Solved: The stability of benzene is due to the fact that

Does the \(\mathrm{AlCl}_{3}\) molecule have a dipole moment?

Carbon dioxide has a linear geometry and is nonpolar. Yet we know that the molecule executes bending and stretching motions that create a dipole moment. How would you reconcile these conflicting descriptions about \(\mathrm{CO}_{2}\)?

How many atoms are directly bonded to the central atom in a tetrahedral molecule, a trigonal bipyramidal molecule, and an octahedral molecule?

Which of the following species has a longer bond length: \(\mathrm{F}_2\) or \(\mathrm{F}_{2}^{-}\)?

One way to account for the fact that an \(\mathrm{O}_2\) molecule contains two unpaired electrons is to draw the following Lewis structure: Suggest two reasons why this structure is unsatisfactory.

Predict the geometries of the following species using the VSEPR method: (a) \(\mathrm{PCl}_3\), (b) \(\mathrm{CHCl}_3\), (c) \(\mathrm{SiH}_4\), (d) \(\mathrm{TeCl}_4\).

Define dipole moment. What are the units and symbol for dipole moment?

What is the relationship between the dipole moment and the bond moment? How is it possible for a molecule to have bond moments and yet be nonpolar?

Explain why an atom cannot have a permanent dipole moment.

Draw a potential energy curve for the bond formation in \(\mathrm{F}_{2}\).

(a) What is the hybridization of atomic orbitals? Why is it impossible for an isolated atom to exist in the hybridized state? (b) How does a hybrid orbital differ from a pure atomic orbital? Can two \(2p\) orbitals of an atom hybridize to give two hybridized orbitals?

What is the angle between the following two hybrid orbitals on the same atom? (a) \(s p\) and \(s p\) hybrid orbitals, (b) \(s p^{2}\) and \(s p^{2}\) hybrid orbitals, (c) \(s p^{3}\) and \(s p^{3}\) hybrid orbitals

The allene molecule \(\mathrm{H}_{2} \mathrm{C}=\mathrm{C}=\mathrm{CH}_{2}\) is linear the three \(\mathrm{C}\) atoms lie on a straight line). What are the hybridization states of the carbon atoms? Draw diagrams to show the formation of sigma bonds and pi bonds in allene.

Describe the hybridization of phosphorus in \(\mathrm{PF}_5\)

How many sigma bonds and pi bonds are there in each of the following molecules?

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 \(\mathrm{HHe}\) as a diatomic molecule with three electrons.)

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.

Use molecular orbital theory to explain why the \(\mathrm{Be}_2\) molecule does not exist.

How does a delocalized molecular orbital differ from a molecular orbital such as that found in \(\mathrm{H}_2\) or \(\mathrm{C}_{2} \mathrm{H}_4\)? What do you think are the minimum conditions (for example, number of atoms and types of orbitals) for forming a delocalized molecular orbital?

In Chapter 9 we saw that the resonance concept is useful for dealing with species such as the benzene molecule and the carbonate ion. How does molecular orbital theory deal with these species?

Both ethylene \((\mathrm{C}_{2} \mathrm{H}_4)\) and benzene \((\mathrm{C}_{6} \mathrm{H}_6)\) contain the \(\mathrm{C}=\mathrm{C}\) bond. The reactivity of ethylene is greater than that of benzene. For example, ethylene readily reacts with molecular bromine, whereas benzene is normally quite inert toward molecular bromine and many other compounds. Explain this difference in reactivity.

Acetaminophen is the active ingredient in Tylenol. (a) Write the molecular formula of the compound. (b) What is the hybridization state of each C, N, and O atom? (c) Describe the geometry about each C, N, and O atom.

Caffeine is a stimulant drug present in coffee. (a) Write the molecular formula of the compound. (b) What is the hybridization state of each \(\mathrm{C}\), \(\mathrm{N}\), and \(\mathrm{O}\) atom? (c) Describe the geometry about each \(\mathrm{C}\), \(\mathrm{N}\), and \(\mathrm{O}\) atom.

Predict the geometry of sulfur dichloride \((\mathrm{SCl}_2)\) and the hybridization of the sulfur atom.

