Chemistry

Steven S. Zumdahl, Susan A. Zumdahl

Chapter 9

Covalent Bonding: Orbitals - all with Video Answers

Educators

Chapter Questions

Problem 1

What are molecular orbitals? How do they compare with atomic orbitals? Can you tell by the shape of the bonding and antibonding orbitals which is lower in energy? Explain.

David Collins

David Collins

Numerade Educator

Problem 2

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?

Lottie Adams

Numerade Educator

Problem 3

Compare Figs. $9.35$ and $9.37 .$ Why are they different? Because $\mathrm{B}_{2}$ is known to be paramagnetic, the $\pi_{2 p}$ and $\sigma_{2 p}$ molecular orbitals must be switched from the first prediction. What is the rationale for this? Why might one expect the $\sigma_{2 p}$ to be lower in energy than the $\pi_{2 p}$ ? Why can't we use diatomic oxygen to help us decide whether the $\sigma_{2 p}$ or $\pi_{2 p}$ is lower in energy?

David Collins

Numerade Educator

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

Lottie Adams

Numerade Educator

Problem 5

Draw the Lewis structure for HCN. Indicate the hybrid orbitals, and draw a picture showing all the bonds between the atoms, labeling each bond as $\sigma$ or $\pi$.

David Collins

Numerade Educator

Problem 6

Which is the more correct statement: "The methane molecule $\left(\mathrm{CH}_{4}\right)$ is a tetrahedral molecule because it is $s p^{3}$ hybridized" or "The methane molecule $\left(\mathrm{CH}_{4}\right)$ is $s p^{3}$ hybridized because it is a tetrahedral molecule"? What, if anything, is the difference between these two statements?

Teesta Dasgupta

Teesta Dasgupta

University of Pittsburgh - Main Campus

Problem 7

Compare and contrast the MO model with the LE model. When is each useful?

David Collins

Numerade Educator

Problem 8

What are the relationships among bond order, bond energy, and bond length? Which of these quantities can be measured?

AP

Anna Pugh

Numerade Educator

Problem 9

In the hybrid 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

David Collins

Numerade Educator

Problem 10

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.

Teesta Dasgupta

Teesta Dasgupta

University of Pittsburgh - Main Campus

Problem 11

Why are $d$ orbitals sometimes used to form hybrid orbitals? Which period of elements does not use $d$ orbitals for hybridization? If necessary, which $d$ orbitals $(3 d, 4 d, 5 d$, or $6 d)$ would sulfur use to form hybrid orbitals requiring $d$ atomic orbitals? Answer the same question for arsenic and for iodine.

David Collins

Numerade Educator

Problem 12

The atoms in a single bond can rotate about the internuclear axis without breaking the bond. The atoms in a double and triple bond cannot rotate about the internuclear axis unless the bond is broken. Why?

Teesta Dasgupta

Teesta Dasgupta

University of Pittsburgh - Main Campus

Problem 13

Compare and contrast bonding molecular orbitals with antibonding molecular orbitals.

Lottie Adams

Numerade Educator

Problem 14

What modification to the molecular orbital model was made from the experimental evidence that $\mathrm{B}_{2}$ is paramagnetic?

Lottie Adams

Numerade Educator

Problem 15

Why does the molecular orbital model do a better job in explaining the bonding in $\mathrm{NO}^{-}$ and NO than the hybrid orbital model?

Lottie Adams

Numerade Educator

Problem 16

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?

Teesta Dasgupta

Teesta Dasgupta

University of Pittsburgh - Main Campus

Problem 17

Use the localized electron model to describe the bonding in $\mathrm{H}_{2} \mathrm{O}$.

Lottie Adams

Numerade Educator

Problem 18

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

Lottie Adams

Numerade Educator

Problem 19

Use the localized electron model to describe the bonding in $\mathrm{H}_{2} \mathrm{CO}$ (carbon is the central atom).

Lottie Adams

Numerade Educator

Problem 20

Use the localized electron model to describe the bonding in $\mathrm{C}_{2} \mathrm{H}_{2}$ (exists as $\mathrm{HCCH}$ ).

Teesta Dasgupta

Teesta Dasgupta

University of Pittsburgh - Main Campus

Problem 21

The space-filling models of ethane and ethanol are shown below.
Use the localized electron model to describe the bonding in ethane and ethanol.

Lottie Adams

Numerade Educator

Problem 22

The space-filling models of hydrogen cyanide and phosgene are shown below.
Use the localized electron model to describe the bonding in hydrogen cyanide and phosgene.

Lottie Adams

Numerade Educator

Problem 23

Give the expected hybridization of the central atom for the molecules or ions in Exercises 81 and 87 from Chapter 8 .

