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CHEMISTRY: The Molecular Nature of Matter and Change 2016

Martin S. Silberberg, Patricia G. Amateis

Chapter 11

Theories of Covalent Bonding

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Problem 1

What type of central-atom orbital hybridization corresponds to each electron-group arrangement: (a) trigonal planar; (b) octahedral; (c) linear; (d) tetrahedral; (e) trigonal bipyramidal?

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Problem 2

What is the orbital hybridization of a central atom that has one lone pair and bonds to: (a) two other atoms; (b) three other atoms; (c) four other atoms; (d) five other atoms?

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Problem 3

How do carbon and silicon differ with regard to the types of orbitals available for hybridization? Explain

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Problem 4

How many hybrid orbitals form when four atomic orbitals of a central atom mix? Explain.

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Problem 5

Give the number and type of hybrid orbital that forms when each set of atomic orbitals mixes:
(a) two d, one s, and three p (b) three p and one s

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Problem 6

Give the number and type of hybrid orbital that forms when each set of atomic orbitals mixes:
(a) one p and one s (b) three p, one d, and one s

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Problem 7

What is the hybridization of nitrogen in each of the following: (a) $\mathrm{NO} ;(\mathrm{b}) \mathrm{NO}_{2} ;(\mathrm{c}) \mathrm{NO}_{2}^{-} ?$

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Problem 8

What is the hybridization of carbon in each of the following:
(a) $\mathrm{CO}_{3}^{2-} ;$ (b) $\mathrm{C}_{2} \mathrm{O}_{4}^{2-} ;$ (c) $\mathrm{NCO}^{-2}$

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Problem 9

What is the hybridization of chlorine in each of the following: (a) $\mathrm{ClO}_{2} ;(\mathrm{b}) \mathrm{ClO}_{3}^{-} ;(\mathrm{c}) \mathrm{ClO}_{4}^{-?}$

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Problem 10

What is the hybridization of bromine in each of the following: (a) $\mathrm{BrF}_{3} ;(\mathrm{b}) \mathrm{BrO}_{2}^{-} ;(\mathrm{c}) \mathrm{BrF}_{5} ?$

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Problem 11

Which types of atomic orbitals of the central atom mix to form hybrid orbitals in (a) $\mathrm{SiClH}_{3} ;$ (b) $\mathrm{CS}_{2} ;(\mathrm{c}) \mathrm{SCl}_{3} \mathrm{F} ;(\mathrm{d}) \mathrm{NF}_{3} ?$

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Problem 12

Which types of atomic orbitals of the central atom mix to form hybrid orbitals in (a) $\mathrm{Cl}_{2} \mathrm{O} ;(\mathrm{b}) \mathrm{BrCl}_{3} ;(\mathrm{c}) \mathrm{PF}_{5} ;(\mathrm{d}) \mathrm{SO}_{3}^{2-} ?$

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Problem 13

Phosphine $\left(\mathrm{PH}_{3}\right)$ reacts with borane $\left(\mathrm{BH}_{3}\right)$ as follows:
$$\mathrm{PH}_{3}+\mathrm{BH}_{3} \longrightarrow \mathrm{H}_{3} \mathrm{P}-\mathrm{BH}_{3}$$
a) Which of the illustrations below depicts the change, if any, in the orbital hybridization of P during this reaction? (b) Which depicts the change, if any, in the orbital hybridization of B?

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Problem 14

The illustrations below depict differences in orbital hybridization of some tellurium (Te) fluorides. (a) Which depicts the difference, if any, between $\mathrm{TeF}_{6}(\text {lef} t)$ and $\mathrm{TeF}_{5}-(\text { right }) ?$ (b) Which depicts the difference, if any, between TeF $_{4}(\text {left})$ and $\operatorname{Te} \mathrm{F}_{6}(\text {right}) ?$

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Problem 15

Use partial orbital diagrams to show how the atomic orbitals of the central atom lead to hybrid orbitals in (a) $\mathrm{GeCl}_{4}$ (b) $\mathrm{BCl}_{3}$ (c) $\mathrm{CH}_{3}^{+}$

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Problem 16

16 Use partial orbital diagrams to show how the atomic orbitals of the central atom lead to hybrid orbitals in (a) $\mathrm{BF}_{4}^{-}$ (b) $\mathrm{PO}_{4}^{3-}$ (c) $\mathrm{SO}_{3}$

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Problem 17

Use partial orbital diagrams to show how the atomic orbitals of the central atom lead to hybrid orbitals in (a) $\operatorname{SeCl}_{2}$ (b) $\mathrm{H}_{3} \mathrm{O}^{+}$ (c) $\mathrm{IF}_{4}^{-}$