Cyclopropane \((\mathrm{C}_{3} \mathrm{H}_6)\) has the shape of a triangle in which a \(\mathrm{C}\) atom is bonded to two \(\mathrm{H}\) atoms and two other \(\mathrm{C}\) atoms at each corner. Cubane \((\mathrm{C}_{8} \mathrm{H}_8)\) has the shape of a cube in which a \(\mathrm{C}\) atom is bonded to one \(\mathrm{H}\) atom and three other \(\mathrm{C}\) atoms at each corner. (a) Draw Lewis structures of these molecules. (b) Compare the \(\mathrm{CCC}\) angles in these molecules with those predicted for an \(sp^3\)-hybridized \(\mathrm{C}\) atom. (c) Would you expect these molecules to be easy to make?

The compound 1,2-dichloroethane \(\left(\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{Cl}_{2}\right)\) is nonpolar, while cis-dichloroethylene \(\left(\mathrm{C}_{2} \mathrm{H}_{2} \mathrm{Cl}_{2}\right)\) has a dipole moment: The reason for the difference is that groups connected by a single bond can rotate with respect to each other, but no rotation occurs when a double bond connects the groups. On the basis of bonding considerations, explain why rotation occurs in 1,2-dichloroethane but not in cis-dichloroethylene.

Does the following molecule have a dipole moment? (Hint: See the answer to Problem 10.39.)

Which of the following molecules are polar?

The stable allotropic form of phosphorus is \(\mathrm{P}_4\), in which each \(\mathrm{P}\) atom is bonded to three other \(\mathrm{P}\) atoms. Draw a Lewis structure of this molecule and describe its geometry. At high temperatures, \(\mathrm{P}_4\) dissociates to form \(\mathrm{P}_2\) molecules containing a \(\mathrm{P}=\mathrm{P}\) bond. Explain why \(\mathrm{P}_4\) is more stable than \(\mathrm{P}_2\).

Which of the following molecules are polar?

The molecule benzyne \((\mathrm{C}_{6} \mathrm{H}_4)\) is a very reactive species. It resembles benzene in that it has a six-membered ring of carbon atoms. Draw a Lewis structure of the molecule and account for the molecule's high reactivity.

Assume that the third-period element phosphorus forms a diatomic molecule, \(\mathrm{P}_2\), in an analogous way as nitrogen does to form \(\mathrm{N}_2\). (a) Write the electronic configuration for \(\mathrm{P}_2\). Use \(\left[\mathrm{Ne}_{2}\right]\) to represent the electron configuration for the first two periods. (b) Calculate its bond order. (c) What are its magnetic properties (diamagnetic or paramagnetic)?

Consider a \(\mathrm{N}_2\) molecule in its first excited electronic state; that is, when an electron in the highest occupied molecular orbital is promoted to the lowest empty molecular orbital. (a) Identify the molecular orbitals involved and sketch a diagram to show the transition. (b) Compare the bond order and bond length of \(\mathrm{N}_{2} *\) with \(\mathrm{N}_2\), where the asterisk denotes the excited molecule. (c) Is \(\mathrm{N}_{2} *\) diamagnetic or paramagnetic? (d) When \(\mathrm{N}_{2} *\) loses its excess energy and converts to the ground state \(\mathrm{N}_2\), it emits a photon of wavelength 470 nm, which makes up part of the auroras lights. Calculate the energy difference between these levels.

Which of the following ions possess a dipole moment? (a) \(\mathrm{ClF}_2^{+}\) (b) \(\mathrm{ClF}_2^{-}\), (c) \(\mathrm{IF}_4^{+}\), (d) \(\mathrm{IF}_4^{-}\).

Given that the order of molecular orbitals for \(\mathrm{NO}\) is similar to that for \(\mathrm{O}_2\), arrange the following species in increasing bond orders: \(\mathrm{NO}^{2-}\), \(\mathrm{NO}^{-}\), \(\mathrm{NO}\), \(\mathrm{NO}^{+}\), \(\mathrm{NO}^{2+}\).

Shown here are molecular models of \(\mathrm{SF}_4\), \(\mathrm{SCl}_4\), and \(\mathrm{SBr}_4\). Comment on the trends in the bond angle between the axial \(\mathrm{S}?\mathrm{F}\) bonds in these molecules.

How is the geometry of a molecule defined and why is the study of molecular geometry important?

Use the VSEPR model to predict the geometry of (a) \(\mathrm{SiBr}_{4}\), (b) \(\mathrm{CS}_{2}\), and (c) \(\mathrm{NO}_{3}^{-}\)

Which of the following geometries has a greater stability for tin(IV) hydride \(\left(\mathrm{SnH}_{4}\right)\)?

