Chapter 11

Indicate several ways in which the valence-bond method is superior to Lewis structures in describing covalent bonds.

Explain why it is necessary to hybridize atomic orbitals when applying the valence-bond method that is, why are there so few molecules that can be described by the overlap of pure atomic orbitals only?

Describe the molecular geometry of \(\mathrm{H}_{2} \mathrm{O}\) suggested by each of the following methods: (a) Lewis theory; (b) valence-bond method using simple atomic orbitals; (c) VSEPR theory; (d) valence-bond method using hybridized atomic orbitals.

Describe the molecular geometry of \(\mathrm{CCl}_{4}\) suggested by each of the following methods: (a) Lewis theory; (b) valence-bond method using simple atomic orbitals; (c) VSEPR theory; (d) valence-bond method using hybridized atomic orbitals.

In which of the following, \(\mathrm{CO}_{3}^{2-}, \mathrm{SO}_{2}, \mathrm{CCl}_{4}, \mathrm{CO}\) \(\mathrm{NO}_{2}^{-},\) would you expect to find \(s p^{2}\) hybridization of the central atom? Explain.

For each of the following species, identify the central atom(s) and propose a hybridization scheme for those \(\operatorname{atom}(\mathrm{s}):(\mathrm{a}) \mathrm{CO}_{2} ;(\mathrm{b}) \mathrm{HONO}_{2} ;(\mathrm{c}) \mathrm{ClO}_{3}^{-} ;(\mathrm{d}) \mathrm{BF}_{4}^{-}\)

Match each of the following species with one of these hybridization schemes: \(s p, s p^{2}, s p^{3}, s p^{3} d, s p^{3} d^{2} .\) (a) \(\mathrm{PF}_{6}^{-}\) (b) \(\operatorname{COS} ;\) (c) \(\operatorname{SiCl}_{4} ;\) (d) \(\mathrm{NO}_{3}^{-}\);(e) AsF \(_{5}\)

Propose a hybridization scheme to account for bonds formed by the central carbon atom in each of the following molecules: (a) hydrogen cyanide, HCN; (b) methyl alcohol, \(\mathrm{CH}_{3} \mathrm{OH} ;\) (c) acetone, \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CO}\) (d) carbamic acid,

Indicate which of the following molecules and ions are linear, which are planar, and which are neither. Then propose hybridization schemes for the central atoms. (a) \(\mathrm{Cl}_{2} \mathrm{C}=\mathrm{CCl}_{2} ;(\mathrm{b}) \mathrm{N} \equiv \mathrm{C}-\mathrm{C} \equiv \mathrm{N} ;(\mathrm{c}) \mathrm{F}_{3} \mathrm{C}-\mathrm{C} \equiv \mathrm{N}\) (d) \([\mathrm{S}-\mathrm{C} \equiv \mathrm{N}]^{-}\)

Write Lewis structures for the following molecules, and then label each \(\sigma\) and \(\pi\) bond. (a) \(\mathrm{HCN} ;\) (b) \(\mathrm{C}_{2} \mathrm{N}_{2}\) (c) \(\mathrm{CH}_{3} \mathrm{CHCHCCl}_{3} ;\) (d) HONO.

Represent bonding in the carbon dioxide molecule, \(\mathrm{CO}_{2},\) by \((\mathrm{a})\) a Lewis structure and \((\mathrm{b})\) the valencebond method. Identify \(\sigma\) and \(\pi\) bonds, the necessary hybridization scheme, and orbital overlap.

The structure of the molecule allene, \(\mathrm{CH}_{2} \mathrm{CCH}_{2}\), is shown here. Propose hybridization schemes for the \(C\) atoms in this molecule.

Explain the essential difference in how the valencebond method and molecular orbital theory describe a covalent bond.

Describe the bond order of diatomic carbon, \(\mathrm{C}_{2},\) with Lewis theory and molecular orbital theory, and explain why the results are different.

\(\mathrm{N}_{2}(\mathrm{g})\) has an exceptionally high bond energy. Would you expect either \(\mathrm{N}_{2}^{-}\) or \(\mathrm{N}_{2}^{2-}\) to be a stable diatomic species in the gaseous state? Explain.

