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CHEMISTRY: The Molecular Nature of Matter and Change 2016

Martin S. Silberberg, Patricia G. Amateis

Chapter 9

Models of Chemical Bonding

Educators


Problem 1

In general terms, how does each of the following atomic properties influence the metallic character of the main-group elements in a period?
(a) Ionization energy
(b) Atomic radius
(c) Number of outer electrons
(d) Effective nuclear charge

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Problem 2

Three solids are represented below. What is the predominant type of intramolecular bonding in each?

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Problem 3

What is the relationship between the tendency of a main-group element to form a monatomic ion and its position in the periodic table? In what part of the table are the main-group elements that typically form cations? Anions?

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Problem 4

Which member of each pair is more metallic?
(a) Na or Cs (b) Mg or Rb (c) As or N

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Problem 5

Which member of each pair is less metallic?
(a) I or O (b) Be or Ba (c) Se or Ge

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Problem 6

State the type of bonding—ionic, covalent, or metallic—you would expect in each: (a) CsF(s); (b) N2(g); (c) Na(s).

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Problem 7

State the type of bonding—ionic, covalent, or metallic—you would expect in each: (a) ICl3(g); (b) N2O(g); (c) LiCl(s).

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Problem 8

State the type of bonding—ionic, covalent, or metallic—you would expect in each: (a) O3(g); (b) MgCl2(s); (c) BrO2(g).

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Problem 9

State the type of bonding—ionic, covalent, or metallic—you would expect in each: (a) Cr(s); (b) H2S(g); (c) CaO(s).

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Problem 10

Draw a Lewis electron-dot symbol for (a) Rb; (b) Si; (c) I.

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Problem 11

Draw a Lewis electron-dot symbol for (a) Ba; (b) Kr; (c) Br.

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Problem 12

Draw a Lewis electron-dot symbol for (a) Sr; (b) P; (c) S.

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Problem 13

Draw a Lewis electron-dot symbol for (a) As; (b) Se; (c) Ga.

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Problem 14

Give the group number and general electron configuration of an element with each electron-dot symbol: (a) $\cdot \ddot{x} :$ (b) $\dot{x}$

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Problem 15

Give the group number and general electron configuration of an element with each electron-dot symbol: (a) $\cdot \dot{x} : \quad(b) \cdot \dot{\chi}$

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Problem 16

If energy is required to form monatomic ions from metals and nonmetals, why do ionic compounds exist?

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Problem 17

(a) In general, how does the lattice energy of an ionic compound depend on the charges and sizes of the ions? (b) Ion arrangements of three general salts are represented below. Rank them in order of increasing lattice energy.

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Problem 18

When gaseous $\mathrm{Na}^{+}$ and $\mathrm{Cl}^{-}$ ions form gaseous NaCl ion pairs, 548 $\mathrm{kJ} / \mathrm{mol}$ of energy is released. Why, then, does $\mathrm{NaCl}$
occur as a solid under ordinary conditions?

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Problem 19

To form $\mathrm{S}^{2-}$ ions from gaseous sulfur atoms requires $214 \mathrm{kJ} / \mathrm{mol},$ but these ions exist in solids such as $\mathrm{K}_{2} \mathrm{S}$ . Explain.

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Problem 20

Use condensed electron configurations and Lewis electron-dot
symbols to depict the ions formed from each of the following atoms,
and predict the formula of their compound:
(a) Ba and Cl (b) Sr and O (c) Al and F (d) Rb and O

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Problem 21

Use condensed electron configurations and Lewis electron-dot symbols to depict the ions formed from each of the following atoms, and predict the formula of their compound:
(a) Cs and S (b) O and Ga (c) N and Mg (d) Br and Li

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Problem 22

For each ionic compound formula, identify the main group to which $\mathrm{X}$ belongs: $(\mathrm{a}) \mathrm{XF}_{2} ;(\mathrm{b}) \mathrm{MgX} ;(\mathrm{c}) \mathrm{X}_{2} \mathrm{SO}_{4}$

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Problem 23

For each ionic compound formula, identify the main group to which $\mathrm{X}$ belongs: $(\text { a }) \mathrm{X}_{3} \mathrm{PO}_{4} ;(\mathrm{b}) \mathrm{X}_{2}\left(\mathrm{SO}_{4}\right)_{3} ;(\mathrm{c}) \mathrm{X}\left(\mathrm{NO}_{3}\right)_{2}$

