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CHEMISTRY: The Molecular Nature of Matter and Change 2016

Martin S. Silberberg, Patricia G. Amateis

Chapter 22

The Elements in Nature and Industry

Educators


Problem None

Diagrams of environmental cycles are simplified to omit minor contributors. For example, the production of lime from limestone is not shown in the cycle for carbon (Figure 22.5, p. 983). Which labeled category in the figure includes this process? Name two other processes that contribute to this category 11

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Problem 1

to retinoic acid. Identify each of these reactions as a reduction or an oxidation. (c) Structure $D$ is that of beta-carotene, found in carrots. Suggest a reason for the importance of beta-carotene in the vision process.

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Problem 2

Metallic elements can be recovered from ores that are oxides, carbonates, halides, or sulfides. Give an example of each type.

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Problem 3

The location of elements in the regions of Earth has enormous practical importance. (a) Define differentiation, and explain which physical property of a substance is primarily responsible
for this process. (b) What a e the four most abundant elements in the crust? (c) Which element is abundant in the crust and mantle
but not the core?

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Problem 4

How does the position of a metal in the periodic table relate to whether it occurs primarily as an oxide or as a sulfide?

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Problem 5

What material is the source for commercial production of each of the following elements: (a) aluminum; (b) nitrogen; (c) chlorine; (d) calcium; (e) sodium?

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Problem 6

Aluminum is widely distributed throughout the world in the form of aluminosilicates. What property of these minerals prevents them from being a source of aluminum?

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Problem 7

Describe two ways in which the biosphere has influenced the composition of Earth’s crust

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Problem 8

Use atomic and molecular properties to explain why life is based on carbon rather than some other element, such as silico

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Problem 9

Define fixation. Name two elements that undergo environmental fixation. What natural forms of them are fixed?

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Problem 12

Describe three pathways for the utilization of atmospheric nitrogen. Is human activity a significant factor? Explain.

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Problem 13

Why don’t the N-containing species in Figure 22.6 (p. 984) include rings or long chains with N—N bonds?

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Problem 14

(a) Which region of Earth’s crust is not involved in the phosphorus cycle? (b) Name two roles organisms play in the cycle.

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Problem 15

Nitrogen fixation requires a great deal of energy because the N2 bond is strong. (a) How do the processes of atmospheric and industrial fixation reflect this energy requirement? (b) How do the
thermodynamics of the two processes differ? (Hint: Examine the respective heats of formation.) (c) In view of the mild conditions for biological fixation, what must be the source of the “great deal
of energy”? (d) What would be the most obvious environmental result of a low activation energy for N2 fixation?

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Problem 16

The following steps are unbalanced half-reactions involved in the nitrogen cycle. Balance each half-reaction to show the number of electrons lost or gained, and state whether it is an oxidation or a reduction (all occur in acidic conditions):

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Problem 17

The use of silica to form slag in the production of phosphorus from phosphate rock was introduced by Robert Boyle more than 300 years ago. When fluorapatite $\left[\mathrm{Ca}_{5}\left(\mathrm{PO}_{4}\right)_{3} \mathrm{F}\right]$ is used in phosphorus production, most of the fluorine atoms appear in the
(a) If 15$\%$ by mass of the fluorine in $100 . \mathrm{kg}$ of $\mathrm{Ca}_{5}\left(\mathrm{PO}_{4}\right)_{3}$ , F forms
$\mathrm{SiF}_{4},$ what volume of this gas is collected at 1.00 $\mathrm{atm}$ and the industrial furnace temperature of $1450 .^{\circ} \mathrm{C} ?$
(b) In some facilities, the $\mathrm{SiF}_{4}$ is used to produce sodium hexafluorosilicate (Na_ilif_ ) which is sold for water fluoridation: $2 \mathrm{SiF}_{4}(g)+\mathrm{Na}_{2} \mathrm{CO}_{3}(s)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow$
$$
\mathrm{Na}_{2} \mathrm{SiF}_{6}(a q)+\mathrm{SiO}_{2}(s)+\mathrm{CO}_{2}(g)+2 \mathrm{HF}(a q)
$$
How many cubic meters of drinking water can be fluoridated to a level of 1.0 ppm of $\mathrm{F}^{-}$ using the $\mathrm{SiF}_{4}$ produced in part ( a )?

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Problem 18

An impurity sometimes found in $\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right),$ is $\mathrm{Fe}_{2} \mathrm{O}_{3},$ which is removed during the production of phosphorus as ferrophospho-
rus $\left(\mathrm{Fe}_{2} \mathrm{P}\right)$ . ( a) Why is this impurity troubling from an economic standpoint? (b) If 50 . metric tons of crude $\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}$ contains
2.0$\% \mathrm{Fe}_{2} \mathrm{O}_{3}$ by mass and the overall yield of phosphorus is $90 . \%,$
how many metric tons of $\mathrm{P}_{4}$ can be isolated?

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Problem 19

Define: (a) ore; (b) mineral; (c) gangue; (d) brine.