Lizabeth Tumminello

Lizabeth Tumminello

Numerade Educator

Problem 24

Give the expected hybridization of the central atom for the molecules or ions in Exercises 82 and 88 from Chapter $8 .$

Lizabeth Tumminello

Lizabeth Tumminello

Numerade Educator

Problem 25

Give the expected hybridization of the central atom for the molecules or ions in Exercise 85 from Chapter 8 .

David Collins

Numerade Educator

Problem 26

Give the expected hybridization of the central atom for the molecules in Exercise 86 from Chapter 8 .

Teesta Dasgupta

Teesta Dasgupta

University of Pittsburgh - Main Campus

Problem 27

Give the expected hybridization of the central atom for the molecules in Exercises 107 and 108 from Chapter 8 .

Lizabeth Tumminello

Lizabeth Tumminello

Numerade Educator

Problem 28

Give the expected hybridization of the central atom for the molecules in Exercises 109 and 110 from Chapter 8 .

David Collins

Numerade Educator

Problem 29

For each of the following molecules, write the Lewis structure(s), predict the molecular structure (including bond angles), give the expected hybrid orbitals on the central atom, and predict the overall polarity.
a. $\mathrm{CF}_{4}$
e. $\mathrm{BeH}_{2}$
i. $\mathrm{KrF}_{4}$
b. $\mathrm{NF}_{3}$
f. $\mathrm{TeF}_{4}$
j. $\mathrm{SeF}_{6}$
c. $\mathrm{OF}_{2}$
g. $\mathrm{AsF}_{5}$
k. $\mathrm{IF}_{5}$
d. $\mathrm{BF}_{3}$
h. $\mathrm{KrF}_{2}$
1. $\mathrm{IF}_{3}$

Anand Jangid

Numerade Educator

Problem 30

For each of the following molecules or ions that contain sulfur, write the Lewis structure(s), predict the molecular structure (including bond angles), and give the expected hybrid orbitals for sulfur.
a. $\mathrm{SO}_{2}$
b. $\mathrm{SO}_{3}$
e. $\mathrm{SO}_{3}^{2-}$
f. $\mathrm{SO}_{4}^{2-}$
g. $\mathrm{SF}_{2}$
h. $\mathrm{SF}_{4}$
i. $\mathrm{SF}_{6}$
j. $\mathrm{F}_{3} \mathrm{~S}-\mathrm{SF}$
k. $\mathrm{SF}_{5}{ }^{+}$

Anand Jangid

Numerade Educator

Problem 31

Why must all six atoms in $\mathrm{C}_{2} \mathrm{H}_{4}$ lie in the same plane?

David Collins

Numerade Educator

Problem 32

The allene molecule has the following Lewis structure:
Must all hydrogen atoms lie the same plane? If not, what is their spatial relationship? Explain.

Lottie Adams

Numerade Educator

Problem 33

Indigo is the dye used in coloring blue jeans. The term navy blue is derived from the use of indigo to dye British naval uniforms in the eighteenth century. The structure of the indigo molecule is
a. How many $\sigma$ bonds and $\pi$ bonds exist in the molecule?
b. What hybrid orbitals are used by the carbon atoms in the indigo molecule?

David Collins

Numerade Educator

Problem 34

Urea, a compound formed in the liver, is one of the ways humans excrete nitrogen. The Lewis structure for urea is
Using hybrid orbital theory, which orbitals overlap to form the various bonds in urea?

Teesta Dasgupta

Teesta Dasgupta

University of Pittsburgh - Main Campus

Problem 35

Biacetyl and acetoin are added to margarine to make it taste more like butter.
Complete the Lewis structures, predict values for all $\mathrm{C}-\mathrm{C}-\mathrm{O}$ bond angles, and give the hybridization of the carbon atoms in these two compounds. Must the four carbon atoms and two oxygen atoms in biacetyl lie the same plane? How many $\sigma$ bonds and how many $\pi$ bonds are there in biacetyl and acetoin?

David Collins

Numerade Educator

Problem 36

Many important compounds in the chemical industry are derivatives of ethylene $\left(\mathrm{C}_{2} \mathrm{H}_{4}\right)$. Two of them are acrylonitrile and methyl methacrylate.
Complete the Lewis structures, showing all lone pairs. Give approximate values for bond angles $a$ through $f$. Give the hybridization of all carbon atoms. In acrylonitrile, how many of the atoms in the molecule must lie in the same plane? How many $\sigma$ bonds and how many $\pi$ bonds are there in methyl methacrylate and acrylonitrile?