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Problem 24

For each ionic compound formula, identify the main group to which $\mathrm{X}$ belongs: $(\mathrm{a}) \mathrm{X}_{2} \mathrm{O}_{3} ;(\mathrm{b}) \mathrm{XCO}_{3} ;(\mathrm{c}) \mathrm{Na}_{2} \mathrm{X} .$

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Problem 25

For each ionic compound formula, identify the main group to which $\mathrm{X}$ belongs: $\left(\text { a) } \mathrm{CaX}_{2} ;(\mathrm{b}) \mathrm{Al}_{2} \mathrm{X}_{3} ;(\mathrm{c}) \mathrm{XPO}_{4}\right.$

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Problem 26

For each pair, choose the compound with the larger lattice energy, and explain your choice: (a) BaS or CsCl; (b) LiCl or CsCl.

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Problem 27

For each pair, choose the compound with the larger lattice energy, and explain your choice: (a) CaO or CaS; (b) BaO or SrO.

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Problem 28

For each pair, choose the compound with the smaller lattice energy, and explain your choice: (a) CaS or BaS; (b) NaF or MgO.

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Problem 29

For each pair, choose the compound with the smaller lattice energy, and explain your choice: (a) NaF or NaCl; (b) $\mathrm{K}_{2} \mathrm{O}$ or $\mathrm{K}_{2} \mathrm{S}$ .

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Problem 30

Use the following to calculate $\Delta H_{\text { latice }}^{\circ}$ of $\mathrm{NaCl}$ :
$$\begin{array}{ll}{\mathrm{Na}(s) \longrightarrow \mathrm{Na}(g)} & {\Delta H^{\circ}=109 \mathrm{kJ}} \\ {\mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{Cl}(g)} & {\Delta H^{\circ}=243 \mathrm{kJ}} \\ {\mathrm{Na}(g) \longrightarrow \mathrm{Na}^{+}(g)+\mathrm{e}^{-}} & {\Delta H^{\circ}=496 \mathrm{kJ}} \\ {\mathrm{Cl}(g)+\mathrm{e}^{-} \longrightarrow \mathrm{Cl}^{-}(g)} & {\Delta H^{\circ}=-349 \mathrm{kJ}} \\ {\mathrm{Na}(s)+\frac{1}{2} \mathrm{Cl}_{2}(g) \longrightarrow \mathrm{NaCl}(s)} & {\Delta H^{\circ}=-411 \mathrm{kJ}}\end{array}$$
Compared with the lattice energy of LiF $(1050 \mathrm{kJ} / \mathrm{mol}),$ is the
magnitude of the value for $\mathrm{NaCl}$ what you expected? Explain.

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Problem 31

Use the following to calculate $\Delta H_{\text { latico of }}^{\circ} \mathrm{MgF}_{2}$
$$\begin{array}{ll}{\mathrm{Mg}(s) \longrightarrow \mathrm{Mg}(g)} & {\Delta H^{\circ}=148 \mathrm{kJ}} \\ {\mathrm{F}_{2}(g) \longrightarrow 2 \mathrm{F}(g)} & {\Delta H^{\circ}=159 \mathrm{kJ}} \\ {\mathrm{Mg}(g) \longrightarrow \mathrm{Mg}^{+}(g)+\mathrm{e}^{-}} & {\Delta H^{\circ}=738 \mathrm{kJ}}\end{array}$$
$$\begin{array}{ll}{\mathrm{Mg}^{+}(g) \longrightarrow \mathrm{Mg}^{2+}(g)+\mathrm{e}^{-}} & {\Delta H^{\circ}=1450 \mathrm{kJ}} \\ {\mathrm{F}(g)+\mathrm{e}^{-} \rightarrow \mathrm{F}^{-}(g)} & {\Delta H^{\circ}=-328 \mathrm{kJ}} \\ {\mathrm{Mg}(s)+\mathrm{F}_{2}(g) \longrightarrow \mathrm{MgF}_{2}(s)} & {\Delta H^{\circ}=-1123 \mathrm{kJ}}\end{array}$$
Compared with the lattice energy of LiF $(1050 \mathrm{kJ} / \mathrm{mol})$ or the lattice energy you calculated for $\mathrm{NaCl}$ in Problem $9.30,$ does the relative magnitude of the value for $\mathrm{MgF}_{2}$ surprise you? Explain.

