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4: Learning to Solve Problems

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17.7 Le Châtelier’s Principle

EXAMPLE 17.6

565

Using Le Châtelier’s Principle: Changes in Temperature

For each of the following reactions, predict how the equilibrium will shift as

the temperature is increased.

a. N2(g) ϩ O2(g) 4

3 2NO( g) (endothermic)

SOLUTION a

This is an endothermic reaction, so energy can be viewed as a reactant.

N2(g) ϩ O2(g) ϩ energy 4

3 2NO(g)

Thus the equilibrium will shift to the right as the temperature is increased

b. 2SO2(g) ϩ O2(g) 4

3 2SO3(g) (exothermic)

SOLUTION b

This is an exothermic reaction, so energy can be regarded as a product.

2SO2(g) ϩ O2(g) 4

3 2SO3(g) ϩ energy

As the temperature is increased, the equilibrium will shift to the left.

Self-Check EXERCISE 17.5 For the exothermic reaction

2SO2(g) ϩ O2(g) 4

3 2SO3(g)

predict the equilibrium shift caused by each of the following changes.

a. SO2 is added.

b. SO3 is removed.

c. The volume is decreased.

d. The temperature is decreased.

See Problems 17.33 through 17.42. ■

We have seen how Le Châtelier’s principle can be used to predict the effects of several types of changes on a system at equilibrium. To summarize

these ideas, Table 17.2 shows how various changes affect the equilibrium position of the endothermic reaction N2O4(g) 4

3 2NO2(g). The effect of a temperature change on this system is depicted in Figure 17.12.

Table 17.2 Shifts in the Equilibrium Position for

3 2NO2(g)

the Reaction N2O4(g) ؉ Energy 4

right

left

removal of N2O4(g)

left

removal of NO2(g)

right

decrease in container volume

left

increase in container volume

right

increase in temperature

right

decrease in temperature

left

566 Chapter 17 Equilibrium

Figure 17.12

a

Shifting the N2O4(g) 4

3 2NO2(g)

equilibrium by changing the

temperature.

b

At 100 °C the flask is definitely

reddish-brown due to a large

amount of NO2 present.

At 0 °C the equilibrium is shifted

toward colorless N2O4(g).

17.8 Applications Involving the

Equilibrium Constant

OBJECTIVE:

To learn to calculate equilibrium concentrations from equilibrium constants.

Knowing the value of the equilibrium constant for a reaction allows us to do

many things. For example, the size of K tells us the inherent tendency of the

reaction to occur. A value of K much larger than 1 means that at equilibrium,

the reaction system will consist of mostly products—the equilibrium lies to

the right. For example, consider a general reaction of the type

A(g) S B(g)

where

[B]

[A]

If K for this reaction is 10,000 (104), then at equilibrium,

[B]

ϭ 10,000

[A]

or

[B]

10,000

ϭ

[A]

1

That is, at equilibrium [B] is 10,000 times greater than [A]. This means that the

reaction strongly favors the product B. Another way of saying this is that the

reaction goes essentially to completion. That is, virtually all of A becomes B.

On the other hand, a small value of K means that the system at equilibrium consists largely of reactants—the equilibrium position is far to the

left. The given reaction does not occur to any significant extent.

Another way we use the equilibrium constant is to calculate the equilibrium concentrations of reactants and products. For example, if we know

the value of K and the concentrations of all the reactants and products except one, we can calculate the missing concentration. This is illustrated in

Example 17.7.

EXAMPLE 17.7

Calculating Equilibrium Concentration

Using Equilibrium Expressions

Gaseous phosphorus pentachloride decomposes to chlorine gas and gaseous

phosphorus trichloride. In a certain experiment, at a temperature where

17.9 Solubility Equilibria

567

K ϭ 8.96 ϫ 10Ϫ2, the equilibrium concentrations of PCl5 and PCl3 were

found to be 6.70 ϫ 10Ϫ3 M and 0.300 M, respectively. Calculate the concentration of Cl2 present at equilibrium.

SOLUTION

Where Are We Going?

We want to determine [Cl2] present at equilibrium.

What Do We Know?

For this reaction, the balanced equation is

PCl5(g) 4

3 PCl3(g) ϩ Cl2(g)

and the equilibrium expression is

[PCl3][Cl2]

ϭ 8.96 ϫ 10Ϫ2

[PCl5]

We know that

[PCl5] ϭ 6.70 ϫ 10Ϫ3 M

[PCl3] ϭ 0.300 M

How Do We Get There?

We want to calculate [Cl2]. We will rearrange the equilibrium expression to

solve for the concentration of Cl2. First we divide both sides of the expression

[PCl3][Cl2]

[PCl5]

by [PCl3] to give

[PCl3][Cl2]

[Cl2]

K

ϭ

ϭ

[PCl3]

[PCl3][PCl5]

[PCl5]

Next we multiply both sides by [PCl5].