Teesta Dasgupta

Teesta Dasgupta

University of Pittsburgh - Main Campus

Problem 37

Two molecules used in the polymer industry are azodicarbonamide and methyl cyanoacrylate. Their structures are
Azodicarbonamide is used in forming polystyrene. When added to the molten plastic, it decomposes to nitrogen, carbon monoxide, and ammonia gases, which are captured as bubbles in the molten polymer. Methyl cyanoacrylate is the main ingredient in super glue. As the glue sets, methyl cyanoacrylate polymerizes across the carbon-carbon double bond. (See Chapter 22.)
a. Complete the Lewis structures showing all lone pairs of electrons.
b. Which hybrid orbitals are used by the carbon atoms in each molecule and the nitrogen atom in azodicarbonamide?
c. How many $\pi$ bonds are present in each molecule?
d. Give approximate values for the bond angles marked $a$ through $h$ in the above structures.

Luz Esteban-Torres

Luz Esteban-Torres

Numerade Educator

Problem 38

Hot and spicy foods contain molecules that stimulate pain-detecting nerve endings. Two such molecules are piperine and capsaicin:
Piperine is the active compound in white and black pepper, and capsaicin is the active compound in chili peppers. The ring structures in piperine and capsaicin are shorthand notation. Each point where lines meet represents a carbon atom.
a. Complete the Lewis structure for piperine and capsaicin showing all lone pairs of electrons.
b. How many carbon atoms are $s p, s p^{2}$, and $s p^{3}$ hybridized in each molecule?
c. Which hybrid orbitals are used by the nitrogen atoms in each molecule?
d. Give approximate values for the bond angles marked $a$ through $l$ in the above structures.

Anand Jangid

Numerade Educator

Problem 39

Which of the following are predicted by the molecular orbital model to be stable diatomic species?
a. $\mathrm{H}_{2}^{+}, \mathrm{H}_{2}, \mathrm{H}_{2}^{-}, \mathrm{H}_{2}^{2-}$
b. $\mathrm{He}_{2}^{2+}, \mathrm{He}_{2}^{+}, \mathrm{He}_{2}$

Lottie Adams

Numerade Educator

Problem 40

Which of the following are predicted by the molecular orbital model to be stable diatomic species?
a. $\mathrm{N}_{2}{ }^{2-}, \mathrm{O}_{2}^{2-}, \mathrm{F}_{2}^{2-}$
b. $\mathrm{Be}_{2}, \mathrm{~B}_{2}, \mathrm{Ne}_{2}$

Teesta Dasgupta

Teesta Dasgupta

University of Pittsburgh - Main Campus

Problem 41

Using the molecular orbital model, write electron configurations for the following diatomic species and calculate the bond orders. Which ones are paramagnetic?
a. $\mathrm{Li}_{2}$
b. $\mathrm{C}_{2}$
c. $\mathrm{S}_{2}$

Lottie Adams

Numerade Educator

Problem 42

Consider the following electron configuration:
$$
\left(\sigma_{3 s}\right)^{2}\left(\sigma_{3 s}^{*}\right)^{2}\left(\sigma_{3 p}\right)^{2}\left(\pi_{3 p}\right)^{4}\left(\pi_{3 p}^{*}\right)^{4}
$$
Give four species that, in theory, would have this electron configuration.

Lottie Adams

Numerade Educator

Problem 43

Using molecular orbital theory, explain why the removal of one electron in $\mathrm{O}_{2}$ strengthens bonding, while the removal of one electron in $\mathrm{N}_{2}$ weakens bonding.

Lottie Adams

Numerade Educator

Problem 44

Using the molecular orbital model to describe the bonding in $\mathrm{F}_{2}{ }^{+}$, $\mathrm{F}_{2}$, and $\mathrm{F}_{2}^{-}$, predict the bond orders and the relative bond lengths for these three species. How many unpaired electrons are present in each species?

Lottie Adams

Numerade Educator

Problem 45

Which charge(s) for the $\mathrm{N}_{2}$ molecule would give a bond order of $2.5$ ?

David Collins

Numerade Educator

Problem 46

A Lewis structure obeying the octet rule can be drawn for $\mathrm{O}_{2}$ as follows:
Use the molecular orbital energy-level diagram for $\mathrm{O}_{2}$ to show that the above Lewis structure corresponds to an excited state.

Teesta Dasgupta

Teesta Dasgupta

University of Pittsburgh - Main Campus

Problem 47

Using the molecular orbital model, write electron configurations for the following diatomic species and calculate the bond orders. Which ones are paramagnetic? Place the species in order of increasing bond length and bond energy.
a. $\mathrm{CO}$
b. $\mathrm{CO}^{+}$
c. $\mathrm{CO}^{2+}$

Lottie Adams

Numerade Educator

Problem 48

Using the molecular orbital model, write electron configurations for the following diatomic species and calculate the bond orders. Which ones are paramagnetic? Place the species in order of increasing bond length and bond energy.
a. $\mathrm{CN}^{+}$
b. $\mathrm{CN}$
c. $\mathrm{CN}^{-}$

Lottie Adams

Numerade Educator

Problem 49

In which of the following diatomic molecules would the bond strength be expected to weaken as an electron is removed?
a. $\mathrm{H}_{2}$
c. $\mathrm{C}_{2}^{2-}$
b. $\mathrm{B}_{2}$
d. $\mathrm{OF}$

David Collins

Numerade Educator

Problem 50

In terms of the molecular orbital model, which species in each of the following two pairs will most likely be the one to gain an electron? Explain.
a. CN or NO
b. $\mathrm{O}_{2}^{2+}$ or $\mathrm{N}_{2}{ }^{2+}$

Lottie Adams

Numerade Educator

Problem 51

Show how two $2 p$ atomic orbitals can combine to form a $\sigma$ or a $\pi$ molecular orbital.