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Problem 32

Aluminum oxide $\left(\mathrm{Al}_{2} \mathrm{O}_{3}\right)$ is a widely used industrial abrasive (emery, corundum), for which the specific application depends on the hardness of the crystal. What does this hardness imply about the magnitude of the lattice energy? Would you have predicted from the chemical formula that $\mathrm{Al}_{2} \mathrm{O}_{3}$ is hard? Explain.

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Problem 33

Born-Haber cycles were used to obtain the first reliable values for electron affinity by considering the EA value as the unknown and using a theoretically calculated value for the lattice energy. Use a Born-Haber cycle for KF and the following values to calculate a value for the electron affinity of fluorine:
$$ \begin{array}{ll}{\mathrm{K}(s) \longrightarrow \mathrm{K}(g)} & {\Delta H^{\circ}=90 \mathrm{kJ}} \\ {\mathrm{K}(g) \longrightarrow \mathrm{K}^{+}(g)+\mathrm{e}^{-}} & {\Delta H^{\circ}=419 \mathrm{kJ}} \\ {\mathrm{F}_{2}(g) \longrightarrow 2 \mathrm{F}(g)} & {\Delta H^{\circ}=159 \mathrm{kJ} \mathrm{kJ}} \\ {\mathrm{K}(s)+\frac{1}{2} \mathrm{F}_{2}(g) \longrightarrow \mathrm{KF}(s)} & {\Delta H^{\circ}=-569 \mathrm{kJ}} \\ {\mathrm{K}^{+}(g)+\mathrm{F}^{-}(g) \longrightarrow \mathrm{KF}(s)} & {\Delta H^{\circ}=-821 \mathrm{kJ}}\end{array}$$

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Problem 34

Describe the interactions that occur between individual chlorine atoms as they approach each other and form Cl2. What combination of forces gives rise to the energy holding the atoms together and to the final internuclear distance?

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Problem 35

Define bond energy using the $\mathrm{H}-\mathrm{Cl}$ bond as an example. When this bond breaks, is energy absorbed or released? Is the accompanying $\Delta H$ value positive or negative? How do the magnitude and sign of this $\Delta H$ value relate to the value that accompanies $\mathrm{H}-\mathrm{Cl}$ bond formation?

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Problem 36

For single bonds between similar types of atoms, how does the strength of the bond relate to the sizes of the atoms? Explain.

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Problem 37

How does the energy of the bond between a given pair of atoms relate to the bond order? Why?

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Problem 38

When liquid benzene $\left(\mathrm{C}_{6} \mathrm{H}_{6}\right)$ boils, does the gas consist of
molecules, ions, or separate atoms? Explain.

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Problem 39

Using the periodic table only, arrange the members of each of the following sets in order of increasing bond strength:
(a) $\mathrm{Br}-\mathrm{Br}, \mathrm{Cl}-\mathrm{Cl}, \mathrm{I}-\mathrm{I}$
(b) $\mathrm{S}-\mathrm{H}, \mathrm{S}-\mathrm{Br}, \mathrm{S}-\mathrm{Cl}$
(c) $\mathrm{C}=\mathrm{N}, \mathrm{C}-\mathrm{N}, \mathrm{C}=\mathrm{N}$

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Problem 40

Using the periodic table only, arrange the members of each of the following sets in order of increasing bond length:
(a) $\mathrm{H}-\mathrm{F}, \mathrm{H}-\mathrm{I}, \mathrm{H}-\mathrm{C}$
(b) $C-S, C=O, C-O$
(c) $\mathrm{N}-\mathrm{H}, \mathrm{N}-\mathrm{S}, \mathrm{N}-\mathrm{O}$

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Problem 41

Formic acid $(\mathrm{HCOOH} ; \text { structural formula shown below) is }$ secreted by certain species of ants when they bite.
$$\begin{array}{c}{0} \\ {\mathrm{H}-\mathrm{C}-\mathrm{O}-\mathrm{H}}\end{array}$$
Rank the relative strengths of $(a)$ the $C-O$ and $C=O$ bonds and
(b) the $H-C$ and $H-O$ bonds. Explain these rankings.

