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8: Calculation of Empirical Formulas

8: Calculation of Empirical Formulas

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Chapter Review

113. For the reaction N2(g) ϩ 3H2(g) S 2NH3(g), list the

types of bonds that must be broken and the type of

bonds that must form for the chemical reaction to

take place.

114. What does the activation energy for a reaction represent? How is the activation energy related to whether

a collision between molecules is successful?

115. What are the catalysts in living cells called? Why are

these biological catalysts necessary?

116. When a reaction system has reached chemical equilibrium, the concentrations of the reactants and

products no longer change with time. Why does the

amount of product no longer increase, even though

large concentrations of the reactants may still be


117. Ammonia, a very important industrial chemical, is

produced by the direct combination of the elements

under carefully controlled conditions.


N2(g) ϩ 3H2(g) 4

3 2NH3(g)

Suppose, in an experiment, that the reaction mixture is

analyzed after equilibrium is reached and it is found,

at a particular temperature, that [NH3(g)] ϭ 0.34 M,

[H2(g)] ϭ 2.1 ϫ 10Ϫ3 M, and [N2(g)] ϭ 4.9 ϫ 10Ϫ4 M.

Calculate the value of K at this temperature.

118. Write the equilibrium expression for each of the following heterogeneous equilibria.

3 Li2CO3(s) ϩ H2O(g) ϩ CO2(g)

a. 2LiHCO3(s) 4

3 PbO(s) ϩ CO2(g)

b. PbCO3(s) 4

3 2Al2O3(s)

c. 4Al(s) ϩ 3O2(g) 4

119. Suppose a reaction has the equilibrium constant K ϭ

4.5 ϫ 10Ϫ6 at a particular temperature. If an experiment is set up with this reaction, will there be large

relative concentrations of products present at equilibrium? Is this reaction useful as a means of producing the products? How might the reaction be made

more useful?

All even-numbered Questions and Problems have answers in the back of this book and solutions in the Solutions Guide.

C U M U L AT I V E R E V I E W f o r C H A P T E R S


1. How are the Arrhenius and Brønsted–Lowry definitions of acids and bases similar, and how do these definitions differ? Could a substance be an Arrhenius

acid but not a Brønsted–Lowry acid? Could a substance be a Brønsted–Lowry acid but not an Arrhenius acid? Explain.

2. Describe the relationship between a conjugate acid–

base pair in the Brønsted–Lowry model. Write balanced chemical equations showing the following

molecules/ions behaving as Brønsted–Lowry acids in

water: HCl, H2SO4, H3PO4, NH4ϩ. Write balanced

chemical equations showing the following molecules/ions behaving as Brønsted–Lowry bases in water: NH3, HCO3Ϫ, NH2Ϫ, H2PO4Ϫ.

3. Acetic acid is a weak acid in water. What does this indicate about the affinity of the acetate ion for protons

compared to the affinity of water molecules for protons? If a solution of sodium acetate is dissolved in

water, the solution is basic. Explain. Write equilibrium reaction equations for the ionization of acetic

acid in water and for the reaction of the acetate ion

with water in a solution of sodium acetate.

4. How is the strength of an acid related to the position of

its ionization equilibrium? Write the equations for the

dissociation (ionization) of HCl, HNO3, and HClO4 in

water. Since all these acids are strong acids, what does

this indicate about the basicity of the ClϪ, NO3Ϫ, and

ClO4Ϫ ions? Are aqueous solutions of NaCl, NaNO3, or

NaClO4 basic?

5. Explain how water is an amphoteric substance. Write

the chemical equation for the autoionization of water. Write the expression for the equilibrium constant, Kw, for this reaction. What values does Kw have

at 25 ЊC? What are [Hϩ] and [OHϪ] in pure water at

25 ЊC? How does [Hϩ] compare to [OHϪ] in an acidic

solution? How does [Hϩ] compare to [OHϪ] in a basic


6. How is the pH scale defined? What range of pH values corresponds to acidic solutions? What range corresponds to basic solutions? Why is pH ϭ 7.00 considered neutral? When the pH of a solution changes

by one unit, by what factor does the hydrogen ion

concentration change in the solution? How is pOH

defined? How are pH and pOH for a given solution related? Explain.