Lottie Adams

Numerade Educator

Problem 52

Show how a hydrogen $1 s$ atomic orbital and a fluorine $2 p$ atomic orbital overlap to form bonding and antibonding molecular orbitals in the hydrogen fluoride molecule. Are these molecular orbitals $\sigma$ or $\pi$ molecular orbitals?

Ronald Prasad

Numerade Educator

Problem 53

Use Figs. $9.42$ and $9.43$ to answer the following questions.
a. Would the bonding molecular orbital in HF place greater electron density near the $\mathrm{H}$ or the $\mathrm{F}$ atom? Why?
b. Would the bonding molecular orbital have greater fluorine $2 p$ character, greater hydrogen $1 s$ character, or an equal contribution from both? Why?
c. Answer the previous two questions for the antibonding molecular orbital in HF.

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 54

The diatomic molecule OH exists in the gas phase. The bond length and bond energy have been measured to be $97.06 \mathrm{pm}$ and $424.7 \mathrm{~kJ} / \mathrm{mol}$, respectively. Assume that the OH molecule is analogous to the HF molecule discussed in the chapter and that molecular orbitals result from the overlap of a lower-energy $p_{z}$ orbital from oxygen with the higher-energy $1 s$ orbital of hydrogen (the $\mathrm{O}-\mathrm{H}$ bond lies along the $z$ -axis).
a. Which of the two molecular orbitals will have the greater hydrogen $1 s$ character?
b. Can the $2 p_{x}$ orbital of oxygen form molecular orbitals with the $1 s$ orbital of hydrogen? Explain.
c. Knowing that only the $2 p$ orbitals of oxygen will interact significantly with the $1 s$ orbital of hydrogen, complete the molecular orbital energy-level diagram for OH. Place the correct number of electrons in the energy levels.
d. Estimate the bond order for OH.
e. Predict whether the bond order of $\mathrm{OH}^{+}$ will be greater than, less than, or the same as that of $\mathrm{OH}$. Explain.

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 55

Acetylene $\left(\mathrm{C}_{2} \mathrm{H}_{2}\right)$ can be produced from the reaction of calcium carbide $\left(\mathrm{CaC}_{2}\right)$ with water. Use both the localized electron and molecular orbital models to describe the bonding in the acetylide anion $\left(\mathrm{C}_{2}^{2-}\right)$

Lottie Adams

Numerade Educator

Problem 56

Describe the bonding in $\mathrm{NO}^{+}, \mathrm{NO}^{-}$, and NO using both the localized electron and molecular orbital models. Account for any discrepancies between the two models.

David Collins

Numerade Educator

Problem 57

Describe the bonding in the $\mathrm{O}_{3}$ molecule and the $\mathrm{NO}_{2}^{-}$ ion using the localized electron model. How would the molecular orbital model describe the $\pi$ bonding in these two species?

Lottie Adams

Numerade Educator

Problem 58

Describe the bonding in the $\mathrm{CO}_{3}^{2-}$ ion using the localized electron model. How would the molecular orbital model describe the $\pi$ bonding in this species?

Lottie Adams

Numerade Educator

Problem 59

Vitamin $\mathrm{B}_{6}$ is an organic compound whose deficiency in the human body can cause apathy, irritability, and an increased susceptibility to infections. On the next page is an incomplete Lewis structure for vitamin $\mathrm{B}_{6}$. Complete the Lewis structure and answer the following questions. Hint: Vitamin $\mathrm{B}_{6}$ can be classified as an organic compound (a compound based on carbon atoms). The majority of Lewis structures for simple organic compounds have all atoms with a formal charge of zero. Therefore, add lone pairs and multiple bonds to the structure below to give each atom a formal charge of zero.
a. How many $\sigma$ bonds and $\pi$ bonds exist in vitamin $\mathrm{B}_{6}$ ?
b. Give approximate values for the bond angles marked $a$ through $g$ in the structure.
c. How many carbon atoms are $s p^{2}$ hybridized?
d. How many carbon, oxygen, and nitrogen atoms are $s p^{3}$ hybridized?
e. Does vitamin $\mathrm{B}_{6}$ exhibit delocalized $\pi$ bonding? Explain.