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Problem 42

Write a solution Plan (without actual numbers, but including the bond energies you would use and how you would combine them algebraically) for calculating the total enthalpy change of the following reaction:
$$\mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{H}_{2} \mathrm{O}_{2}(g) \quad(\mathrm{H}-\mathrm{O}-\mathrm{O}-\mathrm{H})$$

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Problem 43

The text points out that, for similar types of substances, one with weaker bonds is usually more reactive than one with stronger bonds. Why is this generally true?

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Problem 44

Why is there a discrepancy between a heat of reaction obtained from calorimetry and one obtained from bond energies?

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Problem 45

Which of the following gases would you expect to have the greater heat of reaction per mole for combustion? Why?
$$\begin{array}{cc}{\text { methane or }} & {\text { formaldehyde }} \\ {H} & {0} \\ {H-C-H} & {H-C-H} \\ {H}\end{array}$$

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Problem 46

Which of the following gases would you expect to have the greater heat of reaction per mole for combustion? Why?
$$\begin{array}{c}{\text { ethanol }} \\ {\text { H } \mathrm{H}} \\ {\mathrm{H}-\mathrm{C}-\mathrm{C}-\mathrm{C}-\mathrm{O}-\mathrm{H}} \\ {\mathrm{H} \mathrm{H}}\end{array}$$
or
$$\begin{array}{c}{\text { methanol }} \\ {\mathrm{H}} \\ {\mathrm{H}-\mathrm{C}^{-}-\mathrm{O}-\mathrm{H}} \\ {\mathrm{H}}\end{array}$$

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Problem 47

Use bond energies to calculate the heat of reaction:

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Problem 48

Use bond energies to calculate the heat of reaction:

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Problem 49

An important industrial route to extremely pure acetic acid is the reaction of methanol with carbon monoxide:

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Problem 50

Sports trainers treat sprains and soreness with ethyl bromide. It is manufactured by reacting ethylene with hydrogen bromide:

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Problem 51

Describe the vertical and horizontal trends in electronegativity (EN) among the main-group elements. According to Pauling’s scale, what are the two most electronegative elements? The two least electronegative elements?

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Problem 52

What is the general relationship between IE1 and EN for the elements? Why?

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Problem 53

Is the $\mathrm{H}-\mathrm{O}$ bond in water nonpolar covalent, polar covalent, or ionic? Define each term, and explain your choice.

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Problem 54

How does electronegativity differ from electron affinity?

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Problem 55

How is the partial ionic character of a bond in a diatomic molecule related to $\Delta E N$ for the bonded atoms? Why?

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Problem 56

Using the periodic table only, arrange the elements in each set in order of increasing EN: (a) $\mathrm{S}, \mathrm{O}, \mathrm{Si} ;(\mathrm{b}) \mathrm{Mg}, \mathrm{P}, \mathrm{As}$ .

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Problem 57

Using the periodic table only, arrange the elements in each set in order of increasing EN: (a) I, Br, N;(b) Ca, H, F.

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Problem 58

Using the periodic table only, arrange the elements in each set in order of decreasing EN: (a) $\mathrm{N}, \mathrm{P}, \mathrm{Si} ;(\mathrm{b}) \mathrm{Ca}, \mathrm{Ga}, \mathrm{As}$ .

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Problem 59

Using the periodic table only, arrange the elements in each set in order of decreasing EN: (a) $\mathrm{Br}, \mathrm{Cl}, \mathrm{P} ;(\mathrm{b}) \mathrm{I}, \mathrm{F}, \mathrm{O}$ .

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Problem 60

Use Figure $9.21,$ p. $381,$ to indicate the polarity of each bond with a polar arrow: (a) $\mathrm{N}-\mathrm{B} ;(\mathrm{b}) \mathrm{N}-\mathrm{O} ;$ (c) $\mathrm{C}-\mathrm{S} ;(\mathrm{d}) \mathrm{S}-\mathrm{O}$ ; (e) $\mathrm{N}-\mathrm{H} ;(\mathrm{f}) \mathrm{Cl}-\mathrm{O}$ .