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Problem 20

Define: (a) roasting; (b) smelting; (c) flotation; (d) refining.

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Problem 21

What factors determine which reducing agent is selected for producing a specific metal?

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Problem 22

Use atomic properties to explain the reduction of a less active metal by a more active one: (a) in aqueous solution; (b) in the molten state. Give a specific example of each process.

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Problem 23

What class of element is obtained by oxidation of a mineral? What class of element is obtained by reduction of a mineral?

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Problem 24

Which set of elements gives each of the following alloys:
(a) brass;
(b) stainless steel;
(c) bronze;
(d) sterling silver?

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Problem 25

How are each of the following involved in iron metallurgy: (a) slag; (b) pig iron; (c) steel; (d) basic-oxygen process?

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Problem 26

What are the distinguishing features of each extraction process: pyrometallurgy, electrometallurgy, and hydrometallurgy? Explain briefly how the types of metallurgy are used in the production of (a) Fe; (b) Na; (c) Au; (d) Al.

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Problem 27

What property allows copper to be purified in the presence of iron and nickel impurities? Explain

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Problem 28

Why is cryolite used in the electrolysis of aluminum oxide?

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Problem 29

(a) What is a kinetic isotope effect?
(b) Do compounds of hydrogen exhibit a relatively large or small kinetic isotope effect? Explain.
(c) Carbon compounds also exhibit a kinetic isotope effect. How do you expect it to compare in magnitude with that for hydrogen compounds? Why?

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Problem 30

How is Le Châtelier’s principle involved in the production of elemental potassium?

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Problem 31

Elemental Li and Na are prepared by electrolysis of a molten salt, whereas $\mathrm{K}$ , Rb, and $\mathrm{Cs}$ are prepared by chemical reduction. (a) In general terms, explain why the alkali metals cannot be prepared by electrolysis of their aqueous salt solutions. (b) Use ionization energies (see the Family Portraits, pp. 575 and 578 ) to explain why calcium should not be able to isolate Rb from molten $\operatorname{Rb} X(X=\text { halide). }$ (c) Use physical properties to explain why calcium is used to
isolate Rb from molten RbX. (d) Can Ca be used to isolate Cs from molten $\mathrm{Cs} \mathrm{X}$ ? Explain.

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Problem 32

A Downs cell operating at 77.0 A produces 31.0 $\mathrm{kg}$ of $\mathrm{Na}$
(a) What volume of $\mathrm{Cl}_{2}(g)$ is produced at 1.0 atm and $540 .^{\circ} \mathrm{C}$ ?
(b) How many coulombs were passed through the cell?
(c) How long did the cell operate?

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Problem 33

(a) In the industrial production of iron, what is the reducing substance loaded into the blast furnace?
(b) In addition to furnishing the reducing power, what other function does this substance serve?
(c) What is the formula of the active reducting agent in the process?
(d) Write equations for the stepwise reduction of $\mathrm{Fe}_{2} \mathrm{O}_{3}$ to iron in
the furnace.

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Problem 34

One of the substances loaded into a blast furnace is limestone, which produces lime in the furnace.
(a) Give the chemical equation for the reaction forming lime.
(b) Explain the purpose of lime in the furnace. The term flux is
often used as a label for a substance acting as the lime does. What
is the derivation of this word, and how does it relate to the function of the lime?
(c) Write a chemical equation describing the action of lime flux

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Problem 35

The last step in the Dow process for the production of magnesium metal involves electrolysis of molten MgCl.
(a) Why isn't the electrolysis carried out with aqueous $\mathrm{MgCl}_{2} ?$ What are the products of this aqueous electrolysis?
(b) Do the high temperatures required to melt $\mathrm{MgCl}_{2}$ favor products or reactants? (Hint: Consider the $\Delta H_{\mathrm{f}}^{\circ}$ of $\mathrm{MgCl}_{2^{*}} )$

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Problem 36

Iodine is the only halogen that occurs in a positive oxidation state, in NalO, impurities within Chile saltpeter, NaNO,
(a) Is this mode of occurrence consistent with iodine's location in the periodic table? Explain.
(b) In the production of $\mathrm{I}, \mathrm{IO}_{3}^{-}$ reacts with $\mathrm{HSO}_{3}^{-} :$
(c) If 0.78 mol $\%$ of an NaNO $_{3}$ deposit is $\mathrm{NaIO}_{3},$ how much $\mathrm{I}_{2}$ (in g) can be obtained from 1.000 ton ( $2000 .$ lb) of the deposit?

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Problem 37

Selenium is prepared by the reaction of H2SeO3 with gaseous SO2.
(a) What redox process does the sulfur dioxide undergo? What is the oxidation state of sulfur in the product?
(b) Given that the reaction occurs in acidic aqueous solution, what is the formula of the sulfur-containing species?
(c) Write the balanced redox equation for the process.