Lottie Adams

Numerade Educator

Problem 60

The antibiotic thiarubin-A was discovered by studying the feeding habits of wild chimpanzees in Tanzania. The structure for thiarubin-A is
a. Complete the Lewis structure showing all lone pairs of electrons.
b. Indicate the hybrid orbitals used by the carbon and sulfur atoms in thiarubin-A.
c. How many $\sigma$ and $\pi$ bonds are present in this molecule?

Teesta Dasgupta

Teesta Dasgupta

University of Pittsburgh - Main Campus

Problem 61

One of the first drugs to be approved for use in treatment of acquired immune deficiency syndrome (AIDS) was azidothymidine (AZT). Complete the Lewis structure for AZT.
a. How many carbon atoms are $s p^{3}$ hybridized?
b. How many carbon atoms are $s p^{2}$ hybridized?
c. Which atom is $s p$ hybridized?
d. How many $\sigma$ bonds are in the molecule?
e. How many $\pi$ bonds are in the molecule?
f. What is the $\mathrm{N}=\mathrm{N}=\mathrm{N}$ bond angle in the azide $\left(-\mathrm{N}_{3}\right)$ group?
g. What is the $\mathrm{H}-\mathrm{O}-\mathrm{C}$ bond angle in the side group attached to the five-membered ring?
h. What is the hybridization of the oxygen atom in the $-\mathrm{CH}_{2} \mathrm{OH}$ group?

Lottie Adams

Numerade Educator

Problem 62

The transport of $\mathrm{O}_{2}$ in the blood is carried out by hemoglobin. Carbon monoxide can interfere with oxygen transport because hemoglobin has a stronger affinity for $\mathrm{CO}$ than for $\mathrm{O}_{2}$. If $\mathrm{CO}$ is present, normal uptake of $\mathrm{O}_{2}$ is prevented, depriving the body of needed oxygen. Using the molecular orbital model, write the electron configurations for $\mathrm{CO}$ and $\mathrm{for} \mathrm{O}_{2}$. From your configurations, give two property differences between $\mathrm{CO}$ and $\mathrm{O}_{2}$.

Lottie Adams

Numerade Educator

Problem 63

Carbon monoxide (CO) forms bonds to a variety of metals and metal ions. Its ability to bond to iron in hemoglobin is the reason that $\mathrm{CO}$ is so toxic. The bond carbon monoxide forms to metals is through the carbon atom:
$\mathrm{M}-\mathrm{C} \equiv \mathrm{O}$
a. On the basis of electronegativities, would you expect the carbon atom or the oxygen atom to form bonds to metals?
b. Assign formal charges to the atoms in CO. Which atom would you expect to bond to a metal on this basis?
c. In the MO model, bonding MOs place more electron density near the more electronegative atom. (See the HF molecule in Figs. $9.42$ and $9.43 .$ Antibonding MOs place more electron density near the less electronegative atom in the diatomic molecule. Use the MO model to predict which atom of carbon monoxide should form bonds to metals.

David Collins

Numerade Educator

Problem 64

The space-filling model for benzoic acid, a food preservative, is shown below.
Describe the bonding in benzoic acid using the localized electron model combined with the molecular orbital model.

Teesta Dasgupta

Teesta Dasgupta

University of Pittsburgh - Main Campus

Problem 65

Draw the Lewis structures, predict the molecular structures, and describe the bonding (in terms of the hybrid orbitals for the central atom) for the following.
a. $\mathrm{XeO}_{3}$
d. $\mathrm{XeOF}_{2}$
b. $\mathrm{XeO}_{4}$
e. $\mathrm{XeO}_{3} \mathrm{~F}_{2}$
c. $\mathrm{XeOF}_{4}$

Anand Jangid

Numerade Educator

Problem 66

$\mathrm{FClO}_{2}$ and $\mathrm{F}_{3} \mathrm{ClO}$ can both gain a fluoride ion to form stable anions. $\mathrm{F}_{3} \mathrm{ClO}$ and $\mathrm{F}_{3} \mathrm{ClO}_{2}$ will both lose a fluoride ion to form stable cations. Draw the Lewis structures and describe the hybrid orbitals used by chlorine in these ions.

Lottie Adams

Numerade Educator

Problem 67

Two structures can be drawn for cyanuric acid:
a. Are these two structures the same molecule? Explain.
b. Give the hybridization of the carbon and nitrogen atoms in each structure.
c. Use bond energies (Table 8.4) to predict which form is more stable; that is, which contains the strongest bonds?