Sketch the shape of a linear triatomic molecule, a trigonal planar molecule containing four atoms, a tetrahedral molecule, a trigonal bipyramidal molecule, and an octahedral molecule. Give the bond angles in each case.

Determine the hybridization state of the underlined atoms in the following compounds: (a) \(\mathrm{SiBr}_{4}\) and \(\mathrm{BCl}_{3}\).

Compare the Lewis theory and the valence bond theory of chemical bonding.

Discuss the basic features of the VSEPR model. Explain why the magnitude of repulsion decreases in the following order: lone pair-lone pair > lone pair-bonding pair > bonding pair-bonding pair.

Describe the hybridization state of \(\mathrm{Se}\) in \(\mathrm{SeF}_{6}\)

What is the hybridization of \(\mathrm{Xe}\) in \(\mathrm{XeF}_{4}\) (see Example 9.12 on p. 398)?

In the trigonal bipyramidal arrangement, why does a lone pair occupy an equatorial position rather than an axial position?

Describe the bonding in the hydrogen cyanide molecule, \(\mathrm{HCN}\). Assume that \(\mathrm{N}\) is sp-hybridized.

Which of the following pairs of atomic orbitals on adjacent nuclei can overlap to form a sigma bond? a pi bond? Which cannot overlap (no bond)? Consider the \(x\) axis to be the internuclear axis. (a) \(1s\) and \(2s\), (b) \(1s\) and \(2p_{x}\), (c) \(2p_{y}\) and \(2p_{y}\), (d) \(3p_{y}\) and \(3p_{z}\), (e) \(2p_{x}\) and \(3p_{x}\).

The geometry of \(\mathrm{CH}_4\) could be square planar, with the four \(\mathrm{H}\) atoms at the corners of a square and the \(\mathrm{C}\) atom at the center of the square. Sketch this geometry and compare its stability with that of a tetrahedral \(\mathrm{CH}_4\) molecule.

Estimate the bond enthalpy (kJ/mol) of the \(\mathrm{H}_{2}^{+}\) ion.

Predict the geometries of the following species: (a) \(\mathrm{AlCl}_3\), (b) \(\mathrm{ZnCl}_2\), (c) \(\mathrm{ZnCl}_{4}^{2-}\).

Describe the bonding in the nitrate ion \(\left(\mathrm{NO}_{3}^{-}\right)\) in terms of resonance structures and delocalized molecular orbitals.

Predict the geometry of the following molecules and ion using the VSEPR model: (a) \(\mathrm{CBr}_4\) (b) \(\mathrm{BCl}_3\) (c) \(\mathrm{NF}_3\), (d) \(\mathrm{H}_{2} \mathrm{Se}\), (e) \(\mathrm{NO}_{2}^{-}\).

Predict the geometry of the following molecules and ion using the VSEPR model: (a) \(\mathrm{CH}_{3} \mathrm{I}\), (b) \(\mathrm{ClF}_3\), (c) \(\mathrm{H}_{2} \mathrm{S}\), (d) \(\mathrm{SO}_3\), (e) \(\mathrm{SO}_{4}^{2-}\).

Predict the geometry of the following molecules using the VSEPR method: (a) \(\mathrm{HgBr}_2\), (b) \(\mathrm{N}_{2} \mathrm{O}\) (arrangement of atoms is NNO), (c) \(\mathrm{SCN}^{-}\) (arrangement of atoms is SCN).

Predict the geometries of the following ions: (a) \(\mathrm{NH}_{4}^{+}\) (b) \(\mathrm{NH}_{2}^{-}\), (c) \(\mathrm{CO}_{3}^{2-}\) , (d) \(\mathrm{ICl}_{2}^{-}\), (e) \(\mathrm{ICl}_{4}^{-}\), (f) \(\mathrm{AlH}_{4}^{-}\), (g) \(\mathrm{SnCl}_{5}^{-}\), (h) \(\mathrm{H}_{3} \mathrm{O}^{+}\), (i) \(\mathrm{BeF}_{4}^{2-}\)

Describe the geometry around each of the three central atoms in the \(\mathrm{CH}_{3} \mathrm{COOH}\) molecule.

Which of the following species are tetrahedral? \(\mathrm{SiCl}_4\), \(\mathrm{SeF}_4\), \(\mathrm{XeF}_4\), \(\mathrm{Cl}_4\), \(\mathrm{CdCl}_{4}^{2-}\)

The bonds in beryllium hydride \((\mathrm{BeH}_2)\) molecules are polar, and yet the dipole moment of the molecule is zero. Explain.