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Problem 18

Use partial orbital diagrams to show how the atomic orbitals of the central atom lead to hybrid orbitals in (a) $\mathrm{AsCl}_{3}$ (b) $\operatorname{Sn} \mathrm{Cl}_{2}$ $(\mathrm{c}) \mathrm{PF}_{6}-$

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Problem 19

Methyl isocyanate, $\mathrm{CH}_{3}-\mathrm{N}=\mathrm{C}=\ddot{\mathrm{O}}$ is an intermediate in the manufacture of many pesticides. In 1984 a leak from a manufacturing plant resulted in the death of more than 2000 people in Bhopal, India. What are the hybridizations of the N atom and the two C atoms in methyl isocyanate? Sketch the molecular shape.

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Problem 20

Are these statements true or false? Correct any false ones.
a) Two $\sigma$ bonds comprise a double bond.
b) A triple bond consists of one $\pi$ bond and two $\sigma$ bonds.
c) Bonds formed from atomic $s$ orbitals are always $\sigma$ bonds.
d) A $\pi$ bond restricts rotation about the $\sigma$ -bond axis.
e) A $\pi$ bond consists of two pairs of electrons.
f) End-to-end overlap results in a bond with electron density above and below the bond axis.

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Problem 21

Describe the hybrid orbitals used by the central atom and the type(s) of bonds formed in (a) $\mathrm{NO}_{3}^{-} ;$ (b) $\mathrm{CS}_{2} ;(\mathrm{c}) \mathrm{CH}_{2} \mathrm{O}$

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Problem 22

Describe the hybrid orbitals used by the central atom and the type(s) of bonds formed in (a) $\mathrm{O}_{3} ;(\mathrm{b}) \mathrm{I}_{3}^{-} ;(\mathrm{c}) \mathrm{COCl}_{2}(\mathrm{C} \text { is } central).$

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Problem 23

Describe the hybrid orbitals used by the central atom(s) and the type(s) of bonds formed in (a) FNO; $(b) C_{2} F_{4}$ (c) $(\mathrm{CN})_{2}$

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Problem 24

Describe the hybrid orbitals used by the central atom(s) and the type(s) of bonds formed in (a) $\operatorname{BrF}_{3} ;$ (b) $\mathrm{CH}_{3} \mathrm{C} \equiv \mathrm{CH}$ (c) $\mathrm{SO}_{2}$

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Problem 25

2 -Butene $\left(\mathrm{CH}_{3} \mathrm{CH}=\mathrm{CHCH}_{3}\right)$ is a starting material in the manufacture of lubricating oils and many other compounds. Draw two different structures for 2-butene, indicating the $\sigma$ and $\pi$ bonds in each.

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Problem 26

Two p orbitals from one atom and two p orbitals from another atom are combined to form molecular orbitals for the joined atoms. How many MOs will result from this combination? Explain.

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Problem 27

Certain atomic orbitals on two atoms were combined to form the following MOs. Name the atomic orbitals used and the MOs formed, and explain which MO has higher energy:

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Problem 28

How do the bonding and antibonding MOs formed from a given pair of AOs compare to each other with respect to (a) energy; (b) presence of nodes; (c) internuclear electron density?

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Problem 29

Antibonding MOs always have at least one node. Can a bonding MO have a node? If so, draw an example.

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Problem 30

How many electrons does it take to fill (a) a $\sigma$ bonding $\mathrm{MO}$ (b) a $\pi$ antibonding $\mathrm{MO} ;(\mathrm{c})$ the MOs formed from combination of the 1$s$ orbitals of two atoms?

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Problem 31

How many electrons does it take to fill (a) the MOs formed from combination of the 2p orbitals of two atoms; (b) a $\sigma_{2 p}^{+1} \mathrm{MO}$ (c) the MOs formed from combination of the 2s orbitals of two atoms?