Anand Jangid

Numerade Educator

Problem 68

Aspartame is an artificial sweetener marketed under the name NutraSweet. A partial Lewis structure for aspartame is shown below.
Aspartame can be classified as an organic compound (a compound based on carbon atoms). The majority of Lewis structures for simple organic compounds have all atoms with a formal charge of zero. Therefore, add lone pairs and multiple bonds to the structure above to give each atom a formal charge of zero when drawing the Lewis structure. Also note that the six-sided ring is shorthand notation for a benzene ring $\left(-\mathrm{C}_{6} \mathrm{H}_{5}\right) .$ Benzene is discussed in Section 9.5. Complete the Lewis structure for aspartame. How many $\mathrm{C}$ and $\mathrm{N}$ atoms exhibit $s p^{2}$ hybridization? How many $\mathrm{C}$ and $\mathrm{O}$ atoms exhibit $s p^{3}$ hybridization? How many $\sigma$ and $\pi$ bonds are in aspartame?

Teesta Dasgupta

Teesta Dasgupta

University of Pittsburgh - Main Campus

Problem 69

Using bond energies from Table $8.4$, estimate the barrier to rotation about a carbon-carbon double bond. To do this, consider what must happen to go from
in terms of making and breaking chemical bonds; that is, what must happen in terms of the $\pi$ bond?

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 70

The three most stable oxides of carbon are carbon monoxide (CO), carbon dioxide $\left(\mathrm{CO}_{2}\right)$, and carbon suboxide $\left(\mathrm{C}_{3} \mathrm{O}_{2}\right)$. The spacefilling models for these three compounds are
For each oxide, draw the Lewis structure, predict the molecular structure, and describe the bonding (in terms of the hybrid orbitals for the carbon atoms).

Anand Jangid

Numerade Educator

Problem 71

Complete the Lewis structures of the following molecules. Predict the molecular structure, polarity, bond angles, and hybrid orbitals used by the atoms marked by asterisks for each molecule.

David Collins

Numerade Educator

Problem 72

Complete the following resonance structures for $\mathrm{POCl}_{3}$.
a. Would you predict the same molecular structure from each resonance structure?
b. What is the hybridization of $\mathrm{P}$ in each structure?
c. What orbitals can the $\mathrm{P}$ atom use to form the $\pi$ bond in struc-
ture $\mathrm{B}$ ?
d. Which resonance structure would be favored on the basis of formal charges?

Lottie Adams

Numerade Educator

Problem 73

The $\mathrm{N}_{2} \mathrm{O}$ molecule is linear and polar.
a. On the basis of this experimental evidence, which arrangement, NNO or NON, is correct? Explain your answer.
b. On the basis of your answer to part a, write the Lewis structure of $\mathrm{N}_{2} \mathrm{O}$ (including resonance forms). Give the formal charge on each atom and the hybridization of the central atom.
c. How would the multiple bonding in $: \mathrm{N} \equiv \mathrm{N}-\mathrm{O}:$ be described in terms of orbitals?

David Collins

Numerade Educator

Problem 74

Describe the bonding in the first excited state of $\mathrm{N}_{2}$ (the one closest in energy to the ground state) using the molecular orbital model. What differences do you expect in the properties of the molecule in the ground state as compared to the first excited state? (An excited state of a molecule corresponds to an electron arrangement other than that giving the lowest possible energy.)

Teesta Dasgupta

Teesta Dasgupta

University of Pittsburgh - Main Campus

Problem 75

Using an MO energy-level diagram, would you expect $\mathrm{F}_{2}$ to have a lower or higher first ionization energy than atomic fluorine? Why?

Lottie Adams

Numerade Educator

Problem 76

Show how a $d_{x z}$ atomic orbital and a $p_{z}$ atomic orbital combine to form a bonding molecular orbital. Assume the $x$ -axis is the internuclear axis. Is a $\sigma$ or a $\pi$ molecular orbital formed? Explain.

Teesta Dasgupta

Teesta Dasgupta

University of Pittsburgh - Main Campus

Problem 77

What type of molecular orbital would result from the in-phase combination of two $d_{x z}$ atomic orbitals shown below? Assume the $x$ -axis is the internuclear axis.

David Collins

Numerade Educator

Problem 78

Consider three molecules: $\mathrm{A}, \mathrm{B}$, and $\mathrm{C}$. Molecule A has a hybridization of $s p^{3}$. Molecule B has two more effective pairs (electron pairs around the central atom) than molecule A. Molecule C consists of two $\sigma$ bonds and two $\pi$ bonds. Give the molecular structure, hybridization, bond angles, and an example for each molecule.

Lottie Adams

Numerade Educator

Problem 79

Consider the following computer-generated model of caffeine:
Complete a Lewis structure for caffeine in which all atoms have a formal charge of zero (as is typical with most organic compounds). How many $\mathrm{C}$ and $\mathrm{N}$ atoms are $s p^{2}$ hybridized? How many $\mathrm{C}$ and $\mathrm{N}$ atoms are $s p^{3}$ hybridized? $s p$ hybridized? How many $\sigma$ and $\pi$ bonds are there?