7. Describe a buffered solution. Give three examples of

buffered solutions. For each of your examples, write

equations and explain how the components of the

buffered solution consume added strong acids or

bases. Why is buffering of solutions in biological systems so important?

8. Explain the collision model for chemical reactions.

What “collides”? Do all collisions result in the breaking of bonds and formation of products? Why? How



does the collision model explain why higher concentrations and higher temperatures tend to make reactions occur faster?

9. Sketch a graph for the progress of a reaction illustrating the activation energy for the reaction. Define “activation energy.” Explain how an increase in temperature for a reaction affects the number of collisions

that possess an energy greater than Ea. Does an increase in temperature change Ea? How does a catalyst

speed up a reaction? Does a catalyst change Ea for the


10. Explain what it means that a reaction “has reached a

state of chemical equilibrium.” Explain why equilibrium is a dynamic state: Does a reaction really “stop”

when the system reaches a state of equilibrium? Explain why, once a chemical system has reached equilibrium, the concentrations of all reactants remain

constant with time. Why does this constancy of concentration not contradict our picture of equilibrium

as being dynamic? What happens to the rates of the

forward and reverse reactions as a system proceeds to

equilibrium from a starting point where only reactants are present?

11. Describe how we write the equilibrium expression for

a reaction. Give three examples of balanced chemical

equations and the corresponding expressions for

their equilibrium constants.

12. Although the equilibrium constant for a given reaction always has the same value at the same temperature, the actual concentrations present at equilibrium

may differ from one experiment to another. Explain.

What do we mean by an equilibrium position? Is the

equilibrium position always the same for a reaction,

regardless of the amounts of reactants taken?

13. Compare homogeneous and heterogeneous equilibria.

Give a balanced chemical equation and write the corresponding equilibrium constant expression as an example of each of these cases. How does the fact that

an equilibrium is heterogeneous influence the expression we write for the equilibrium constant for the


14. In your own words, paraphrase Le Châtelier’s principle. Give an example (including a balanced chemical

equation) of how each of the following changes can

affect the position of equilibrium in favor of additional products for a system: the concentration of

one of the reactants is increased; one of the products

is selectively removed from the system; the reaction

system is compressed to a smaller volume; the temperature is increased for an endothermic reaction; the

temperature is decreased for an exothermic process.

15. Explain how dissolving a slightly soluble salt to form a

saturated solution is an equilibrium process. Give three

balanced chemical equations for solubility processes

and write the expressions for Ksp corresponding to the

Cumulative Review for Chapters 16–17

reactions you have chosen. When writing expressions

for Ksp, why is the concentration of the sparingly soluble salt itself not included in the expression? Given the

value for the solubility product for a sparingly soluble

salt, explain how the molar solubility, and the solubility in g/L, may be calculated.


16. Choose 10 species that might be expected to behave

as Brønsted–Lowry acids or bases in aqueous solution. For each of your choices, (a) write an equation

demonstrating how the species behaves as an acid or

base in water, and (b) write the formula of the conjugate base or acid for each of the species you have


17. a. Write the conjugate base for each of the following

Brønsted–Lowry acids.


HNO3, H2SO4, HClO4, NH4 , H2CO3

b. Write the conjugate acid for each of the following

Brønsted–Lowry bases.

ClϪ, HSO4Ϫ, NH2Ϫ, NH3, CO32Ϫ

18. Identify the Brønsted–Lowry conjugate acid–base

pairs in each of the following.






NH3(aq) ϩ H2O(l) 4

3 NH4ϩ(aq) ϩ OHϪ(aq)

H2SO4(aq) ϩ H2O(l) 4

3 HSO4Ϫ(aq) ϩ H3Oϩ(aq)

O2Ϫ(s) ϩ H2O(l) 4

3 2OHϪ(aq)

NH2Ϫ(aq) ϩ H2O(l) 4

3 NH3(aq) ϩ OHϪ(aq)



H2PO4 (aq) ϩ OH (aq) 4

3 HPO42Ϫ(aq) ϩ H2O(l)

19. For each of the following, calculate the indicated








[OHϪ] ϭ 2.11 ϫ 10Ϫ4 M, [Hϩ] ϭ ?