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Problem 38

$\mathrm{F}_{2}$ and $\mathrm{Cl}_{2}$ are produced by electrolytic oxidation, whereas $\mathrm{Br}_{2}$ and $\mathrm{I}_{2}$ are produced by chemical oxidation of the halide ions in a concentrated aqueous solution (brine) by a more electronegative halogen. Give two reasons why $\mathrm{Cl}_{2}$ isn't prepared this way.

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Problem 39

Silicon is prepared by the reduction of $\mathrm{K}_{2} \mathrm{SiF}_{6}$ with Al. Write the equation for this reaction. (Hint: Can $\mathrm{F}^{-}$ be oxidized in this reaction? Can $\mathrm{K}^{+}$ be reduced?)

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Problem 40

What is the mass percent of iron in each of the following iron ores: $\mathrm{Fe}_{2} \mathrm{O}_{3}, \mathrm{Fe}_{3} \mathrm{O}_{4}, \mathrm{FeS}_{2} ?$

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Problem 41

Phosphorus is one of the impurities present in pig iron that is removed in the basic-oxygen process. Assuming that phosphorus is present as P atoms, write equations for its oxidation and
subsequent reaction in the basic slag.

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Problem 41

Among the exothermic steps in the manufacture of sulfuric acid is the process of hydrating $\mathrm{SO}_{3}$ . (a) Write two chemical reactions that show this process. (b) Why is the direct reaction of $\mathrm{SO}_{3}$ with water not feasible?

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Problem 42

The final step in the smelting of FeCuS, is
$$
\mathrm{Cu}_{2} \mathrm{S}(s)+2 \mathrm{Cu}_{2} \mathrm{O}(s) \longrightarrow 6 \mathrm{Cu}(l)+\mathrm{SO}_{2}(g)
$$
(a) Give the oxidation states of copper in $\mathrm{Cu}_{2} \mathrm{S}, \mathrm{Cu}_{2} \mathrm{O},$ and $\mathrm{Cu}$ .
(b) What are the oxidizing and reducing agents in this reaction?

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Problem 43

Use equations to show how acid-base properties are used to separate $\mathrm{Fe}_{2} \mathrm{O}_{3}$ and $\mathrm{Ti} \mathrm{O}_{2}$ from $\mathrm{Al}_{2} \mathrm{O}_{3}$ in the Bayer process.

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Problem 44

A piece of Al with a surface area of 2.5 m2 is anodized to produce a film of Al2O3 that is 23 mm (2331026 m) thick. (a) How many coulombs flow through the cell in this process (assume that
the density of the Al2O3 layer is 3.97 g/cm3)? (b) If it takes 18 min to produce this film, what current must flow through the cell?

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Problem 45

The production of $\mathrm{H}_{2}$ gas by the electrolysis of water typically requires about 400 $\mathrm{kJ}$ of energy per mole.
(a) Use the relationship between work and cell potential (Section 21.4$)$ to calculate the minimum work needed to form 1.0 mol of $\mathrm{H}_{2}$ gas at a cell potential of 1.24 $\mathrm{V}$ .
(b) What is the energy efficiency of the cell operation?
(c) Find the cost of producing 500 . mol of $\mathrm{H}_{2}$ if electricity is $\$ 0.06$ per kilowatt-hour ( 1 watt-second $=1$ joule).

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Problem 46

(a) What are the components of the reaction mixture following the water-gas shift reaction? (b) Explain how zeolites are used to purify the H2 formed.

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Problem 47

Metal sulfides are often first converted to oxides by roasting in air and then reduced with carbon to produce the metal. Why aren’t the metal sulfides reduced directly by carbon to yield CS2? Give a thermodynamic analysis of both processes for ZnS.

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Problem 48

Explain in detail why a catalyst is used to produce SO3.

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Problem 49

Among the exothermic steps in the manufacture of sulfuric acid is the process of hydrating $\mathrm{SO}_{3}$ . (a) Write two chemical reactions that show this process. (b) Why is the direct reaction of $\mathrm{SO}_{3}$ with water not feasible?

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Problem 50

Why is commercial $\mathrm{H}_{2} \mathrm{SO}_{4}$ so inexpensive?

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Problem 51

(a) What are the three commercial products formed in the chlor-alkali process?
(b) State an advantage and a disadvantage of the mercury-cell method for this process.

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Problem 52

Consider the reaction of $\mathrm{SO}_{2}$ to form $\mathrm{SO}_{3}$ at standard conditions.
(a) Calculate $\Delta G^{\circ}$ at $25^{\circ} \mathrm{C}$ . Is the reaction spontaneous?
(b) Why is the reaction not performed at $25^{\circ} \mathrm{C} ?$
(c) Is the reaction spontaneous at $500 .^{\circ} \mathrm{C}$ (Assume that $\Delta H^{\circ}$ and
$\Delta S^{\circ}$ are constant with changing $T$ )
(d) Compare $K$ at $500 .$ ' and at $25^{\circ} \mathrm{C}$ .
(e) What is the highest $T$ at which the reaction is spontaneous?