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Problem 61

Use Figure $9.21,$ p. $381,$ to indicate the polarity of each bond with partial charges: (a) Br $-\mathrm{Cl} ;$ (b) $\mathrm{F}-\mathrm{Cl} ;(\mathrm{c}) \mathrm{H}-\mathrm{O} ;$
(d) $\mathrm{Se}-\mathrm{H} ;(\mathrm{e}) \mathrm{As}-\mathrm{H} ;(\mathrm{f}) \mathrm{S}-\mathrm{N} .$

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Problem 62

Which is the more polar bond in each of the following pairs from Problem $9.60 :(\text { a })$ or $(b) ;(c)$ or $(d) ;(\text { e })$ or $(f) ?$

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Problem 63

Which is the more polar bond in each of the following pairs from Problem $9.61 :(a)$ or $(b) ;(c)$ or $(d) ;(e)$ or $(f) ?$

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Problem 64

Are the bonds in each of the following substances ionic, non-polar covalent, or polar covalent? Arrange the substances with polar covalent bonds in order of increasing bond polarity:
$\begin{array}{llll}{\text { (a) } \mathrm{S}_{8}} & {\text { (b) } \mathrm{RbCl}} & {\text { (c) } \mathrm{PF}_{3}} & {\text { (d) } \mathrm{SCl}_{2}} & {\text { (e) } \mathrm{F}_{2}} & {\text { (f) } \mathrm{SF}_{2}}\end{array}$

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Problem 65

Are the bonds in each of the following substances ionic, non- polar covalent, or polar covalent? Arrange the substances with polar covalent bonds in order of increasing bond polarity:
(a) $\mathrm{KCl} \quad$ (b) $\mathrm{P}_{4} \quad(\mathrm{c}) \mathrm{BF}_{3} \quad$ (d) $\mathrm{SO}_{2} \quad$ (e) $\mathrm{Br}_{2} \quad$ (f) $\mathrm{NO}_{2}$

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Problem 66

Rank the members of each set of compounds in order of increasing ionic character of their bonds. Use polar arrows to indicate the bond polarity of each:
(a) HBr, HCl, HI (b) $\mathrm{H}_{2} \mathrm{O}, \mathrm{CH}_{4}, \mathrm{HF} \quad$ (c) $\mathrm{SCl}_{2}, \mathrm{PCl}_{3}, \mathrm{SiCl}_{4}$

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Problem 67

Rank the members of each set of compounds in order of decreasing ionic character of their bonds. Use partial charges to indicate the bond polarity of each:
(a) $\mathrm{PCl}_{3}, \mathrm{PBr}_{3}, \mathrm{PF}_{3} \quad$ (b) $\mathrm{BF}_{3}, \mathrm{NF}_{3}, \mathrm{CF}_{4} \quad$ (c) $\mathrm{SeF}_{4}, \mathrm{TeF}_{4}, \mathrm{BrF}_{3}$

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Problem 68

The energy of the C¬C bond is 347 kJ/mol, and that of the
Cl¬Cl bond is 243 kJ/mol. Which of the following values might
you expect for the C¬Cl bond energy? Explain.
(a) 590 kJ/mol (sum of the values given)
(b) 104 kJ/mol (difference of the values given)
(c) 295 kJ/mol (average of the values given)
(d) 339 kJ/mol (greater than the average of the values given)

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Problem 69

(a) List four physical characteristics of a solid metal.
(b) List two chemical characteristics of a metallic element.

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Problem 70

Briefly account for the following relative values:
(a) The melting points of Na and $\mathrm{K}$ are $89^{\circ} \mathrm{C}$ and $63^{\circ} \mathrm{C},$ respectively.
(b) The melting points of Li and Be are $180^{\circ} \mathrm{C}$ and $1287^{\circ} \mathrm{C},$ respectively.
(c) Li boils more than $1100^{\circ} \mathrm{C}$ higher than it melts.

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Problem 71

Magnesium metal is easily deformed by an applied force, whereas magnesium fluoride is shattered. Why do these two solids behave so differently?

