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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 H鈧� 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 H鈧�, two 1s orbitals from two H atoms interact and form a bonding molecular orbital (蟽) and an antibonding molecular orbital (蟽*). In an H鈧� molecule, there are two electrons, which fill the lower energy bonding orbital (蟽).
02

Exciting an electron in the H鈧� molecule

In scenario (a), we add enough energy to excite one electron from the bonding (蟽) to the antibonding (蟽*) 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 H鈧� 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 H鈧� 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

Explain the difference between the \(\sigma\) and \(\pi\) MOs for homonuclear diatomic molecules. How are bonding and antibonding orbitals different? Why are there two \(\pi\) MOs and one \(\sigma\) MO? Why are the \(\pi\) MOs degenerate?

The three \(\mathrm{NO}\) bonds in \(\mathrm{NO}_{3}^{-}\) are all equivalent in length and strength. How is this explained even though any valid Lewis structure for \(\mathrm{NO}_{3}^{-}\) has one double bond and two single bonds to nitrogen?

Use the localized electron model to describe the bonding in \(\mathrm{CCl}_{4}\).

In Exercise 89 in Chapter 8, the Lewis structures for benzene \(\left(\mathrm{C}_{6} \mathrm{H}_{6}\right)\) were drawn. Using one of the Lewis structures, estimate \(\Delta H_{\mathrm{f}}^{\circ}\) for \(\mathrm{C}_{6} \mathrm{H}_{6}(g)\) using bond energies and given that the standard enthalpy of formation of \(\mathrm{C}(g)\) is \(717 \mathrm{~kJ} / \mathrm{mol}\). The experimental \(\Delta H_{\mathrm{f}}^{\circ}\) value of \(\mathrm{C}_{6} \mathrm{H}_{6}(g)\) is \(83 \mathrm{~kJ} / \mathrm{mol} .\) Explain the discrepancy between the experimental value and the calculated \(\Delta H_{\mathrm{f}}^{\circ}\) value for \(\mathrm{C}_{6} \mathrm{H}_{6}(g)\)

In the molecular orbital model, compare and contrast \(\sigma\) bonds with \(\pi\) bonds. What orbitals form the \(\sigma\) bonds and what orbitals form the \(\pi\) bonds? Assume the \(z\) -axis is the internuclear axis.
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