[OHϪ] ϭ 7.34 ϫ 10Ϫ6 M, pH ϭ ?

[OHϪ] ϭ 9.81 ϫ 10Ϫ8 M, pOH ϭ ?

pH ϭ 9.32, pOH ϭ ?

[Hϩ] ϭ 5.87 ϫ 10Ϫ11 M, pH ϭ ?

pH ϭ 5.83, [Hϩ] ϭ ?


20. Calculate the pH and pOH values for each of the following solutions.





0.00141 M HNO3

2.13 ϫ 10Ϫ3 M NaOH

0.00515 M HCl

5.65 ϫ 10Ϫ5 M Ca(OH)2

21. Write the equilibrium constant expression for each of

the following reactions.






4NO( g) 4

3 2N2O(g) ϩ O2(g)

4PF3(g) 4

3 P4(s) ϩ 6F2(g)

CO(g) ϩ 3H2(g) 4

3 CH4(g) ϩ H2O(g)

2BrF5(g) 4

3 Br2(g) ϩ 5F2(g)

S(s) ϩ 2HCl(g) 4

3 H2S(g) ϩ Cl2(g)

22. Suppose that for the following reaction

3 2BrCl(g)

Br2(g) ϩ Cl2(g) 4

it is determined that, at a particular temperature, the

equilibrium concentrations are as follows: [Br2(g)] ϭ

7.2 ϫ 10Ϫ8 M, [Cl2(g)] ϭ 4.3 ϫ 10ϫ6 M, [BrCl( g)] ϭ

4.9 ϫ 10Ϫ4 M. Calculate the value of K for the reaction

at this temperature.

23. Write expressions for Ksp for each of the following

sparingly soluble substances.













24. The solubility product of magnesium carbonate,

MgCO3, has the value Ksp ϭ 6.82 ϫ 10Ϫ6 at 25 ЊC. How

many grams of MgCO3 will dissolve in 1.00 L of water?


18.1 Oxidation–Reduction


18.2 Oxidation States

18.3 Oxidation–Reduction

Reactions Between


18.4 Balancing Oxidation–

Reduction Reactions by

the Half-Reaction Method

18.5 Electrochemistry: An


18.6 Batteries

18.7 Corrosion

18.8 Electrolysis


Reactions and


Workers in China apply paint to a wall

to prevent rust. (China Daily Information


18.1 Oxidation–Reduction Reactions


hat do a forest fire, rusting steel, combustion in an automobile engine, and the metabolism of food in a human body have in common? All

of these important processes involve oxidation–reduction reactions. In

fact, virtually all of the processes that provide energy to heat buildings,

power vehicles, and allow people to work and play depend on oxidation–

reduction reactions. And every

time you start your car, turn on

your calculator, look at your digital watch, or listen to a radio at

the beach, you are depending on

an oxidation–reduction reaction

to power the battery in each of

these devices. In addition, batterypowered cars have become more

common on U.S. roads. This will

lead to increased reliance of our

society on batteries and will spur

the search for new, more efficient


In this chapter we will explore the properties of oxidation–

reduction reactions, and we will The power generated by an alkaline AA

battery, a lithium battery, and a mercury

see how these reactions are used battery results from oxidation–reduction


to power batteries.

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18.1 Oxidation–Reduction Reactions


To learn about metal–nonmetal oxidation–reduction reactions.

In Section 7.5 we discussed the chemical reactions between metals and nonmetals. For example, sodium chloride is formed by the reaction of elemental

sodium and chlorine.

2Na(s) ϩ Cl2(g) S 2NaCl(s)

Because elemental sodium and chlorine contain uncharged atoms and

because sodium chloride is known to contain Naϩ and ClϪ ions, this reaction

must involve a transfer of electrons from sodium atoms to chlorine atoms.

