario

Comparing scenarios (a) and (b), we can conclude that two separate H atoms (scenario b) would be more energetically favorable than an H₂ molecule with one electron excited to the antibonding MO (scenario a). Exciting an electron to the antibonding orbital increases the overall energy of the system, making it less energetically stable than two separate H atoms in their ground state.