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Problem 53

If a chlor-alkali cell used a current of $3 \times 10^{4} \mathrm{A},$ how many pounds of $\mathrm{Cl}_{2}$ would be produced in a typical 8 -h operating day?

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Problem 54

The products of the chlor-alkali process, Cl2 and NaOH, are kept separated
(a) Why is this necessary when $\mathrm{Cl}_{2}$ is the desired product?
(b) $\mathrm{ClO}^{-}$ or $\mathrm{ClO}_{3}-$ may form by disproportionation of $\mathrm{Cl}_{2}$ in basic solution. What determines which product forms?
(c) What mole ratio of $\mathrm{Cl}_{2}$ to $\mathrm{OH}^{-}$ will produce $\mathrm{ClO}^{-} ? \mathrm{ClO}_{3}^{-} ?$

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Problem 55

The key step in the manufacture of sulfuric acid is the oxidation of sulfur dioxide in the presence of a catalyst, such as $\mathrm{V}_{2} \mathrm{O}_{5}$ . At $727^{\circ} \mathrm{C}, 0.010 \mathrm{mol}$ of $\mathrm{SO}_{2}$ is injected into an empty $2.00-\mathrm{L}$ container $\left(K_{\mathrm{p}}=3.18\right) .$
(a) What is the equilibrium pressure of $\mathrm{O}_{2}$ that is needed to maintain a 1$/ 1$ mole ratio of $\mathrm{SO}_{3}$ to $\mathrm{SO}_{2} ?$
(b) What is the equilibrium pressure of $\mathrm{O}_{2}$ needed to maintain a 95$/ 5$ mole ratio of $\mathrm{SO}_{3}$ to $\mathrm{SO}_{2} ?$

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Problem 56

Tetraphosphorus decoxide $\left(\mathrm{P}_{4} \mathrm{O}_{10}\right)$ is made from phosphate rock and used as a drying agent in the laboratory.
(a) Write a balanced equation for its reaction with water.
(b) What is the pH of a solution formed from the addition of 8.5 $\mathrm{g}$ of $\mathrm{P}_{4} \mathrm{O}_{10}$ in sufficient water to form 0.750 $\mathrm{L} ?$ (See Table 18.5 p. $797,$ for additional information.)

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Problem 57

Heavy water $\left(\mathrm{D}_{2} \mathrm{O}\right)$ is used to make deuterated chemicals.
(a) What major species, aside from the starting compounds, do you expect to find in a solution of $\mathrm{CH}_{3} \mathrm{OH}$ and $\mathrm{D}_{2} \mathrm{O} ?$ (b) Write equations to explain how these various species arise. (Hint: Consider the autoionization of both components.)

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Problem 58

A blast furnace uses $\mathrm{Fe}_{2} \mathrm{O}_{3}$ to produce 8400 . to fe per day.
(a) What mass of $\mathrm{CO}_{2}$ is produced each day?
(b) Compare this amount of $\mathrm{CO}_{2}$ with that produced by 1.0 million automobiles, each burning 5.0 gal of gasoline a day. Assume that gasoline has the formula $\mathrm{C}_{8} \mathrm{H}_{18}$ and a density of 0.74 $\mathrm{g} / \mathrm{mL}$ , and that it bums completely. (Note that U.S. gasoline consumption is over $4 \times 10^{8}$ gal/day.)

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Problem 59

A major use of $C l_{2}$ is in the manufacture of vinyl chloride, the monomer of poly(vinyl chloride). The two-step sequence for formation of vinyl chloride is depicted below.
(a) Write a balanced equation for each step.
(b) Write the overall equation.
(c) What type of organic reaction is shown in step 1$?$
(d) What type of organic reaction is shown in step 2$?$
(e) If each molecule depicted in the initial reaction mixture represents 0.15 mol of substance, what mass (in g) of vinyl chloride forms?

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Problem 60

In the production of magnesium, $\mathrm{Mg}(\mathrm{OH})_{2}$ is precipitated by using
$\mathrm{Ca}(\mathrm{OH})_{2},$ which itself is "insoluble." (a) Use $K_{\mathrm{sp}}$ values to show that $\mathrm{Mg}(\mathrm{OH})_{2}$ can be precipitated from seawater in which $\left[\mathrm{Mg}^{2+}\right]$ is initially 0.052$M .$ (b) If the seawater is saturated with
$\mathrm{Ca}(\mathrm{OH})_{2},$ what fraction of the $\mathrm{Mg}^{2+}$ is precipitated?