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Problem 72

Geologists have a rule of thumb: when molten rock cools and solidifies, crystals of compounds with the smallest lattice energies appear at the bottom of the mass. Suggest a reason for this

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Problem 73

Acetylene gas (ethyne; $\mathrm{HC} \equiv \mathrm{CH}$ ) burns in an oxyacetylene torch to produce carbon dioxide and water vapor. The heat of reaction for the combustion of acetylene is 1259 $\mathrm{kJ} / \mathrm{mol} .$ (a) Calculate the $\mathrm{C} \equiv \mathrm{C}$ bond energy, and compare your value with that in Table $9.2,$ p. $371 .$ (b) When 500.0 g of acetylene burns, how many kilojoules of heat are given off? (c) How many grams of
$\mathrm{CO}_{2}$ form? (d) How many liters of $\mathrm{O}_{2}$ at 298 $\mathrm{K}$ and 18.0 atm are consumed?

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Problem 74

Use Lewis electron-dot symbols to represent the formation of (a) $\mathrm{BrF}_{3}$ from bromine and fluorine atoms; (b) AlF $_{3}$ from aluminum and fluorine atoms.

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Problem 75

Even though so much energy is required to form a metal cation with a $2+$ charge, the alkaline earth metals form halides with general formula $\mathrm{MX}_{2},$ rather than $\mathrm{MX}$ .(a) Use the following data to calculate $\Delta H_{\mathrm{f}}^{\circ}$ of MgCl:
$$\begin{array}{ll}{\mathrm{Mg}(s) \longrightarrow \mathrm{Mg}(g)} & {\Delta H^{\circ}=148 \mathrm{kJ}} \\ {\mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{Cl}(g)} & {\Delta H^{\circ}=243 \mathrm{kJ}} \\ {\mathrm{Mg}(g) \longrightarrow \mathrm{Mg}^{+}(g)+\mathrm{e}^{-}} & {\Delta H^{\circ}=738 \mathrm{kJ}} \\ {\mathrm{Cl}(g)+\mathrm{e}^{-} \longrightarrow \mathrm{Cl}^{\circ}(g)} & {\Delta H^{\circ}=-349 \mathrm{kJ}} \\ {\Delta H_{\text { latice }}^{\circ} \text { of } \mathrm{MgCl}=783.5 \mathrm{kJ} / \mathrm{mol}}\end{array}$$
(b) Is MgCl favored energetically relative to Mg and Cl,? Explain.
(c) Use Hess's law to calculate $\Delta H^{\circ}$ for the conversion of $\mathrm{MgCl}$ to
$\mathrm{MgCl}_{2}$ and $\mathrm{Mg}\left(\Delta H_{\mathrm{f}}^{\circ} \text { of } \mathrm{MgCl}_{2}=-641.6 \mathrm{kJ} / \mathrm{mol}\right)$
(d) Is MgCl favored energetically relative to MgCl,? Explain.

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Problem 76

Gases react explosively if the heased when the reaction begins is sufficient to cause more reaction, which leads to a rapid expansion of the gases. Use bond energies to calculate
$\Delta H^{\circ}$ of each of the following reactions, and predict which occurs explosively:
(a) $\mathrm{H}_{2}(g)+\mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{HCl}(g)$
(b) $\mathrm{H}_{2}(g)+\mathrm{I}_{2}(g) \longrightarrow 2 \mathrm{HI}(g)$
(c) $2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(g)$

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Problem 77

By using photons of specific wavelengths, chemists can dissociate gaseous HI to produce H atoms with certain speeds. When HI dissociates, the H atoms move away rapidly, whereas
the heavier I atoms move more slowly. (a) What is the longest wavelength (in nm) that can dissociate a molecule of HI? (b) If a photon of 254 nm is used, what is the excess energy (in J) over that needed for dissociation? (c) If this excess energy is carried away by the H atom as kinetic energy, what is its speed (in m/s)?