Referring to Table 10.3, arrange the following molecules in order of increasing dipole moment: \(\mathrm{H}_{2} \mathrm{O}\), \(\mathrm{H}_{2} \mathrm{S}\), \(\mathrm{H}_{2} \mathrm{Te}\), \(\mathrm{H}_{2} \mathrm{Se}\).

The dipole moments of the hydrogen halides decrease from \(\mathrm{HF}\) to \(\mathrm{HI}\) (see Table 10.3). Explain this trend.

List the following molecules in order of increasing dipole moment: \(\mathrm{H}_{2} \mathrm{O}\), \(\mathrm{CBr}_{4}\), \(\mathrm{H}_{2} \mathrm{S}\), \(\mathrm{HF}\), \(\mathrm{NH}_{3}\), \(\mathrm{CO}_{2}\).

Does the molecule \(\mathrm{OCS}\) have a higher or lower dipole moment than \(\mathrm{CS}_{2}\)?

Which of the following molecules has a higher dipole moment?

Arrange the following compounds in order of increasing dipole moment:

What is valence bond theory? How does it differ from the Lewis concept of chemical bonding?

Use valence bond theory to explain the bonding in \(\mathrm{Cl}_{2}\) and \(\mathrm{HCl}\). Show how the atomic orbitals overlap when a bond is formed.

How would you distinguish between a sigma bond and a pi bond?

Describe the bonding scheme of the \(\mathrm{AsH}_3\) molecule in terms of hybridization.

What is the hybridization state of \(\mathrm{Si}\) in \(\mathrm{SiH}_4\) and in \(\mathrm{H}_{3} \mathrm{Si}?\mathrm{SiH}_{3}\)?

Describe the change in hybridization (if any) of the A1 atom in the following reaction:

Consider the reaction \(\mathrm{BF}_3+\mathrm{NH}_3\longrightarrow\mathrm{F}_3\mathrm{B}-\mathrm{NH}_3\) Describe the changes in hybridization (if any) of the \(\mathrm{B}\) and \(\mathrm{N}\) atoms as a result of this reaction.

What hybrid orbitals are used by nitrogen atoms in the following species? (a) \(\mathrm{NH}_3\), (b) \(\mathrm{H}_{2} \mathrm{N}?\mathrm{NH}_2\), (c) \(\mathrm{NO}_{3}^{-}\).

What are the hybrid orbitals of the carbon atoms in the following molecules? (a) \(\mathrm{H}_{3} \mathrm{C}?\mathrm{CH}_3\) (b) \(\mathrm{H}_{4} \mathrm{C}?\mathrm{CH}=\mathrm{CH}_2\) (c) \(\mathrm{CH}_{3}?\mathrm{C} \equiv \mathrm{C}?\mathrm{CH}_{2} \mathrm{OH}\) (d) \(\mathrm{CH}_{3} \mathrm{CH}=\mathrm{O}\) (e) \(\mathrm{CH}_{3} \mathrm{COOH}\)

Specify which hybrid orbitals are used by carbon atoms in the following species: (a) \(\mathrm{CO}\), (b) \(\mathrm{CO}_2\), (c) \(\mathrm{CN}^{-}\).

What is the hybridization state of the central \(\mathrm{N}\) atom in the azide ion, \(\mathrm{N}_{3}^{-}\)? (Arrangement of atoms: NNN.)

How many pi bonds and sigma bonds are there in the tetracyanoethylene molecule?

Give the formula of a cation comprised of iodine and fluorine in which the iodine atom is \(s p^{3} d\)-hybridized.

Give the formula of an anion comprised of iodine and fluorine in which the iodine atom is \(s p^{3} d^{2}\)-hybridized.

Problem 45P What is molecular orbital theory? How does it differ from valence bond theory?

Sketch the shapes of the following molecular orbitals: \(\sigma_{1 s}\), \(\sigma_{1 s}^{\star}\), \(\pi_{2 p}\), and \(\pi_{2 p}^{\star}\). How do their energies compare?

Compare the Lewis theory, valence bond theory, and molecular orbital theory of chemical bonding.

Explain the significance of bond order. Can bond order be used for quantitative comparisons of the strengths of chemical bonds?

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 \(\mathrm{H}_{2}^{+}\) then to \(\mathrm{H}_{2}^{2+}\).