The paramagnetism of gaseous \(\mathrm{B}_{2}\) has been established. Explain how this observation confirms that the \(\pi_{2 p}\) orbitals are at a lower energy than the \(\sigma_{2 p}\) orbital for \(\mathrm{B}_{2}\)

Is it correct to say that when a diatomic molecule loses an electron, the bond energy always decreases (that is, that the bond is always weakened)? Explain.

For the following pairs of molecular orbitals, indicate the one you expect to have the lower energy, and state the reason for your choice. (a) \(\sigma_{1 s}\) or \(\sigma_{1 s}^{*} ;\) (b) \(\sigma_{2 s}\) or \(\sigma_{2 p}\) (c) \(\sigma_{1 s}^{*}\) or \(\sigma_{2 s} ;\) (d) \(\sigma_{2 p}\) or \(\sigma_{2 p}^{*}\)

For each of the species \(\mathrm{C}_{2}^{+}, \mathrm{O}_{2}^{-}, \mathrm{F}_{2}^{+},\) and \(\mathrm{NO}^{+}\) (a) Write the molecular orbital diagram (as in Example \(11-6)\) (b) Determine the bond order, and state whether you expect the species to be stable or unstable. (c) Determine if the species is diamagnetic or paramagnetic; and if paramagnetic, indicate the number of unpaired electrons.

Write plausible molecular orbital diagrams for the following heteronuclear diatomic species: (a) \(\mathrm{NO} ;\) (b) \(\mathrm{NO}^{+}\) (c) \(\mathrm{CO} ;\) (d) \(\mathrm{CN} ;\) (e) \(\mathrm{CN}^{-} ;\) (f) \(\mathrm{CN}^{+} ;\) (g) BN.

Consider the molecules \(\mathrm{NO}^{+}\) and \(\mathrm{N}_{2}^{+}\) and use molecular orbital theory to answer the following: (a) Write the molecular orbital configuration of each ion (ignore the 1 s electrons). (b) Predict the bond order of each ion. (c) Which of these ions is paramagnetic? Which is diamagnetic? (d) Which of these ions do you think has the greater bond length? Explain.

Consider the molecules \(\mathrm{CO}^{+}\) and \(\mathrm{CN}^{-}\) and use molecular orbital theory to answer the following: (a) Write the molecular orbital configuration of each ion (ignore the 1 s electrons). (b) Predict the bond order of each ion. (c) Which of these ions is paramagnetic? Which is diamagnetic? (d) Which of these ions do you think has the greater bond length? Explain.

Construct the molecular orbital diagram for CF. Would you expect the bond length of \(\mathrm{CF}^{+}\) to be longer or shorter than that of CF?

Construct the molecular orbital diagram for CaF. Would you expect the bond length of \(\mathrm{CaF}^{+}\) to be longer or shorter than that of CaF?

Explain why the concept of delocalized molecular orbitals is essential to an understanding of bonding in the benzene molecule, \(\mathrm{C}_{6} \mathrm{H}_{6}\)

Explain how it is possible to avoid the concept of resonance by using molecular orbital theory.

In which of the following molecules would you expect to find delocalized molecular orbitals: (a) \(\mathrm{C}_{2} \mathrm{H}_{4}\) (b) \(\mathrm{SO}_{2} ;\) (c) \(\mathrm{H}_{2} \mathrm{CO}\) ? Explain.

In which of the following ions would you expect to find delocalized molecular orbitals: (a) \(\mathrm{HCO}_{2}^{-} ;\) (b) \(\mathrm{CO}_{3}^{2-}\) (c) \(\mathrm{CH}_{3}^{+} ?\) Explain.

Which of the following factors are especially important in determining whether a substance has metallic properties: (a) atomic number; (b) atomic mass; (c) number of valence electrons; (d) number of vacant atomic orbitals; (e) total number of electronic shells in the atom? Explain.

Magnesium is an excellent electrical conductor even though it has a full \(3 s\) subshell with the electron configuration: [Ne]3s^. Use band theory to explain why magnesium conducts electricity.