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Problem 78

In developing the concept of electronegativity, Pauling used the term excess bond energy for the difference between the actual bond energy of $\mathrm{X}-\mathrm{Y}$ and the average bond energies of $\mathrm{X}-\mathrm{X}$ and $\mathrm{Y}-\mathrm{Y}(\text { see text discussion for the case of } \mathrm{HF}) .$ Based on the values in Figure $9.21, \mathrm{p} .381,$ which of the following substances contains bonds with no excess bond energy?
(a) $\mathrm{PH}_{3}$ (b) $\mathrm{CS}_{2}$ (c) BrCl (d) $\mathrm{BH}_{3}$ (e) $\mathrm{Se}_{8}$

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Problem 79

Use condensed electron configurations to predict the relative hardnesses and melting points of rubidium $(Z=37),$ vanadium $(Z=23)$ , and cadmium $(Z=48)$ .

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Problem 80

Without stratospheric ozone $\left(\mathrm{O}_{3}\right),$ harmful solar radiation would cause gene alterations. Ozone forms when the bond in $\mathrm{O}_{2}$ breaks and each $\mathrm{O}$ atom reacts with another $\mathrm{O}_{2}$ molecule. It is destroyed by reaction with Clatoms formed when the $\mathrm{C}-\mathrm{Cl}$ bond in synthetic chemicals breaks. Find the wavelengths of light that can break the C-Cl bond and the bond in $\mathrm{O}_{2}$ .

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Problem 81

"Inert" xenon actually forms many compounds, especially with highly electronegative fluorine. The $\Delta H_{\mathrm{f}}^{\circ}$ values for xenon difluoride, tetrafluoride, and hexafluoride are $-105,-284,$ and $-402 \mathrm{kJ} / \mathrm{mol}$ , respectively. Find the average bond energy of the $\mathrm{Xe}-\mathrm{F}$ bonds in each fluoride.

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Problem 82

The HF bond length is 92 pm, 16% shorter than the sum of the covalent radii of H (37 pm) and F (72 pm). Suggest a reason for this difference. Similar data show that the difference becomes smaller down the group, from HF to HI. Explain.

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Problem 83

There are two main types of covalent bond breakage. In homolytic breakage (as in Table 9.2, p. 371), each atom in the bond gets one of the shared electrons. In some cases, the electronegativity of adjacent atoms affects the bond energy. In heterolytic breakage, one atom gets both electrons and the other gets none; thus, a cation and an anion form.
(a) Why is the $\mathrm{C}-\mathrm{C}$ bond in $\mathrm{H}_{3} \mathrm{C}-\mathrm{CF}_{3}(423 \mathrm{kJ} / \mathrm{mol})$ stronger than that in $\mathrm{H}_{3} \mathrm{C}-\mathrm{CH}_{3}(376 \mathrm{kJ} / \mathrm{mol}) ?$
(b) Use bond energy and any other data to calculate the enthalpy of reaction for the heterolytic cleavage of $\mathrm{O}_{2}$ .

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Problem 84

Find the longest wavelengths of light that can cleave the bonds in elemental nitrogen, oxygen, and fluorine.

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Problem 85

The work function ( $\phi )$ of a metal is the minimum energy needed to remove an electron from its surface. (a) Is it easier to remove an electron from a gaseous silver atom or from the
surface of solid silver $\left(\phi=7.59 \times 10^{-19} \mathrm{J} ; \mathrm{IE}=731 \mathrm{kJ} / \mathrm{mol}\right) ?$
(b) Explain the results in terms of the electron-sea model of metal-
lic bonding.

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Problem 86

Lattice energies can also be calculated for covalent solids using a Born-Haber cycle, and the network solid silicon dioxidehas one of the highest $\Delta H_{\text { latice values. Silues. Silicon dioxide is found in }}$ pure crystalline form as transparent rock quartz. Much harder than
glass, this material was once prized for making lenses for optical devices and expensive spectacles. Use Appendix $\mathrm{B}$ and the following data to calculate $\Delta H_{\text { latices. of }}^{\circ} \mathrm{SiO}_{2} :$
$$\begin{array}{ll}{\mathrm{Si}(g) \longrightarrow \mathrm{Si}(g)} & {\Delta H^{\circ}=454 \mathrm{kJ}} \\ {\mathrm{Si}(g) \longrightarrow \mathrm{Si}^{4+}(g)+4 \mathrm{e}^{-}} & {\Delta H^{\circ}=9949 \mathrm{kJ}} \\ {\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{O}(g)} & {\Delta H^{\circ}=498 \mathrm{kJ}} \\ {\mathrm{O}(g)+2 \mathrm{e}^{-} \longrightarrow \mathrm{O}^{2-}(g)} & {\Delta H^{\circ}=737 \mathrm{kJ}}\end{array}$$