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Problem 32

The molecular orbitals depicted below are derived from 2p atomic orbitals in $\mathrm{F}_{2}^{+},$ (a) Give the orbital designations. (b) Which is occupied by at least one electron in $\mathrm{F}_{2}^{+},?$ (c) Which is occupied by only one electron in $\mathrm{F}_{2}^{+},?$

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Problem 33

The molecular orbitals depicted below are derived from n = 2 atomic orbitals. (a) Give the orbital designations. (b) Which is highest in energy? (c) Lowest in energy? (d) Rank the MOs in order of increasing energy for $\mathrm{B}_{2}$

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Problem 34

Use an MO diagram and the bond order you obtain from it to answer: (a) Is $\mathrm{Be}_{2}^{+}$ stable? (b) Is $\mathrm{Be}_{2}^{+}$ diamagnetic? (c) What is the outer (valence) electron configuration of $\mathrm{Be}_{2}+2$

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Problem 35

Use an MO diagram and the bond order you obtain from it to answer (a) Is $\mathrm{O}_{2}^{-}$ stable? (b) Is $\mathrm{O}_{2}$ - paramagnetic? (c) What is the outer (valence) electron configuration of $\mathrm{O}_{2}^{-2}$

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Problem 36

Use MO diagrams to place $\mathrm{C}_{2}^{-}, \mathrm{C}_{2},$ and $\mathrm{C}_{2}+$ in order of (a) increasing bond energy; (b) increasing bond length.

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Problem 37

Use MO diagrams to place $\mathrm{B}_{2}^{+}, \mathrm{B}_{2},$ and $\mathrm{B}_{2}^{-}$ in order of (a) decreasing bond energy; (b) decreasing bond length.

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Problem 38

Predict the shape, state the hybridization of the central atom, and give the ideal bond angle(s) and any expected deviations for:
(a) ${BrO}_{3}-$ (b) ${AsCl}_{4}^{-}$ (c) ${SeO}_{4}^{2-}$ (d) ${BiF}_{5}^{2-}$
(e) ${SbF}_{4}^{+}$ (f) ${AlF}_{6}^{3-}$ (g) ${IF}_{4}^{+}$

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Problem 39

Butadiene (right) is a colorless gas used to make synthetic rubber and many other compounds. (a) How many $\sigma$ bonds and $\pi$ bonds does the molecule have? (b) Are cis-trans arrangements about the double bonds possible? Explain.

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Problem 40

Epinephrine (or adrenaline; below) is a naturally occurring hormone that is also manufactured commercially for use as a heart stimulant, a nasal decongestant, and a glaucoma treatment.
(a) What is the hybridization of each $C, O,$ and $N$ atom? (b) How many $\sigma$ bonds does the molecule have? (c) How many $\pi$ electrons are delocalized in the ring?

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Problem 41

Use partial orbital diagrams to show how the atomic orbitals of the central atom lead to the hybrid orbitals in:
(a) $\mathrm{IF}_{2}^{-}$ (b) $\mathrm{ICl}_{3}$ (c) $\mathrm{XeOF}_{4}$ (d) $\mathrm{BHF}_{2}$

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Problem 42

Isoniazid (below) is an antibacterial agent that is very useful against many common strains of tuberculosis.
(a) How many $\sigma$ bonds are in the molecule? (b) What is the hybridization of each $\mathrm{C}$ and $\mathrm{N}$ atom?

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Problem 43

Hydrazine, $\mathrm{N}_{2} \mathrm{H}_{4}$ and carbon disulfide, $\mathrm{CS}_{2}$ form a cyclic
molecule (below). (a) Draw Lewis structures for $\mathrm{N}_{2} \mathrm{H}_{4}$ and $\mathrm{CS}_{2}$ (b) How do electron-group arrangement, molecular shape, and hybridization of N change when $\mathrm{N}_{2} \mathrm{H}_{4}$ reacts to form the product?
(c) How do electron-group arrangement, molecular shape, and hybridization of C change when $\mathrm{CS}_{2}$ reacts to form the product?

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Problem 44

In each of the following equations, what hybridization change, if any, occurs for the underlined atom?
a) $\underline{\mathrm{BF}}_{3}+\mathrm{NaF} \longrightarrow \mathrm{Na}^{+} \mathrm{BF}_{4}^{-}$
b) $\mathrm{PCl}_{3}+\mathrm{Cl}_{2} \longrightarrow \mathrm{PCl}_{5}$
c) $\mathrm{HC} \equiv \mathrm{CH}+\mathrm{H}_{2} \longrightarrow \mathrm{H}_{2} \mathrm{C}=\mathrm{CH}_{2}$
d) $\underline{\mathrm{SiF}}_{4}+2 \mathrm{F}^{-} \longrightarrow \mathrm{SiF}_{6}^{2-}$
e)$\underline{\mathrm{SO}}_{2}+\frac{\mathrm{l}}{2} \mathrm{O}_{2} \longrightarrow \mathrm{so}_{3}$

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Problem 45

The ionosphere lies about 100 km above Earth’s surface. This layer consists mostly of $\mathrm{NO}, \mathrm{O}_{2},$ and $\mathrm{N}_{2},$ and photoionization creates $\mathrm{NO}^{+}, \mathrm{O}_{2}^{+},$ and $\mathrm{N}_{2}^{+},$ (a) Use MO theory to compare the bond orders of the molecules and ions. (b) Does the magnetic behavior of each species change when its ion forms?