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?

Which of these species has a longer bond, \(\mathrm{B}_2\) or \(\mathrm{B}_{2}^{+}\)? Explain in terms of molecular orbital theory.

Acetylene \((\mathrm{C}_{2} \mathrm{H}_2)\) has a tendency to lose two protons \((\mathrm{H}^{+})\) and form the carbide ion \((\mathrm{C}_{2}^{2-})\), 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 \(\mathrm{C}_2\).

Compare the Lewis and molecular orbital treatments of the oxygen molecule.

Compare the relative stability of the following species and indicate their magnetic properties (that is, diamagnetic or paramagnetic): \(\mathrm{O}_2\), \(\mathrm{O}_{2}^{+}\), \(\mathrm{O}_{2}^{-}\) (superoxide ion), \(\mathrm{O}_{2}^{2-}\) (peroxide ion).

Explain why the bond order of \(\mathrm{N}_2\) is greater than that of \(\mathrm{N}_{2}^{+}\), but the bond order of \(\mathrm{O}_2\) is less than that of \(\mathrm{O}_{2}^{+}\).

Use molecular orbital theory to compare the relative stabilities of \(\mathrm{F}_2\) and \(\mathrm{F}_{2}^{+}\).

A single bond is almost always a sigma bond, and a double bond is almost always made up of a sigma bond and a pi bond. There are very few exceptions to this rule. Show that the \(\mathrm{B}_2\) and \(\mathrm{C}_2\) molecules are examples of the exceptions.

In 2009 the ion \(\mathrm{N}_{2}^{3-}\) was isolated. Use a molecular orbital diagram to compare its properties (bond order and magnetism) with the isoelectronic ion \(\mathrm{O}_{2}^{-}\).

The following potential energy curve represents the formation of \(\mathrm{F}_2\) from two \(\mathrm{F}\) atoms. Describe the state of bonding at the marked regions.

Explain why the symbol on the left is a better representation of benzene molecules than that on the right.

Determine which of these molecules has a more delocalized orbital and justify your choice. (Hint: Both molecules contain two benzene rings. In naphthalene, the two rings are fused together. In biphenyl, the two rings are joined by a single bond, around which the two rings can rotate.)

Nitryl fluoride \((\mathrm{FNO}_2)\) is very reactive chemically. The fluorine and oxygen atoms are bonded to the nitrogen atom. (a) Write a Lewis structure for \(\mathrm{FNO}_2\). (b) Indicate the hybridization of the nitrogen atom. (c) Describe the bonding in terms of molecular orbital theory. Where would you expect delocalized molecular orbitals to form?

Describe the bonding in the nitrate ion \(\mathrm{NO}_{3}^{-}\) in terms of delocalized molecular orbitals.

What is the state of hybridization of the central \(\mathrm{O}\) atom in \(\mathrm{O}_3\)? Describe the bonding in \(\mathrm{O}_3\) in terms of delocalized molecular orbitals.

Which of the following species is not likely to have a tetrahedral shape? (a) \(\mathrm{SiBr}_4\), (b) \(\mathrm{NF}_{4}^{+}\), (c) \(\mathrm{SF}_4\), (d) \(\mathrm{BeCl}_{4}^{2-}\), (e) \(\mathrm{BF}_{4}^{-}\), (f) \(\mathrm{AlCl}_{4}^{-}\)

Draw the Lewis structure of mercury(II) bromide. Is this molecule linear or bent? How would you establish its geometry?

Sketch the bond moments and resultant dipole moments for the following molecules: \(\mathrm{H}_{2} \mathrm{O}\), \(\mathrm{PCl}_3\), \(\mathrm{XeF}_4\), \(\mathrm{PCl}_5\), \(\mathrm{SF}_6\)

Although both carbon and silicon are in Group 4A, very few \(\mathrm{Si}=\mathrm{Si}\) bonds are known. Account for the instability of silicon-to-silicon double bonds in general. (Hint: Compare the atomic radii of \(\mathrm{C}\) and \(\mathrm{Si}\) in Figure 8.5. What effect would the larger size have on pi bond formation?)

Antimony pentafluoride, \(\mathrm{SbF}_5\), reacts with \(\mathrm{XeF}_4\) and \(\mathrm{XeF}_6\) to form ionic compounds, \(\mathrm{XeF}_{3}^{+} \mathrm{SbF}_{6}^{-}\) and \(\mathrm{XeF}_{5}^{+} \mathrm{SbF}_{6}^{-}\) . Describe the geometries of the cations and anion in these two compounds.