Lottie Adams

Numerade Educator

Problem 80

Cholesterol $\left(\mathrm{C}_{27} \mathrm{H}_{46} \mathrm{O}\right)$ has the following structure:
In such shorthand structures, each point where lines meet represents a carbon atom and most $\mathrm{H}$ atoms are not shown. Draw the complete structure showing all carbon and hydrogen atoms. (There will be four bonds to each carbon atom.) Indicate which carbon atoms use $s p^{2}$ or $s p^{3}$ hybrid orbitals. Are all carbon atoms in the same plane, as implied by the structure?

Lottie Adams

Numerade Educator

Problem 81

Cyanamide $\left(\mathrm{H}_{2} \mathrm{NCN}\right)$, an important industrial chemical, is produced by the following steps:
$$
\begin{aligned}
\mathrm{CaC}_{2}+\mathrm{N}_{2} & \longrightarrow \mathrm{CaNCN}+\mathrm{C} \\
\mathrm{CaNCN} & \stackrel{\text { Acid }}{\longrightarrow} \mathrm{H}_{2} \mathrm{NCN}
\end{aligned}
$$
Cyanamid
Calcium cyanamide (CaNCN) is used as a direct-application fertilizer, weed killer, and cotton defoliant. It is also used to make cyanamide, dicyandiamide, and melamine plastics:
a. Write Lewis structures for $\mathrm{NCN}^{2-}, \mathrm{H}_{2} \mathrm{NCN}$, dicyandiamide, and melamine, including resonance structures where appropriate.
b. Give the hybridization of the $\mathrm{C}$ and $\mathrm{N}$ atoms in each species.
c. How many $\sigma$ bonds and how many $\pi$ bonds are in each species?
d. Is the ring in melamine planar?
e. There are three different $\mathrm{C}-\mathrm{N}$ bond distances in dicyandiamide, $\mathrm{NCNC}\left(\mathrm{NH}_{2}\right)_{2}$, and the molecule is nonlinear. Of all the resonance structures you drew for this molecule, predict which should be the most important.

David Collins

Numerade Educator

Problem 82

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 $\mathrm{C}_{6} \mathrm{H}_{6}(g)$

David Collins

Numerade Educator

Problem 83

A flask containing gaseous $\mathrm{N}_{2}$ is irradiated with $25-\mathrm{nm}$ light.
a. Using the following information, indicate what species can form in the flask during irradiation.
$$
\begin{aligned}
\mathrm{N}_{2}(g) & \longrightarrow 2 \mathrm{~N}(g) & \Delta H &=941 \mathrm{~kJ} / \mathrm{mol} \\
\mathrm{N}_{2}(g) & \longrightarrow \mathrm{N}_{2}^{+}(g)+\mathrm{e}^{-} & \Delta H &=1501 \mathrm{~kJ} / \mathrm{mol} \\
\mathrm{N}(g) & \longrightarrow \mathrm{N}^{+}(g)+\mathrm{e}^{-} & \Delta H &=1402 \mathrm{~kJ} / \mathrm{mol}
\end{aligned}
$$
b. What range of wavelengths will produce atomic nitrogen in the flask but will not produce any ions?
c. Explain why the first ionization energy of $\mathrm{N}_{2}(1501 \mathrm{~kJ} / \mathrm{mol})$ is greater than the first ionization energy of atomic nitrogen $(1402 \mathrm{~kJ} / \mathrm{mol})$.

David Collins

Numerade Educator

Problem 84

As compared with $\mathrm{CO}$ and $\mathrm{O}_{2}, \mathrm{CS}$ and $\mathrm{S}_{2}$ are very unstable molecules. Give an explanation based on the relative abilities of the sulfur and oxygen atoms to form $\pi$ bonds.

Lottie Adams

Numerade Educator

Problem 85

Values of measured bond energies may vary greatly depending on the molecule studied. Consider the following reactions:
$$
\begin{aligned}
\mathrm{NCl}_{3}(g) & \longrightarrow \mathrm{NCl}_{2}(g)+\mathrm{Cl}(g) & \Delta H &=375 \mathrm{~kJ} / \mathrm{mol} \\
\mathrm{ONCl}(g) & \longrightarrow \mathrm{NO}(g)+\mathrm{Cl}(g) & \Delta H &=158 \mathrm{~kJ} / \mathrm{mol}
\end{aligned}
$$
Rationalize the difference in the values of $\Delta H$ for these reactions, even though each reaction appears to involve only the breaking of one $\mathrm{N}-\mathrm{Cl}$ bond. (Hint: Consider the bond order of the NO bond in ONCl and in NO.)