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Problem 61

Step 1 of the Ostwald process for nitric acid production is
$$
4 \mathrm{NH}_{3}(g)+5 \mathrm{O}_{2}(g) \stackrel{\mathrm{P}_{\text { lRh catalys }}}{\longrightarrow} 4 \mathrm{NO}(g)+6 \mathrm{H}_{2} \mathrm{O}(g)
$$
An unwanted side reaction for this step is
$$
4 \mathrm{NH}_{3}(g)+3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{N}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(g)
$$
(a) Calculate $K_{p}$ for these two $\mathrm{NH}_{3}$ oxidations at $25^{\circ} \mathrm{C}$ .
(b) Calculate $K_{\mathrm{p}}$ for these two $\mathrm{NH}_{3}$ oxidations at $900 .^{\circ} \mathrm{C} .$
(c) The Pt/Rh catalyst is one of the most efficient in the chemical industry, achieving 96$\%$ yield in 1 millisecond of contact with $850^{\circ} \mathrm{C} ),$ about 175 $\mathrm{mg}$ of $\mathrm{Pt}$ is lost per metric ton $(\mathrm{t})$ of $\mathrm{HNO}_{3} \mathrm{pro}$ -duced. If the annual U.S. production of $\mathrm{HNO}_{3}$ is $1.01 \times 10^{\prime} \mathrm{t}$ and
the market price of $\mathrm{Pt}$ is $\$ 1557 / \mathrm{troy}$ oz, what is the annual cost of the lost $\mathrm{Pt}(1 \mathrm{kg}=32.15 \text { troy oz )? }$

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Problem 62

Several transition metals are prepared by reduction of the metal halide with magnesium. Titanium is prepared by the Kroll method, in which ore (ilmenite) is converted to the gaseous chloride, which is then reduced to Ti metal by molten Mg (see p. 1003 ). Assuming yields of 84$\%$ for step 1 and 93$\%$ for step 2 , and an excess of the other reactants, what mass of Ti metal can be prepared from 21.5 metric tons of ilmenite?

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Problem 63

The production of $\mathrm{S}_{8}$ from the $\mathrm{H}_{2} \mathrm{S}(g)$ found in natural gas deposits occurs through the Claus process (Section $22.5 ) :$
(a) Use these two unbalanced steps to write an overall balanced equation for this process:
$$
\begin{array}{l}{\text { (1) } \mathrm{H}_{2} \mathrm{S}(g)+\mathrm{O}_{2}(g) \rightarrow \mathrm{S}_{8}(g)+\mathrm{SO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)} \\ {\text { (2) } \mathrm{H}_{2} \mathrm{S}(g)+\mathrm{SO}_{2}(g) \longrightarrow \mathrm{S}_{8}(g)+\mathrm{H}_{2} \mathrm{O}(g)}\end{array}
$$
(b) Write the overall reaction with $\mathrm{Cl}_{2}$ as the oxidizing agent instead of $\mathrm{O}_{2}$ . Use thermodynamic data to show whether $\mathrm{Cl}_{2}(g)$ can be used to oxidize $\mathrm{H}_{2} \mathrm{S}(g) .$
(c) Why is oxidation by $\mathrm{O}_{2}$ preferred to oxidation by $\mathrm{Cl}_{2} ?$

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Problem 64

Acid mine drainage (AMD) occurs when geologic deposits containing pyrite $\left(\mathrm{FeS}_{2}\right)$ are exposed to oxygen and moisture. AMD is generated in a multistep process catalyzed by acidophilic (acid-loving) bacteria. Balance each step and identify those that
increase acidity:
$$
\begin{array}{l}{\text { (1) FeS }_{2}(s)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{Fe}^{2+}(a q)+\mathrm{SO}_{4}^{2-}(a q)} \\ {\text { (2) } \mathrm{Fe}^{2+}(a q)+\mathrm{O}_{2}(g) \rightarrow \mathrm{Fe}^{3+}(a q)+\mathrm{H}_{2} \mathrm{O}(l)} \\ {\text { (3) } \mathrm{Fe}^{3+}(a q)+\mathrm{H}_{2} \mathrm{O}(I) \longrightarrow \mathrm{Fe}(\mathrm{OH})_{3}(s)+\mathrm{H}^{+}(a q)} \\ {\text { (4) } \mathrm{FeS}_{2}(s)+\mathrm{Fe}^{3+}(a q) \longrightarrow \mathrm{Fe}^{2+}(a q)+\mathrm{SO}_{4}^{2-}(a q)}\end{array}
$$

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Problem 65

Below $912^{\circ} \mathrm{C},$ pure iron crystallizes in a body-centered cubic structure (ferrite) with $d=7.86 \mathrm{g} / \mathrm{cm}^{3}$ ; from $912^{\circ} \mathrm{C}$ to $1394^{\circ} \mathrm{C},$
it adopts a face-centered cubic structure (austenite) with $d=$ 7.40 $\mathrm{g} / \mathrm{cm}^{3} .$ Both types of iron form interstitial alloys with carbon. The maximum amount of carbon is 0.0218 mass $\%$ in ferrite and 2.08 mass $\%$ in austenite. Calculate the density of each alloy.