Draw Lewis structures and give the other information requested for the following molecules: (a) \(\mathrm{BF}_3\). Shape: planar or nonplanar? (b) \(\mathrm{ClO}_3^{-}\). Shape: planar or nonplanar? (c) \(\mathrm{H}_2 \mathrm{O}\). Show the direction of the resultant dipole moment. (d) \(\mathrm{OF}_2\). Polar or nonpolar molecule? (e) \(\mathrm{NO}_2\). Estimate the \(\mathrm{ONO}\) bond angle.

Problem 80P Predict the bond angles for the following molecules: (a) BeCl2, (b) BC13, (C) CC14, (d) CH3C1, (e) Hg2Cl2(arrangement of atoms: CIHgHgCl), (f) SnCl2, (g)H2O2, (h) SnH4.

Briefly compare the VSEPR and hybridization approaches to the study of molecular geometry.

Describe the hybridization state of arsenic in arsenic pentafluoride \((\mathrm{AsF}_5)\).

Draw Lewis structures and give the other information requested for the following: (a) \(\mathrm{SO}_3\). Polar or nonpolar molecule? (b) PF \(\mathrm{P}_3\). Polar or nonpolar molecule? (c) \(\mathrm{F}_3 \mathrm{SiH}\). Show the direction of the resultant dipole moment. (d) \(\mathrm{SiH}_3^{-}\). Planar or pyramidal shape? (e) \(\mathrm{Br}_2 \mathrm{CH}_2\). Polar or nonpolar molecule?

Which of the following molecules and ions are linear? \(\mathrm{ICl}_{2}^{-}\), \(\mathrm{IF}_{2}^{+}\), \(\mathrm{OF}_2\), \(\mathrm{SnI}_2\), \(\mathrm{CdBr}_2\)

Draw the Lewis structure for the \(\mathrm{BeCl}_4^{2-}\) ion. Predict its geometry and describe the hybridization state of the Be atom.

Problem 86P The N2F2 molecule can exist in either of the following two forms (a) What is the hybridization of N in the molecule? (b) Which structure has a dipole moment?

So-called greenhouse gases, which contribute to global warming, have a dipole moment or can be bent or distorted into shapes that have a dipole moment. Which of the following gases are greenhouse gases? \(\mathrm{N}_2\), \(\mathrm{O}_2\), \(\mathrm{O}_3\), \(\mathrm{CO}\), \(\mathrm{CO}_2\), \(\mathrm{NO}_2\), \(\mathrm{N}_{2} \mathrm{O}\), \(\mathrm{CH}_4\), \(\mathrm{CFCl}_3\)

The bond angle of \(\mathrm{SO}_2\) is very close to \(120^{\circ}\), even though there is a lone pair on \(\mathrm{S}\). Explain.

3'-azido-3'-deoxythymidine, shown here, commonly known as \(\mathrm{AZT}\), is one of the drugs used to treat acquired immune deficiency syndrome (AIDS). What are the hybridization states of the \(\mathrm{C}\) and \(\mathrm{N}\) atoms in this molecule?

The following molecules \(\left(\mathrm{AX}_{4} \mathrm{Y}_{2}\right)\) all have octahedral geometry. Group the molecules that are equivalent to each other.

The compounds carbon tetrachloride \(\left(\mathrm{CCl}_{4}\right)\) and silicon tetrachloride \(\left(\mathrm{SiCl}_{4}\right)\) are similar in geometry and hybridization. However, \(\mathrm{CCl}_{4}\), does not react with water but \(\mathrm{SiCl}_{4}\) does. Explain the difference in their chemical reactivities. (Hint: The first step of the reaction is believed to be the addition of a water molecule to the \(\mathrm{Si}\) atom in \(\mathrm{SiCl}_{4}\).)

Write the ground-state electron configuration for \(\mathrm{B}_{2}\). Is the molecule diamagnetic or paramagnetic?

Use molecular orbital theory to explain the difference between the bond enthalpies of \(\mathrm{F}_2\) and \(\mathrm{F}_{2}^{-}\) (see Problem 9.110).

What are the hybridization states of the \(\mathrm{C}\) and \(\mathrm{N}\) atoms in this molecule?

