Chapter 11

Pentadiene, \(\mathrm{C}_{5} \mathrm{H}_{8},\) has three isomers, depending on the position of the two double bonds. Determine the shape of these isomers by using VSEPR theory. Describe the bonding in these molecules by using the valence-bond method. Do the shapes agree in the two theories? Use molecular orbital theory to decide which of these molecules has a delocalized \(\pi\) system. Sketch the molecular orbital and an energy-level diagram.

A conjugated hydrocarbon has an alternation of double and single bonds. Draw the molecular orbitals of the \(\pi\) system of 1,3,5 -hexatriene. If the energy required to excite an electron from the HOMO to the LUMO corresponds to a wavelength of \(256 \mathrm{nm},\) do you expect the wavelength for the corresponding excitation in 1,3,5,7 -octatetraene to be a longer or shorter wavelength?

The 60 -cycle alternating electric current (AC) commonly used in households changes direction 120 times per second. That is, in a one-second time period a terminal at an electric outlet is positive 60 times and negative 60 times. In direct electric current (DC), the flow between terminals is in one direction only. A rectifer is a device that converts alternating to direct current. One type of rectifier is the \(p-n\) junction rectifier. It is commonly incorporated in adapters required to operate electronic devices from ordinary house current. In the operation of this rectifier, a \(p\) -type semiconductor and an \(n\) -type semiconductor are in contact along a boundary, or junction. Each semiconductor is connected to one of the terminals in an AC electrical outlet. Describe how this rectifier works. That is, show that when the semiconductors are connected to the terminals in an AC outlet, half the time a large flow of charge occurs and half the time essentially no charge flows across the \(p-n\) junction.

Furan, \(\mathrm{C}_{4} \mathrm{H}_{4} \mathrm{O},\) is a substance derivable from oat hulls, corn cobs, and other cellulosic waste. It is a starting material for the synthesis of other chemicals used as pharmaceuticals and herbicides. The furan molecule is planar and the \(\mathrm{C}\) and \(\mathrm{O}\) atoms are bonded into a fivemembered pentagonal ring. The H atoms are attached to the C atoms. The chemical behavior of the molecule suggests that it is a resonance hybrid of several contributing structures. These structures show that the double bond character is associated with the entire ring in the form of a \(\pi\) electron cloud. (a) Draw Lewis structures for the several contributing structures to the resonance hybrid mentioned above. (b) Draw orbital diagrams to show the orbitals that are involved in the \(\sigma\) and \(\pi\) bonding in furan. [Hint: You need use only one of the contributing structures, such as the one with no formal charges.] (c) How many \(\pi\) electrons are there in the furan molecule? Show that this number of \(\pi\) electrons is the same, regardless of the contributing structure you use for this assessment.

Borazine, \(\mathrm{B}_{3} \mathrm{N}_{3} \mathrm{H}_{6}\) is often referred to as inorganic benzene because of its similar structure. Like benzene, borazine has a delocalized \(\pi\) system. Describe the molecular orbitals of the \(\pi\) system. Identify the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). How many nodes does the LUMO possess?

Construct a molecular orbital diagram for \(\mathrm{HF}\), and label the molecular orbitals as bonding, antibonding, or nonbonding.

In your own words, define the following terms or symbols: (a) \(s p^{2} ;\) (b) \(\sigma_{2 p}^{*} ;\) (c) bond order; (d) \(\pi\) bond.

Briefly describe each of the following ideas: (a) hybridization of atomic orbitals; (b) \(\sigma\) -bond framework; (c) Kekulé structures of benzene, \(\mathrm{C}_{6} \mathrm{H}_{6}\) (d) band theory of metallic bonding.

Explain the important distinctions between the terms in each of the following pairs: (a) \(\sigma\) and \(\pi\) bonds; (b) localized and delocalized electrons; (c) bonding and antibonding molecular orbitals; (d) metal and semiconductor.