2Na ϩ Cl2









Some students use the

mnemonic OIL RIG:

Oxidation Is Loss;

Reduction Is Gain.

Reactions like this one, in which one or more electrons are transferred, are

called oxidation–reduction reactions, or redox reactions. Oxidation is defined as a loss of electrons. Reduction is defined as a gain of electrons. In the reaction of elemental sodium and chlorine, each sodium atom

loses one electron, forming a 1ϩ ion. Therefore, sodium is oxidized. Each

584 Chapter 18 Oxidation–Reduction Reactions and Electrochemistry

chlorine atom gains one electron, forming a negative chloride ion, and is

thus reduced. Whenever a metal reacts with a nonmetal to form an ionic

compound, electrons are transferred from the metal to the nonmetal. So

these reactions are always oxidation–reduction reactions where the metal is

oxidized (loses electrons) and the nonmetal is reduced (gains electrons).


Identifying Oxidation and Reduction in a Reaction

In the following reactions, identify which element is oxidized and which element is reduced.

a. 2Mg(s) ϩ O2(g) S 2MgO(s)

b. 2Al(s) ϩ 3I2(s) S 2AlI3(s)


© Cengage Learning

a. We have learned that Group 2 metals form 2ϩ cations and that

Group 6 nonmetals form 2Ϫ anions, so we can predict that

magnesium oxide contains Mg2ϩ and O2Ϫ ions. This means that in

the reaction given, each Mg loses two electrons to form Mg2ϩ and so

is oxidized. Also each O gains two electrons to form O2Ϫ and so is


Magnesium burns in air to give a

bright, white flame.

b. Aluminum iodide contains the Al3ϩ and IϪ ions. Thus aluminum

atoms lose electrons (are oxidized). Iodine atoms gain electrons (are


Self-Check EXERCISE 18.1 For the following reactions, identify the element oxidized and the element


a. 2Cu(s) ϩ O2(g) S 2CuO(s)

b. 2Cs(s) ϩ F2(g) S 2CsF(s)

See Problems 18.3 through 18.6. ■

Although we can identify reactions between metals and nonmetals as

redox reactions, it is more difficult to decide whether a given reaction between nonmetals is a redox reaction. In fact, many of the most significant

redox reactions involve only nonmetals. For example, combustion reactions

such as methane burning in oxygen,

CH4(g) ϩ 2O2(g) S CO2(g) ϩ 2H2O(g) ϩ energy

are oxidation–reduction reactions. Even though none of the reactants or

products in this reaction is ionic, the reaction does involve a transfer of electrons from carbon to oxygen. To explain this, we must introduce the concept

of oxidation states.

18.2 Oxidation States


To learn how to assign oxidation states.

The concept of oxidation states (sometimes called oxidation numbers) lets

us keep track of electrons in oxidation–reduction reactions by assigning

charges to the various atoms in a compound. Sometimes these charges are

18.2 Oxidation States


quite apparent. For example, in a binary ionic compound the ions have easily identified charges: in sodium chloride, sodium is ϩ1 and chlorine is Ϫ1;

in magnesium oxide, magnesium is ϩ2 and oxygen is Ϫ2; and so on. In

such binary ionic compounds the oxidation states are simply the charges of

the ions.






Oxidation State





In an uncombined element, all of the atoms are uncharged (neutral).

For example, sodium metal contains neutral sodium atoms, and chlorine gas

is made up of Cl2 molecules, each of which contains two neutral chlorine

atoms. Therefore, an atom in a pure element has no charge and is assigned

an oxidation state of zero.

In a covalent compound such as water, although no ions are actually

present, chemists find it useful to assign imaginary charges to the elements

in the compound. The oxidation states of the elements in these compounds

are equal to the imaginary charges we determine by assuming that the most

electronegative atom (see Section 12.2) in a bond controls or possesses both

of the shared electrons. For example, in the OOH bonds in water, it is assumed for purposes of assigning oxidation states that the much more electronegative oxygen atom controls both of the shared electrons in each bond.

This gives the oxygen eight valence electrons.


