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Problem 46

Glyphosate (below) is a common herbicide that is relatively harmless to animals but deadly to most plants. Describe the shape around and the hybridization of the P, N, and three numbered C atoms.

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Problem 47

Tryptophan is one of the amino acids found in proteins:
(a) What is the hybridization of each of the numbered $C, N,$ and O atoms? (b) How many $\sigma$ bonds are present in tryptophan? (c) Predict the bond angles at points a, b, and c.

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Problem 48

Some species with two oxygen atoms only are the oxygen molecule, $\mathrm{O}_{2},$ the peroxide ion, $\mathrm{O}_{2}^{2-},$ the superoxide ion, $\mathrm{O}_{2}^{-}$ and the dioxygenyl ion $\mathrm{O}_{2}^{+}$. Draw an MO diagram for each, rank them in order of increasing bond length, and find the number of unpaired electrons in each.

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Problem 49

Molecular nitrogen, carbon monoxide, and cyanide ion are isoelectronic. (a) Draw an MO diagram for each. (b) CO and $C N^{-}$ are toxic. What property may explain why $\mathrm{N}_{2}$ isn't?

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Problem 50

There is concern in health-related government agencies that the American diet contains too much meat, and numerous recommendations have been made urging people to consume more fruit and vegetables. One of the richest sources of vegetable protein is soy, available in many forms. Among these is soybean curd, or tofu, which is a staple of many Asian diets. Chemists have isolated an anticancer agent called genistein from tofu, which may explain the much lower incidence of cancer among people in the Far East. A valid Lewis structure for genistein is
(a) Is the hybridization of each C in the right-hand ring the same? Explain. (b) Is the hybridization of the O atom in the center ring the same as that of the O atoms in the OH groups? Explain. (c) How many carbon-oxygen $\sigma$ bonds are there? How many carbon-oxygen $\pi$ bonds? (d) Do all the lone pairs on oxygens occupy the same type of hybrid orbital? Explain.

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Problem 51

An organic chemist synthesizes the molecule below:
(a) Which of the orientations of hybrid orbitals shown below are present in the molecule? (b) Are there any present that are not shown below? If so, what are they? (c) How many of each type of hybrid orbital are present?

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Problem 52

Simple proteins consist of amino acids linked together in a long chain; a small portion of such a chain is
Experiment shows that rotation about the C—N bond (indicated by the arrow) is somewhat restricted. Explain with resonance structures, and show the types of bonding involved.

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Problem 53

Sulfur forms oxides, oxoanions, and halides. What is the hybridization of the central S in $\mathrm{SO}_{2}, \mathrm{SO}_{3}, \mathrm{SO}_{3}^{2-}, \mathrm{SCl}_{4}, \mathrm{SCl}_{6},$ and $\mathrm{S}_{2} \mathrm{Cl}_{2}$ (atom sequence $\mathrm{Cl}-\mathrm{S}-\mathrm{S}-\mathrm{Cl} ) ?$

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Problem 54

The compound 2,6-dimethylpyrazine (below) gives chocolate its odor and is used in flavorings. (a) Which atomic orbitals mix to form the hybrid orbitals of N? (b) In what type of hybrid orbital do the lone pairs of N reside? (c) Is $\mathrm{C}$ in $\mathrm{CH}_{3}$ hybridized the same as any $\mathrm{C}$ in the ring? Explain.

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Problem 55

Use an MO diagram to find the bond order and predict whether $\mathrm{H}_{2}-$ exists.

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Problem 56

Acetylsalicylic acid (aspirin), the most widely used medicine in the world, has the Lewis structure shown below. (a) What is the hybridization of each C and each O atom? (b) How many localized $\pi$ bonds are present? (c) How many $C$ atoms have a trigonal planar shape around them? A tetrahedral shape?

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Problem 57

Linoleic acid is an essential fatty acid found in many vegetable oils, such as soy, peanut, and cottonseed. A key structural feature of the molecule is the cis orientation around its two double bonds, where $R_{1}$ and $R_{2}$ represent two different groups that form the rest of the molecule.
(a) How many different compounds are possible, changing only the cis-trans arrangements around these two double bonds?
(b) How many are possible for a similar compound with three double bonds?

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