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Problem 66

Why isn't nitric acid produced by oxidizing $\mathrm{N}_{2}$ as follows?
$$
\begin{array}{c}{\mathrm{N}_{2}(g)+2 \mathrm{O}_{2}(g) \rightarrow 2 \mathrm{NO}_{2}(g)} \\ {3 \mathrm{NO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow 2 \mathrm{HNO}_{3}(a q)+\mathrm{NO}(g)} \\ {2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \rightarrow 2 \mathrm{NO}_{2}(g)} \\ {3 \mathrm{N}_{2}(g)+6 \mathrm{O}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l) \rightarrow 4 \mathrm{HNO}_{3}(a q)+2 \mathrm{NO}(g)}\end{array}
$$

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Problem 67

Before the development of the Downs cell, the Castner cell was used for the industrial production of Na metal. The Castner cell was based on the electrolysis of molten NaOH.
(a) Write balanced cathode and anode half-reactions for this cell.
(b) A major problem with this cell was that the water produced at one electrode diffused to the other and reacted with the Na. If all the water produced reacted with Na, what would be the maximum efficiency of the Castner cell expressed as moles of Na produced per mole of electrons flowing through the cell?

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Problem 68

When gold ores are leached with CN- solutions, gold forms a complex ion, Au(CN) $_{2}^{-},$ (a) Find $E_{\text { cell }}$ for the oxidation in air $\left(P_{0,}=0.21\right)$ of Au to Aut in basic (ph 13.55$)$ solution with $\left[\mathrm{Au}^{+}\right]=0.50 \mathrm{M}$ . Is the reaction $\mathrm{Au}^{+}(a q)+\mathrm{e}^{-} \longrightarrow \mathrm{Au}(s)$ $E^{\circ}=1.68 \mathrm{V},$ spontaneous? (b) How does formation of the complex ion change $E^{\circ}$ so that the oxidation can be accomplished?

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Problem 69

Nitric oxide occurs in the tropospheric nitrogen cycle, but it destroys ozone in the stratosphere.
(a) Write equations for its reaction with ozone and for the reverse reaction.
(b) Given that the forward and reverse steps are first order in each component, write general rate laws for them.
(c) Calculate $\Delta G^{\circ}$ for this reaction at $280 . \mathrm{K}$ , the average temperature in the stratosphere. (Assume that the $\Delta H^{\circ}$ and $S^{\circ}$ values in Appendix $\mathrm{B}$ do not change with temperature.)
(d) What ratio of rate constants is consistent with $K$ at this temperature?

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Problem 70

A key part of the carbon cycle is the fixation of $\mathrm{CO}_{2}$ by photosynthesis to produce carbohydrates and oxygen gas.
(a) Using the formula $\left(\mathrm{CH}_{2} \mathrm{O}\right)_{n}$ to represent a carbohydrate, write
a balanced equation for the photosynthetic reaction.
(b) If a tree fixes 48 $\mathrm{g}$ of $\mathrm{CO}_{2}$ per day, what volume of $\mathrm{O}_{2}$ gas measured at 1.0 $\mathrm{atm}$ and $78^{\circ} \mathrm{F}$ does the tree produce per day?
(c) What volume of air $\left(0.040 \mathrm{mol} \% \mathrm{CO}_{2}\right)$ at the same conditions
contains this amount of $\mathrm{CO}_{2} ?$

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Problem 71

Farmers use ammonium sulfate as a fertilizer. In the soil, nitrifying bacteria oxidize $\mathrm{NH}_{4}+$ to $\mathrm{NO}_{3}^{-},$ a groundwater contaminant that causes methemoglobinemia ( "blue baby" syndrome). The World Health Organization standard for maximum $\left[\mathrm{NO}_{3}-\right]$ in groundwater is 45 $\mathrm{mg} / \mathrm{L}$ . A farmer adds $210 . \mathrm{kg}$ of $\left(\mathrm{NH}_{4}\right)_{2} \mathrm{SO}_{4}$ to a field and 37$\%$ is oxidized to $\mathrm{NO}_{3}$ -. What is the groundwater $\left[\mathrm{NO}_{3}-\right](\text { in } \mathrm{mg} / \mathrm{L})$ if $1000 . \mathrm{m}^{3}$ of the water is contaminated?

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Problem 72

The key reaction (unbalanced) in the manufacture of synthetic cryolite for aluminum electrolysis is
$$
\mathrm{HF}(g)+\mathrm{Al}(\mathrm{OH})_{3}(s)+\mathrm{NaOH}(a q) \rightarrow \mathrm{Na}_{3} \mathrm{AlF}_{6}(a q)+\mathrm{H}_{2} \mathrm{O}(l)
$$
Assuming a 95.6$\%$ yield of dried, crystallized product, what mass (in kg) of cryolite can be obtained from the reaction of 365 $\mathrm{kg}$ of $\mathrm{Al}(\mathrm{OH})_{3}, 1.20 \mathrm{m}^{3}$ of 50.0$\%$ by mass aqueous $\mathrm{NaOH}$ $(d=1.53 \mathrm{g} / \mathrm{mL}),$ and 265 $\mathrm{m}^{3}$ of gaseous $\mathrm{HF}$ at 305 $\mathrm{kPa}$ and $91.5^{\circ} \mathrm{C} ?$ (Assume that the ideal gas law holds.)