Julian Taurozzi

Julian Taurozzi

Numerade Educator

Problem 86

Use the MO model to explain the bonding in $\mathrm{BeH}_{2}$. When constructing the MO energy-level diagram, assume that the Be's $1 s$ electrons are not involved in bond formation.

Anand Jangid

Numerade Educator

Problem 87

Bond energy has been defined in the text as the amount of energy required to break a chemical bond, so we have come to think of the addition of energy as breaking bonds. However, in some cases the addition of energy can cause the formation of bonds. For example, in a sample of helium gas subjected to a high-energy source, some $\mathrm{He}_{2}$ molecules exist momentarily and then dissociate. Use MO theory (and diagrams) to explain why $\mathrm{He}_{2}$ molecules can come to exist and why they dissociate.

Lottie Adams

Numerade Educator

Problem 88

Arrange the following from lowest to highest ionization energy:
$\mathrm{O}, \mathrm{O}_{2}, \mathrm{O}_{2}^{-}, \mathrm{O}_{2}^{+} .$ Explain your answer.

Teesta Dasgupta

Teesta Dasgupta

University of Pittsburgh - Main Campus

Problem 89

Use the MO model to determine which of the following has the smallest ionization energy: $\mathrm{N}_{2}, \mathrm{O}_{2}, \mathrm{~N}_{2}^{2-}, \mathrm{N}_{2}^{-}, \mathrm{O}_{2}^{+} .$ Explain your
answer.

David Collins

Numerade Educator

Problem 90

Given that the ionization energy of $\mathrm{F}_{2}^{-}$ is $290 \mathrm{~kJ} / \mathrm{mol}$ do the following:
a. Calculate the bond energy of $\mathrm{F}_{2}^{-}$. You will need to look up the bond energy of $\mathrm{F}_{2}$ and ionization energy of $\mathrm{F}^{-}$.
b. Explain the difference in bond energy between $\mathrm{F}_{2}^{-}$ and $\mathrm{F}_{2}$ using MO theory.

Lottie Adams

Numerade Educator

Problem 91

As the head engineer of your starship in charge of the warp drive, you notice that the supply of dilithium is critically low. While searching for a replacement fuel, you discover some diboron, $\mathrm{B}_{2}$.
a. What is the bond order in $\mathrm{Li}_{2}$ and $\mathrm{B}_{2}$ ?
b. How many electrons must be removed from $\mathrm{B}_{2}$ to make it isoelectronic with $\mathrm{Li}_{2}$ so that it might be used in the warp drive?
c. The reaction to make $\mathrm{B}_{2}$ isoelectronic with $\mathrm{Li}_{2}$ is generalized (where $n=$ number of electrons determined in part b) as follows:
$$
\mathrm{B}_{2} \longrightarrow \mathrm{B}_{2}^{n+}+n \mathrm{e}^{-} \quad \Delta H=6455 \mathrm{~kJ} / \mathrm{mol}
$$
How much energy is needed to ionize $1.5 \mathrm{~kg} \mathrm{~B}_{2}$ to the desired isoelectronic species?

Lottie Adams

Numerade Educator

Problem 92

An unusual category of acids known as superacids, which are defined as any acid stronger than $100 \%$ sulfuric acid, can be prepared by seemingly simple reactions similar to the one below. In this example, the reaction of anhydrous HF with $\mathrm{SbF}_{5}$ produces the superacid $\left[\mathrm{H}_{2} \mathrm{~F}\right]^{+}\left[\mathrm{SbF}_{6}\right]^{-}$ :
$$
2 \mathrm{HF}(l)+\mathrm{SbF}_{5}(l) \longrightarrow\left[\mathrm{H}_{2} \mathrm{~F}\right]^{+}\left[\mathrm{SbF}_{6}\right]^{-}(l)
$$
a. What are the molecular structures of all species in this reaction? What are the hybridizations of the central atoms in each species?
b. What mass of $\left[\mathrm{H}_{2} \mathrm{~F}\right]^{+}\left[\mathrm{SbF}_{6}\right]^{-}$ can be prepared when $2.93 \mathrm{~mL}$
anhydrous HF (density $=0.975 \mathrm{~g} / \mathrm{mL}$ ) and $10.0 \mathrm{~mL} \mathrm{SbF}_{5}$
(density $=3.10 \mathrm{~g} / \mathrm{mL}$ ) are allowed to react?

Teesta Dasgupta

Teesta Dasgupta

University of Pittsburgh - Main Campus

Problem 93

Determine the molecular structure and hybridization of the central atom $\mathrm{X}$ in the polyatomic ion $\mathrm{XY}_{3}{ }^{+}$ given the following information: A neutral atom of $X$ contains 36 electrons, and the element Y makes an anion with a 1 - charge, which has the electron configuration $1 s^{2} 2 s^{2} 2 p^{6}$.

David Collins

Numerade Educator