Problem 46
Sketch the shapes of the following molecular orbitals: \(\sigma_{1 s}, \sigma_{1 s}^{*}, \pi_{2 p}, \pi_{2 p}^{*} .\) How do their energies compare?
Problem 47
Explain the significance of bond order. Can bond order be used for quantitative comparisons of the strengths of chemical bonds?
Problem 48
Explain in molecular orbital terms the changes in \(\mathrm{H}-\mathrm{H}\) internuclear distance that occur as the molecular \(\mathrm{H}_{2}\) is ionized first to \(\mathrm{H}_{2}^{+}\) and then to \(\mathrm{H}_{2}^{2+}\).
Problem 49
The formation of \(\mathrm{H}_{2}\) from two \(\mathrm{H}\) atoms is an energetically favorable process. Yet statistically there is less than a 100 percent chance that any two \(\mathrm{H}\) atoms will undergo the reaction. Apart from energy considerations, how would you account for this observation based on the electron spins in the two \(\mathrm{H}\) atoms?
Problem 50
Draw a molecular orbital energy level diagram for each of the following species: \(\mathrm{He}_{2}, \mathrm{HHe}, \mathrm{He}_{2}^{+}\). Compare their relative stabilities in terms of bond orders. (Treat HHe as a diatomic molecule with three electrons.)
Problem 51
Arrange the following species in order of increasing stability: \(\mathrm{Li}_{2}, \mathrm{Li}_{2}^{+}, \mathrm{Li}_{2}^{-}\). Justify your choice with a molecular orbital energy level diagram.
Problem 52
Use molecular orbital theory to explain why the \(\mathrm{Be}_{2}\) molecule does not exist.
Problem 53
Which of these species has a longer bond, \(\mathrm{B}_{2}\) or \(\mathrm{B}_{2}^{+} ?\) Explain in terms of molecular orbital theory.
Problem 54
Acetylene \(\left(\mathrm{C}_{2} \mathrm{H}_{2}\right)\) has a tendency to lose two protons \(\left(\mathrm{H}^{+}\right)\) and form the carbide ion \(\left(\mathrm{C}_{2}^{2-}\right),\) which is present in a number of ionic compounds, such as \(\mathrm{CaC}_{2}\) and \(\mathrm{MgC}_{2}\). Describe the bonding scheme in the \(\mathrm{C}_{2}^{2-}\) ion in terms of molecular orbital theory. Compare the bond order in \(\mathrm{C}_{2}^{2-}\) with that in \(\mathrm{C}_{2}\).
Problem 55
Compare the Lewis and molecular orbital treatments of the oxygen molecule.