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Problem 73

Because of their different molar masses, $\mathrm{H}_{2}$ and $\mathrm{D}_{2}$ effuse at different rates (Section 5.5$)$
(a) If it takes 16.5 min for 0.10 mol of $\mathrm{H}_{2}$ to effuse, how long does it take for 0.10 $\mathrm{mol}$ of $\mathrm{D}_{2}$ to do so in the same apparatus at the same $T$ and $P ?$
(b) How many effusion steps does it take to separate an equimolar mixture of $D_{2}$ and $\mathrm{H}_{2}$ to 99 mol $\%$ purity?

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Problem 74

The disproportionation of $\mathrm{CO}$ to graphite and $\mathrm{CO},$ is thermo dynamically favored but slow.
(a) What does this mean in terms of the magnitudes of the equilibrium constant $(K),$ rate constant $(k),$ and activation energy $\left(E_{2}\right) ?$
(b) Write a balanced equation for the disproportionation of $\mathrm{CO}$ .
(c) Calculate $K_{\mathrm{c}}$ at 298 $\mathrm{K}$ . (d) Calculate $K_{\mathrm{p}}$ at 298 $\mathrm{K}$ .

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Problem 75

The overall cell reaction for aluminum production is
$$
2 \mathrm{Al}_{2} \mathrm{O}_{3}\left(\text { in } \mathrm{Na}_{3} \mathrm{AlF}_{6}\right)+3 \mathrm{C}(\text { graphite }) \rightarrow 4 \mathrm{Al}(I)+3 \mathrm{CO}_{2}(g)
$$
(a) Assuming 100$\%$ efficiency, how many metric tons (t) of $\mathrm{Al}_{2} \mathrm{O}_{3}$ are consumed per metric ton of Al produced?
(b) Assuming 100$\%$ efficiency, how many metric tons of the graphite anode are consumed per metric ton of Al produced?
(c) Actual conditions in an aluminum plant require 1.89 $\mathrm{t}$ of $\mathrm{Al}_{2} \mathrm{O}_{3}$ and 0.45 $\mathrm{t}$ of graphite per metric ton of Al. What is the percent yield of Al with respect to $\mathrm{Al}_{2} \mathrm{O}_{3} ?$
(d) What is the percent yield of Al with respect to graphite?
(e) What volume of $\mathrm{CO}_{2}\left(\text { in } \mathrm{m}^{3}\right)$ is produced per metric ton of Al at operating conditions of $960 .^{\circ} \mathrm{C}$ and exactly 1 $\mathrm{atm} ?$

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Problem 76

World production of chromite $\left(\mathrm{FeCr}_{2} \mathrm{O}_{4}\right),$ the main ore of chromium, was $1.97 \times 10^{7}$ metric tons in 2006 . To isolate chromium, a mixture of chromite and sodium carbonate is heated in air to form sodium chromate, iron(II) oxide, and carbon dioxide. The sodium chromate is dissolved in water, and this solution is acidified with sulfuric acid to produce the less soluble sodium dichromate. The sodium dichromate is filtered out and reduced with carbon to produce chromium(Il) oxide, sodium carbonate, and carbon monoxide. The chromium(Il) oxide is then reduced to chromium with aluminum metal.
(a) Write balanced equations for each step.
(b) What mass of chromium (in kg) could be prepared from the 2006 world production of chromite?

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Problem 77

Like heavy water $\left(\mathrm{D}_{2} \mathrm{O}\right),$ so-called "semi-heavy water" $(\mathrm{HDO})$ undergoes $\mathrm{H} / \mathrm{D}$ exchange. The molecular scenes depict an
initial mixture of $\mathrm{HDO}$ and $\mathrm{H}_{2}$ reaching equlibrium.
(a) Write the balanced equation for the reaction.
(b) Is the value of $K$ greater or less than 1$?$
(c) If each molecule depicted represents $0.10 M,$ calculate $K$ .

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Problem 78

Even though most metal sulfides are sparingly soluble in water, their solubilities differ by several orders of magnitude. This difference is sometimes used to separate the metals by controlling the pH. Use the following data to find the pH at which you can separate 0.10$M \mathrm{Cu}^{2+}$ and $0.10 M \mathrm{Ni}^{2+} :$ Saturated $\mathrm{H}_{2} \mathrm{S}=0.10 \mathrm{M}$
$$
\begin{array}{ll}{K_{\mathrm{al}} \text { of } \mathrm{H}_{2} \mathrm{S}=9 \times 10^{-8}} & {K_{\mathrm{a} 2} \text { of } \mathrm{H}_{2} \mathrm{S}=1 \times 10^{-17}} \\ {K_{\mathrm{sp}} \text { of } \mathrm{NiS}=1.1 \times 10^{-18}} & {K_{\mathrm{sp}} \text { of } \mathrm{CuS}=8 \times 10^{-34}}\end{array}
$$

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Problem 79

Ores with as little as 0.25% by mass of copper are used as sources of the metal
(a) How many kilograms of such an ore would be needed to con- struct another Statue of Liberty, which contains $2.0 \times 10^{5}$ lb of copper?
(b) If the mineral in the ore is chalcopyrite (FeCuS_), what is the mass $\mathscr{Y}$ of chalcopyrite in the ore?