A molecule in which \(s p^{2}\) hybrid orbitals are used by the central atom in forming covalent bonds is (a) \(\mathrm{PCl}_{5}\) (b) \(\mathrm{N}_{2} ;\) (c) \(\mathrm{SO}_{2} ;\) (d) \(\mathrm{He}_{2}\)

The bond angle in \(\mathrm{H}_{2} \mathrm{Se}\) is best described as (a) between \(109^{\circ}\) and \(120^{\circ} ;\) (b) less than in \(\mathrm{H}_{2} \mathrm{S} ;\) (c) less than in \(\mathrm{H}_{2} \mathrm{S},\) but not less than \(90^{\circ} ;(\mathrm{d})\) less than \(90^{\circ}\)

The hybridization scheme for the central atom includes a \(d\) orbital contribution in (a) \(\mathrm{I}_{3}^{-} ;\) (b) \(\mathrm{PCl}_{3}\) (c) \(\mathrm{NO}_{3}^{-} ;\) (d) \(\mathrm{H}_{2}\) Se.

Of the following, the species with a bond order of 1 is (a) \(\mathrm{H}_{2}^{+} ;\) (b) \(\mathrm{Li}_{2} ;\) (c) \(\mathrm{He}_{2} ;\) (d) \(\mathrm{H}_{2}^{-}\)

The hybridization scheme for Xe in \(\mathrm{XeF}_{2}\) is (a) \(s p\) (b) \(s p^{3} ;\) (c) \(s p^{3} d ;\) (d) \(s p^{3} d^{2}\)

Delocalized molecular orbitals are found in (a) \(\mathrm{H}_{2}\) (b) \(\mathrm{HS}^{-} ;\) (c) \(\mathrm{CH}_{4} ;\) (d) \(\mathrm{CO}_{3}^{2-}\) .

The best electrical conductor of the following materials is (a) \(\mathrm{Li}(\mathrm{s}) ;\) (b) \(\mathrm{Br}_{2}(\mathrm{l}) ;\) (c) \(\mathrm{Ge}(\mathrm{s}) ;\) (d) \(\mathrm{Si}(\mathrm{s})\).

A substance in which the valence and conduction bands overlap is (a) a semiconductor; (b) a metalloid; (c) a metal; (d) an insulator.

Explain why the molecular structure of \(\mathrm{BF}_{3}\) cannot be adequately described through overlaps involving pure \(s\) and \(p\) orbitals.

Why does the hybridization \(s p^{3} d\) not account for bonding in the molecule BrF \(_{5} ?\) What hybridization scheme does work? Explain.

What is the total number of (a) \(\sigma\) bonds and (b) \(\pi\) bonds in the molecule \(\mathrm{CH}_{3} \mathrm{NCO}\) ?

102\. Which of the following species are paramagnetic? (a) \(\mathrm{B}_{2} ;\) (b) \(\mathrm{B}_{2}^{-} ;\) (c) \(\mathrm{B}_{2}^{+}\). Which species has the strongest bond?

Use the valence molecular orbital configuration to determine which of the following species is expected to have the lowest ionization energy: (a) \(\mathrm{C}_{2}^{+} ;\) (b) \(\mathrm{C}_{2}\) (c) \(\mathrm{C}_{2}^{-}\)

Use the valence molecular orbital configuration to determine which of the following species is expected to have the greatest electron affinity: (a) \(\mathrm{C}_{2}^{+} ;\) (b) \(\mathrm{Be}_{2}\) (c) \(\mathrm{F}_{2} ;\) (d) \(\mathrm{B}_{2}^{+}\)

Which of these diatomic molecules do you think has the greater bond energy, \(\mathrm{Li}_{2}\) or \(\mathrm{C}_{2} ?\) Explain.

Construct a concept map that embodies the ideas of valence bond theory.

Construct a concept map that connects the ideas of molecular orbital theory.

Construct a concept map that describes the interconnection between valence- bond theory and molecular orbital theory in the description of resonance structures.