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Chapter 9: Problem 4

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

Expert verified
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

01

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).
02

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.
03

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.
04

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.

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Most popular questions from this chapter

The allene molecule has the following Lewis structure: Must all hydrogen atoms lie the same plane? If not, what is their spatial relationship? Explain.

Describe the bonding in the first excited state of \(\mathrm{N}_{2}\) (the one closest in energy to the ground state) using the molecular orbital model. What differences do you expect in the properties of the molecule in the ground state as compared to the first excited state? (An excited state of a molecule corresponds to an electron arrangement other than that giving the lowest possible energy.)

Using the molecular orbital model, write electron configurations for the following diatomic species and calculate the bond orders. Which ones are paramagnetic? Place the species in order of increasing bond length and bond energy. a. \(\mathrm{CO}\) b. \(\mathrm{CO}^{+}\) c. \(\mathrm{CO}^{2+}\)

What are the relationships among bond order, bond energy, and bond length? Which of these quantities can be measured?

Values of measured bond energies may vary greatly depending on the molecule studied. Consider the following reactions: $$ \begin{aligned} \mathrm{NCl}_{3}(g) & \longrightarrow \mathrm{NCl}_{2}(g)+\mathrm{Cl}(g) & \Delta H &=375 \mathrm{~kJ} / \mathrm{mol} \\ \mathrm{ONCl}(g) & \longrightarrow \mathrm{NO}(g)+\mathrm{Cl}(g) & \Delta H &=158 \mathrm{~kJ} / \mathrm{mol} \end{aligned} $$ Rationalize the difference in the values of \(\Delta H\) for these reactions, even though each reaction appears to involve only the breaking of one \(\mathrm{N}-\mathrm{Cl}\) bond. (Hint: Consider the bond order of the NO bond in ONCl and in NO.)
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