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Problem 80

How does acid rain affect the leaching of phosphate into groundwater from terrestrial phosphate rock? Calculate the solubility of $\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}$ in each of the following:
(a) Pure water, pH 7.0 (Assume that $\mathrm{PO}_{4}^{3-}$ does not react with water.)
(b) Moderately acidic rainwater, pH 4.5 (Hint: Assume that all the phosphate exists in the form that predominates at this pH.)

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Problem 81

The lead(IV) oxide used in car batteries is prepared by coating the electrode plate with $\mathrm{PbO}$ and then oxidizing it to lead dioxide $\left(\mathrm{PbO}_{2}\right) .$ Despite its name, $\mathrm{PbO}_{2}$ has a nonstoichiometric mole ratio of lead to oxygen of about 1$/ 1.98 .$ In fact, the holes in the PbO, crystal structure due to missing $\mathrm{O}$ atoms are responsible for the oxide's conductivity.
(a) What is the mole $\%$ of $\mathrm{O}$ missing from the PbO, structure?
(b) What is the molar mass of the nonstoichiometric compound?

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Problem 82

Chemosynthetic bacteria reduce $\mathrm{CO}_{2}$ by "splitting" $\mathrm{H}_{2} \mathrm{S}(g)$ instead of the $\mathrm{H}_{2} \mathrm{O}(g)$ used by photosynthetic organisms. Com- pare the free energy change for splitting $\mathrm{H}_{2} \mathrm{S}$ with that for splitting $\mathrm{H}_{2} \mathrm{O}$ . Is there an advantage to using $\mathrm{H}_{2} \mathrm{S}$ instead of $\mathrm{H}_{2} \mathrm{O} ?$

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Problem 83

Silver has a face-centered cubic structure with a unit cell edge length of 408.6 pm. Sterling silver is a substitutional alloy that contains 7.5% copper atoms. Assuming the unit cell remains the same, find the density of silver and of sterling silver.

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Problem 84

Earth's mass is estimated to be $5.98 \times 10^{24} \mathrm{kg},$ and titanium represents 0.05$\%$ by mass of this total.
(a) How many moles of Ti are present?
(b) If half of the Ti is found as ilmenite (Fe TiO $_{3} ),$ what mass of ilmenite is present?
(c) If the airline and auto industries use $1.00 \times 10^{5}$ tons of Ti per year, how many years will it take to use up all the Ti $(1 \text { ton }=$ 2000 lb $) ?$

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Problem 85

In $1790,$ Nicolas Leblanc found a way to form $\mathrm{Na}_{2} \mathrm{CO}_{3}$ from NaCl. His process, now obsolete, consisted of three steps:
$$
\begin{array}{c}{2 \mathrm{NaCl}(s)+\mathrm{H}_{2} \mathrm{SO}_{4}(a q) \longrightarrow \mathrm{Na}_{2} \mathrm{SO}_{4}(a q)+2 \mathrm{HCl}(g)} \\ {\mathrm{Na}_{2} \mathrm{SO}_{4}(s)+2 \mathrm{C}(s) \longrightarrow \mathrm{Na}_{2} \mathrm{S}(s)+2 \mathrm{CO}_{2}(g)} \\ {\mathrm{Na}_{2} \mathrm{S}(s)+\mathrm{CaCO}_{3}(s) \rightarrow \mathrm{Na}_{2} \mathrm{CO}_{3}(s)+\mathrm{CaS}(s)}\end{array}
$$
(a) Write a balanced overall equation for the process.
(b) Calculate the $\Delta H_{f}^{\circ}$ of $\mathrm{CaS}$ if $\Delta H_{\mathrm{xa}}^{\circ}$ is 351.8 $\mathrm{kJ} / \mathrm{mol}$ .
(c) Is the overall process spontaneous at standard-state conditions and 298 $\mathrm{K}$ ?
(d) How many grams of $\mathrm{Na}_{2} \mathrm{CO}_{3}$ form from 250. $\mathrm{g}$ of $\mathrm{NaCl}$ if the process is 73$\%$ efficient?

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Problem 86

Limestone $\left(\mathrm{CaCO}_{3}\right)$ is the second most abundant mineral on Earth after $\mathrm{SiO}_{2}$ . For many uses, it is first decomposed thermally to quicklime (CaO). MgO is prepared similarly from $\mathrm{MgCO}_{3}$ .
(a) At what $T$ is each decomposition spontaneous?
(b) Quicklime reacts with $\mathrm{SiO}_{2}$ to form a slag (CaSiO_ ), a byproduct of steelmaking. In 2010 , the total steelmaking capacity of the U.S. steel industry was $2,236,000$ tons per week, but only 84$\%$ of this capacity was utilized. If $50 .$ kg of slag is produced per ton of steel, what mass (in kg) of limestone was used to make slag in 2010$?$

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