Referring to the Chemistry in Action on p. 428, answer the following questions: (a) If you wanted to cook a roast (beef or lamb), would you use a microwave oven or a conventional oven? (b) Radar is a means of locating an object by measuring the time for the echo of a microwave from the object to return to the source and the direction from which it returns. Would radar work if oxygen, nitrogen, and carbon dioxide were polar molecules? (c) In early tests of radar at the English Channel during World War II, the results were inconclusive even though there was no equipment malfunction. Why? (Hint: The weather is often foggy in the region.)

Referring to Table 9.4, explain why the bond enthalpy for \(\mathrm{Cl}_2\) is greater than that for \(\mathrm{F}_2\). (Hint: The bond lengths of \(\mathrm{F}_2\) and \(\mathrm{Cl}_2\) are 142 pm and 199 pm, respectively.)

Use molecular orbital theory to explain the bonding in the azide ion \((\mathrm{N}_{3}^{-})\). (Arrangement of atoms is \(\mathrm{NNN}\).)

The ionic character of the bond in a diatomic molecule can be estimated by the formula \(\frac{\mu}{e d} \times 100 \%\) where \(\mu\) is the experimentally measured dipole moment (in \(\mathrm{C}\) m), \(e\) the electronic charge, and \(d\) the bond length in meters. (The quantity \(ed\) is the hypothetical dipole moment for the case in which the transfer of an electron from the less electronegative to the more electronegative atom is complete.) Given that the dipole moment and bond length of \(\mathrm{HF}\) are 1.92 D and 91.7 pm, respectively, calculate the percent ionic character of the molecule.

Draw three Lewis structures for compounds with the formula \(\mathrm{C}_{2} \mathrm{H}_2 \mathrm{F}_2\). Indicate which of the compound(s) are polar.

Greenhouse gases absorb (and trap) outgoing infrared radiation (heat) from Earth and contribute to global warming. The molecule of a greenhouse gas either possesses a permanent dipole moment or has a changing dipole moment during its vibrational motions. Consider three of the vibrational modes of carbon dioxide where the arrows indicate the movement of the atoms. (During a complete cycle of vibration, the atoms move toward one extreme position and then reverse their direction to the other extreme position.) Which of the preceding vibrations are responsible for \(\mathrm{CO}_2\) to behave as a greenhouse gas? Which of the following molecules can act as a greenhouse gas: \(\mathrm{N}_2\), \(\mathrm{O}_2\), \(\mathrm{CO}\), \(\mathrm{NO}_2\), and \(\mathrm{N}_{2} \mathrm{O}\)?

Aluminum trichloride \((\mathrm{AlCl}_3)\) is an electron-deficient molecule. It has a tendency to form a dimer (a molecule made of two \(\mathrm{AlCl}_3\) units): \(\mathrm{AlCl}_{3}+\mathrm{AlCl}_{3} \rightarrow \mathrm{Al}_{2} \mathrm{Cl}_{6}\) (a) Draw a Lewis structure for the dimer. (b) Describe the hybridization state of \(\mathrm{Al}\) in \(\mathrm{AlCl}_3\) and \(\mathrm{Al}_{2} \mathrm{Cl}_6\). (c) Sketch the geometry of the dimer. (d) Do these molecules possess a dipole moment?

The molecules cis-dichloroethylene and trans-dichloroethylene shown on p.427 can be interconverted by heating or irradiation. (a) Starting with cisdichloroethylene, show that rotating the \(\mathrm{C}=\mathrm{C}\) bond by \(180^{\circ}\) will break only the pi bond but will leave the sigma bond intact. Explain the formation of trans dichloroethylene from this process. (Treat the rotation as two stepwise \(90^{\circ}\) rotations.) (b) Account for the difference in the bond enthalpies for the pi bond (about \(270 \mathrm{~kJ} / \mathrm{mol}\) ) and the sigma bond (about \(350 \mathrm{~kJ} / \mathrm{mol}\) ). (C) Calculate the longest wavelength of light needed to bring about this conversion.

Progesterone is a hormone responsible for female sex characteristics. In the usual shorthand structure, each point where lines meet represent a \(\mathrm{C}\) atom, and most \(\mathrm{H}\) atoms are not shown. Draw the complete structure of the molecule, showing all \(\mathrm{C}\) and \(\mathrm{H}\) atoms. Indicate which \(\mathrm{C}\) atoms are \(sp^2-\) and \(sp^3-\) hybridized.