From this list of terms-electrical conductor, insulator, semiconductor- -choose the one that best characterizes each of the following materials: (a) stainless steel; (b) solid sodium chloride; (c) sulfur; (d) germanium; (e) seawater; (f) solid iodine.

In what type of material is the energy gap between the valence band and the conduction band greatest: metal, semiconductor, or insulator? Explain.

Which of the following substances, when added in trace amounts to silicon, would produce a \(p\) -type semiconductor: (a) sulfur, (b) arsenic, (c) lead, (d) boron, (e) gallium arsenide, (f) gallium? Explain.

Which of the following substances, when added in trace amounts to germanium, would produce an n-type semiconductor: (a) sulfur, (b) aluminum, (c) tin, (d) cadmium sulfide, (e) arsenic, (f) gallium arsenide? Explain.

Explain why the electrical conductivity of a semiconductor is significantly increased if trace amounts of either donor or acceptor atoms are present, but is unchanged if both are present in equal number.

The energy gap, \(\Delta E\), for silicon is \(110 \mathrm{kJ} / \mathrm{mol}\). What is the minimum wavelength of light that can promote an electron from the valence band to the conduction band in silicon? In what region of the electromagnetic spectrum is this light?

The Lewis structure of \(\mathrm{N}_{2}\) indicates that the nitrogento-nitrogen bond is a triple covalent bond. Other evidence suggests that the \(\sigma\) bond in this molecule involves the overlap of \(s p\) hybrid orbitals. (a) Draw orbital diagrams for the N atoms to describe bonding in \(\mathrm{N}_{2}\) (b) Can this bonding be described by either \(s p^{2}\) or \(s p^{3}\) hybridization of the \(\mathrm{N}\) atoms? Can bonding in \(\mathrm{N}_{2}\) be described in terms of unhybridized orbitals? Explain.

Show that both the valence-bond method and molecular orbital theory provide an explanation for the existence of the covalent molecule \(\mathrm{Na}_{2}\) in the gaseous state. Would you predict \(\mathrm{Na}_{2}\) by the Lewis theory?

Lewis theory is satisfactory to explain bonding in the ionic compound \(\mathrm{K}_{2} \mathrm{O},\) but it does not readily explain formation of the ionic compounds potassium superoxide, \(\mathrm{KO}_{2}\), and potassium peroxide, \(\mathrm{K}_{2} \mathrm{O}_{2}\) (a) Show that molecular orbital theory can provide this explanation. (b) Write Lewis structures consistent with the molecular orbital explanation.

The compound potassium sesquoxide has the empirical formula \(\mathrm{K}_{2} \mathrm{O}_{3}\). Show that this compound can be described by an appropriate combination of potassium, peroxide, and superoxide ions. Write a Lewis structure for a formula unit of the compound.

Draw a Lewis structure for the urea molecule, \(\mathrm{CO}\left(\mathrm{NH}_{2}\right)_{2},\) and predict its geometric shape with the VSEPR theory. Then revise your assessment of this molecule, given the fact that all the atoms lie in the same plane, and all the bond angles are \(120^{\circ} .\) Propose a hybridization and bonding scheme consistent with these experimental observations.

Methyl nitrate, \(\mathrm{CH}_{3} \mathrm{NO}_{3}\), is used as a rocket propellant. The skeletal structure of the molecule is \(\mathrm{CH}_{3} \mathrm{ONO}_{2}\). The N and three O atoms all lie in the same plane, but the \(\mathrm{CH}_{3}\) group is not in the same plane as the \(\mathrm{NO}_{3}\) group. The bond angle \(\mathrm{C}-\mathrm{O}-\mathrm{N}\) is \(105^{\circ},\) and the bond angle \(\mathrm{O}-\mathrm{N}-\mathrm{O}\) is \(125^{\circ} .\) One nitrogen-to-oxygen bond length is \(136 \mathrm{pm},\) and the other two are \(126 \mathrm{pm}\) (a) Draw a sketch of the molecule showing its geometric shape. (b) Label all the bonds in the molecule as \(\sigma\) or \(\pi\), and indicate the probable orbital overlaps involved. (c) Explain why all three nitrogen-to-oxygen bond lengths are not the same.