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Problem 87

The average $\mathrm{C}-\mathrm{H}$ bond energy in $\mathrm{CH}_{4}$ is 415 $\mathrm{kJ} / \mathrm{mol}$ . Use Table 9.2$(\mathrm{p} .371)$ and the following to calculate the average $\mathrm{C}-\mathrm{H}$ bond energy in ethane $\left(\mathrm{C}_{2} \mathrm{H}_{6} ; \mathrm{C}-\mathrm{C} \text { bond), in ethene }\left(\mathrm{C}_{2} \mathrm{H}_{4} ; \mathrm{C}=\mathrm{C}\right.\right.$ bond), and in ethyne $\left(\mathrm{C}_{2} \mathrm{H}_{2} ; \mathrm{C}=\mathrm{C} \text { bond): }\right.$
$$\begin{array}{ll}{\mathrm{C}_{2} \mathrm{H}_{6}(g)+\mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{CH}_{4}(g)} & {\Delta H_{\mathrm{rxn}}^{\circ}=-65.07 \mathrm{kJ} / \mathrm{mol}} \\ {\mathrm{C}_{2} \mathrm{H}_{4}(g)+2 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{CH}_{4}(g)} & {\Delta H_{\mathrm{rxn}}^{\circ}=-202.21 \mathrm{kJ} / \mathrm{mol}} \\ {\mathrm{C}_{2} \mathrm{H}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{CH}_{4}(g)} & {\Delta H_{\mathrm{rxn}}^{\circ}=-376.74 \mathrm{kJ} / \mathrm{mol}}\end{array}$$

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Problem 88

Carbon-carbon bonds form the “backbone” of nearly every organic and biological molecule. The average bond energy of the C¬C bond is 347 kJ/mol. Calculate the frequency and wavelength of the least energetic photon that can break an average C¬C bond. In what region of the electromagnetic spectrum is this radiation?

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Problem 89

In a future hydrogen-fuel economy, the cheapest source of $\mathrm{H}_{2}$ will certainly be water. It takes 467 $\mathrm{kJ}$ to produce 1 $\mathrm{mol}$ of $\mathrm{H}$ atoms from water. What is the frequency, wavelength, and minimum energy of a photon that can free an H atom from water?

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Problem 90

Dimethyl ether $\left(\mathrm{CH}_{3} \mathrm{OCH}_{3}\right)$ and ethanol $\left(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}\right)$ are constitutional isomers (see Table $3.4, \mathrm{p} .113 ) .$ (a) Use Table 9.2 (p. 371$)$ to calculate $\Delta H_{\mathrm{rxn}}^{\circ}$ for the formation of each compound as a gas from methane and oxygen; water vapor also forms. (b) State which reaction is more exothermic. (c) Calculate $\Delta H_{\text { rxn }}^{\circ}$ for the conversion of ethanol to dimethyl ether.

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Problem 91

Enthalpies of reaction calculated from bond energies and from enthalpies of formation are often, but not always, close to each other.
(a) Industrial ethanol $\left(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}\right)$ is produced by a catalytic reaction of ethylene $\left(\mathrm{CH}_{2}=\mathrm{CH}_{2}\right)$ with water at high pressures and temperatures. Calculate $\Delta H_{\mathrm{rxn}}^{\circ}$ for this gas-phase hydration of ethylene to ethanol, using bond energies and then using enthalpies of formation.
(b) Ethylene glycol is produced by the catalytic oxidation of ethylene to ethylene oxide, which then reacts with water to form ethylene glycol:
The $\Delta H_{\mathrm{rxn}}^{\circ}$ for this hydrolysis step, based on enthalpies of
formation, is $-97 \mathrm{kJ} / \mathrm{mol}$ . Calculate $\Delta H_{\mathrm{rxn}}^{\circ}$ for the hydrolysis using bond energies.
(c) Why are the two values relatively close for the hydration in
part (a) but not close for the hydrolysis in part (b)?

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