In effect, we say that each hydrogen has lost its single electron to the oxygen. This gives each hydrogen an oxidation state of ϩ1 and the oxygen an

oxidation state of Ϫ2 (the oxygen atom has formally gained two electrons).

In virtually all covalent compounds, oxygen is assigned an oxidation state of

Ϫ2 and hydrogen is assigned an oxidation state of ϩ1.

Because fluorine is so electronegative, it is always assumed to control

any shared electrons. So fluorine is always assumed to have a complete octet

of electrons and is assigned an oxidation state of Ϫ1. That is, for purposes of

assigning oxidation states, fluorine is always imagined to be FϪ in its covalent compounds.

The most electronegative elements are F, O, N, and Cl. In general, we

give each of these elements an oxidation state equal to its charge as an anion (fluorine is Ϫ1, chlorine is Ϫ1, oxygen is Ϫ2, and nitrogen is Ϫ3). When

two of these elements are found in the same compound, we assign them in

order of electronegativity, starting with the element that has the largest electronegativity.

F Ͼ O Ͼ N Ͼ Cl





For example, in the compound NO2, because oxygen has a greater electronegativity than nitrogen, we assign each oxygen an oxidation state of Ϫ2.

This gives a total “charge” of Ϫ4 (2 ϫ Ϫ2) on the two oxygen atoms. Because

the NO2 molecule has zero overall charge, the N must be ϩ4 to exactly balance the Ϫ4 on the oxygens. In NO2, then, the oxidation state of each oxygen is Ϫ2 and the oxidation state of the nitrogen is ϩ4.

586 Chapter 18 Oxidation–Reduction Reactions and Electrochemistry

The rules for assigning oxidation states are given below and are illustrated in Table 18.1. Application of these rules allows us to assign oxidation

states in most compounds. The principles are illustrated by Example 18.2.

Rules for Assigning Oxidation States

1. The oxidation state of an atom in an uncombined element is 0.

2. The oxidation state of a monatomic ion is the same as its charge.

3. Oxygen is assigned an oxidation state of Ϫ2 in most of its covalent

compounds. Important exception: peroxides (compounds containing the

O22Ϫ group), in which each oxygen is assigned an oxidation state of Ϫ1.

4. In its covalent compounds with nonmetals, hydrogen is assigned an

oxidation state of ϩ1.

5. In binary compounds, the element with the greater electronegativity is

assigned a negative oxidation state equal to its charge as an anion in its

ionic compounds.

6. For an electrically neutral compound, the sum of the oxidation states must

be zero.

7. For an ionic species, the sum of the oxidation states must equal the

overall charge.

Table 18.1 Examples of Oxidation States


© Cengage Learning


sodium metal, Na

Na, 0

rule 1

phosphorus, P

P, 0

rule 1

sodium fluoride, NaF

Na, ϩ1

F, Ϫ1

rule 2

rule 2

magnesium sulfide, MgS

Mg, ϩ2

S, Ϫ2

rule 2

rule 2

carbon monoxide, CO

C, ϩ2

O, Ϫ2

rule 3

sulfur dioxide, SO2

S, ϩ4

O, Ϫ2

rule 3

H, ϩ1

O, Ϫ1

rule 3 (exception)

ammonia, NH3

H, ϩ1

N, Ϫ3

rule 4

rule 5

hydrogen sulfide, H2S

H, ϩ1

S, Ϫ2

rule 4

rule 5

hydrogen iodide, HI

H, ϩ1

I, Ϫ1

rule 4

rule 5

sodium carbonate,


Na, ϩ1

O, Ϫ2

C, ϩ4

rule 2

rule 3

For CO32Ϫ, the sum of the

oxidation states is

ϩ4 ϩ 3(Ϫ2) ϭ Ϫ2.

rule 7

ammonium chloride,


N, Ϫ3

H, ϩ1

rule 5

rule 4

For NH4ϩ, the sum of the

oxidation states is

Ϫ3 ϩ 4(ϩ1) ϭ ϩ1.

rule 7

rule 2

hydrogen peroxide, H2O2

Hydrogen peroxide can be used

to disinfect a wound.

Oxidation States

Cl, Ϫ1

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