Fluorine nitrate, \(\mathrm{FONO}_{2}\), is an oxidizing agent used as a rocket propellant. A reference source lists the following data for \(\mathrm{FO}_{\mathrm{a}} \mathrm{NO}_{2}\). (The subscript "a" shows that this O atom is different from the other two.) Bond lengths: \(\mathrm{N}-\mathrm{O}=129 \mathrm{pm}\) $$ \mathrm{N}-\mathrm{O}_{\mathrm{a}}=139 \mathrm{pm} ; \mathrm{O}_{\mathrm{a}}-\mathrm{F}=142 \mathrm{pm} $$ Bond angles: \(\mathrm{O}-\mathrm{N}-\mathrm{O}=125^{\circ}\) $$ \mathrm{F}-\mathrm{O}_{\mathrm{a}}-\mathrm{N}=105^{\circ} $$ \(\mathrm{NO}_{\mathrm{a}} \mathrm{F}\) plane is perpendicular to the \(\mathrm{O}_{2} \mathrm{NO}_{\mathrm{a}}\) plane Use these data to construct a Lewis structure(s), a three-dimensional sketch of the molecule, and a plausible bonding scheme showing hybridization and orbital overlaps.

Draw a Lewis structure(s) for the nitrite ion, \(\mathrm{NO}_{2}^{-}\) Then propose a bonding scheme to describe the \(\sigma\) and the bonding in this ion. What conclusion can you reach about the number and types of \(\pi\) molecular orbitals in this ion? Explain.

Think of the reaction shown here as involving the transfer of a fluoride ion from \(\mathrm{ClF}_{3}\) to \(\mathrm{AsF}_{5}\) to form the ions \(\mathrm{ClF}_{2}^{+}\) and \(\mathrm{AsF}_{6}^{-}\). As a result, the hybridization scheme of each central atom must change. For each reactant molecule and product ion, indicate (a) its geometric structure and (b) the hybridization scheme for its central atom. $$ \mathrm{ClF}_{3}+\mathrm{AsF}_{5} \longrightarrow\left(\mathrm{ClF}_{2}^{+}\right)\left(\mathrm{AsF}_{6}^{-}\right) $$

\(\mathrm{He}_{2}\) does not exist as a stable molecule, but there is evidence that such a molecule can be formed between electronically excited He atoms. Write a molecular orbital diagram to account for this.

The molecule formamide, \(\mathrm{HCONH}_{2}\), has the approximate bond angles \(\mathrm{H}-\mathrm{C}-\mathrm{O}, 123^{\circ} ; \mathrm{H}-\mathrm{C}-\mathrm{N}, 113^{\circ}\) \(\mathrm{N}-\mathrm{C}-\mathrm{O}, 124^{\circ} ; \mathrm{C}-\mathrm{N}-\mathrm{H}, 119^{\circ} ; \mathrm{H}-\mathrm{N}-\mathrm{H}, 119^{\circ}\) The \(\mathrm{C}-\mathrm{N}\) bond length is \(138 \mathrm{pm}\). Two Lewis structures can be written for this molecule, with the true structure being a resonance hybrid of the two. Propose a hybridization and bonding scheme for each structure.

The ion \(\mathrm{F}_{2} \mathrm{Cl}^{-}\) is linear, but the ion \(\mathrm{F}_{2} \mathrm{Cl}^{+}\) is bent. Describe hybridization schemes for the central \(\mathrm{Cl}\) atom consistent with this difference in structure.

A solar cell that is \(15 \%\) efficient in converting solar to electric energy produces an energy flow of \(1.00 \mathrm{kW} / \mathrm{m}^{2}\) when exposed to full sunlight. (a) If the cell has an area of \(40.0 \mathrm{cm}^{2}\), what is the power output of the cell, in watts? (b) If the power calculated in part (a) is produced at \(0.45 \mathrm{V},\) how much current does the cell deliver?

The anion \(I_{4}^{2-}\) is linear, and the anion \(I_{5}^{-}\) is V-shaped, with a \(95^{\circ}\) angle between the two arms of the V. For the central atoms in these ions, propose hybridization schemes that are consistent with these observations.