For each pair listed here, state which one has a higher first ionization energy and explain your choice: (a) \(\mathrm{H}\) or \(\mathrm{H}_2\), (b) \(\mathrm{N}\) or \(\mathrm{N}_2\), (c) \(\mathrm{O}\) or \(\mathrm{O}_2\), (d) \(\mathrm{F}\) or \(\mathrm{F}_2\).

As mentioned in the chapter, the Lewis structure for \(\mathrm{O}_2\) is Use the molecular orbital theory to show that the structure actually corresponds to an excited state of the oxygen molecule.

Referring to Problem 9.137, describe the hybridization state of the \(\mathrm{N}\) atoms and the overall shape of the ion.

Describe the geometry and hybridization for the reactants and product in the following reaction \(\mathrm{ClF}_{3}+\mathrm{AsF}_{5} \longrightarrow\left[\mathrm{ClF}_{2}^{+}\right]\left[\mathrm{AsF}_{6}^{-}\right]\)

Draw the Lewis structure of ketene \(\left(\mathrm{C}_{2} \mathrm{H}_{2} \mathrm{O}\right)\) and describe the hybridization states of the \(\mathrm{C}\) atoms. The molecule does not contain \(\mathrm{O}?\mathrm{H}\) bonds. On separate diagrams, sketch the formation of sigma and pi bonds

TCDD, or 2,3,7,8-tetrachlorodibenzo-p-dioxin, is a highly toxic compound It gained considerable notoriety in 2004 when it was implicated in the murder plot of a Ukrainian politician. (a) Describe its geometry and state whether the molecule has a dipole moment. (b) How many pi bonds and sigma bonds are there in the molecule?

Write the electron configuration of the cyanide ion \((\mathrm{CN}^{-})\). Name a stable molecule that is isoelectronic with the ion.

Carbon monoxide \((\mathrm{CO})\) is a poisonous compound due to its ability to bind strongly to \(\mathrm{Fe}^{2+}\) in the hemoglobin molecule. The molecular orbitals of \(\mathrm{CO}\) have the same energy order as those of the \(\mathrm{N}_2\) molecule. (a) Draw a Lewis structure of \(\mathrm{CO}\) and assign formal charges. Explain why \(\mathrm{CO}\) has a rather small dipole moment of 0.12 D. (b) Compare the bond order of \(\mathrm{CO}\) with that from molecular orbital theory. (c) Which of the atoms (\(\mathrm{C}\) or \(\mathrm{O}\)) is more likely to form bonds with the\(\mathrm{Fe}^{2+}\) ion in hemoglobin?

The geometries discussed in this chapter all lend themselves to fairly straightforward elucidation of bond angles. The exception is the tetrahedron, because its bond angles are hard to visualize. Consider the \(\mathrm{CCl}_4\) molecule, which has a tetrahedral geometry and is nonpolar. By equating the bond moment of a particular \(\mathrm{C}?\mathrm{Cl}\) bond to the resultant bond moments of the other three \(\mathrm{C}?\mathrm{Cl}\) bonds in opposite directions, show that the bond angles are all equal to \(109.5^{\circ}\).

Carbon suboxide \((\mathrm{C}_{3} \mathrm{O}_2)\) is a colorless pungent-smelling gas. Does it possess a dipole moment?

Based on what you have learned from this chapter and Chapter 9, name a diatomic molecule that has the strongest known chemical bond and one with the weakest known chemical bond.

The stability of benzene is due to the fact that we can draw reasonable resonance structures for the molecule, which is equivalent to saying that there is electron delocalization. Resonance energy is a measure of how much more stable benzene is compared to the hypothetical molecule, which can be represented by just a single resonance structure. Shown on p. 466 are the enthalpies of hydrogenation (the addition of hydrogen) of cyclohexene \(\left(\mathrm{C}_6 \mathrm{H}_{10}\right)\) to cyclohexane \(\left(\mathrm{C}_6 \mathrm{H}_{12}\right)\) and benzene to cyclohexane. (In these simplified structures, each point where lines meet represents a C atom. There is a H atom attached to a \(s p^2\)-hybridized C atom and there are two H atoms attached to a \(s p^3\)-hybridized C atom.) Estimate the resonance energy of benzene from these data.

How many carbon atoms are contained in one square centimeter of graphene (see the Chemistry in Action on p. 457 for a description of graphene)? What would be the mass of a \(1-\mathrm{cm}^{2}\) section of graphene?