K[PCl5]

[Cl2][PCl5]

ϭ

ϭ [Cl2]

[PCl3]

[PCl5]

Then we can calculate [Cl2] by substituting the known information.

(6.70 ϫ 10Ϫ3)

[PCl5]

Ϫ2

[Cl2] ϭ K ϫ

ϭ (8.96 ϫ 10 )

[PCl3]

(0.300)

Ϫ3

[Cl2] ϭ 2.00 ϫ 10

The equilibrium concentration of Cl2 is 2.00 ϫ 10Ϫ3 M. ■

17.9 Solubility Equilibria

OBJECTIVE:

To learn to calculate the solubility product of a salt, given its solubility,

and vice versa.

Solubility is a very important phenomenon. Consider the following examples.

• Because sugar and table salt dissolve readily in water, we can flavor

foods easily.

568 Chapter 17 Equilibrium

â Cengage Learning

Because calcium sulfate is less soluble in hot water than in cold

water, it coats tubes in boilers, reducing thermal efficiency.

Toothpastes containing sodium

fluoride, an additive that helps

prevent tooth decay.

• When food lodges between teeth, acids form that dissolve tooth

enamel, which contains the mineral hydroxyapatite, Ca5(PO4)3OH.

Tooth decay can be reduced by adding fluoride to toothpaste.

Fluoride replaces the hydroxide in hydroxyapatite to produce the

corresponding fluorapatite, Ca5(PO4)3F, and calcium fluoride, CaF2,

both of which are less soluble in acids than the original enamel.

• The use of a suspension of barium sulfate improves the clarity of X

rays of the digestive tract. Barium sulfate contains the toxic ion

Ba2ϩ, but its very low solubility makes ingestion of solid BaSO4 safe.

In this section we will consider the equilibria associated with dissolving

solids in water to form aqueous solutions. When a typical ionic solid dissolves in water, it dissociates completely into separate cations and anions.

For example, calcium fluoride dissolves in water as follows:

H2O(l)

Science Photo Library, Photo Researchers, Inc.

CaF2(s) — Ca2ϩ (aq) ϩ 2FϪ(aq)

When the solid salt is first added to the water, no Ca2ϩ and FϪ ions are present. However, as dissolving occurs, the concentrations of Ca2ϩ and FϪ increase, and it becomes more and more likely that these ions will collide and

re-form the solid. Thus two opposite (competing) processes are occurring—

the dissolving reaction shown above and the reverse reaction to re-form the

solid:

Ca2ϩ (aq) ϩ 2FϪ(aq) S CaF2(s)

This X ray of the large intestine

has been enhanced by the

patient’s consumption of barium

sulfate.

Ultimately, equilibrium is reached. No more solid dissolves and the solution

is said to be saturated.

We can write an equilibrium expression for this process according to

the law of chemical equilibrium.

Ksp ϭ [Ca2ϩ ][F Ϫ]2

Pure liquids and pure solids are

never included in an equilibrium

expression.

EXAMPLE 17.8

where [Ca2ϩ] and [FϪ] are expressed in mol/L. The constant Ksp is called the

solubility product constant, or simply the solubility product.

Because CaF2 is a pure solid, it is not included in the equilibrium expression. It may seem strange at first that the amount of excess solid present

does not affect the position of the solubility equilibrium. Surely more solid

means more surface area exposed to the solvent, which would seem to result

in greater solubility. This is not the case, however, because both dissolving

and re-forming of the solid occur at the surface of the excess solid. When a

solid dissolves, it is the ions at the surface that go into solution. And when

the ions in solution re-form the solid, they do so on the surface of the solid.

So doubling the surface area of the solid doubles not only the rate of dissolving but also the rate of re-formation of the solid. The amount of excess

solid present therefore has no effect on the equilibrium position. Similarly,

although either increasing the surface area by grinding up the solid or stirring the solution speeds up the attainment of equilibrium, neither procedure

changes the amount of solid dissolved at equilibrium.

Writing Solubility Product Expressions

Write the balanced equation describing the reaction for dissolving each of

the following solids in water. Also write the Ksp expression for each solid.

a. PbCl2(s)

b. Ag2CrO4(s)

c. Bi2S3(s)

17.9 Solubility Equilibria

569

SOLUTION

a. PbCl2(s) 4

3 Pb2ϩ(aq) ϩ 2ClϪ(aq); Ksp ϭ [Pb2ϩ][ClϪ]2

b. Ag2CrO4(s) 4

3 2Agϩ(aq) ϩ CrO42Ϫ(aq); Ksp ϭ [Agϩ]2[CrO42Ϫ]

c. Bi2S3(s) 4

3 2Bi3ϩ(aq) ϩ 3S2Ϫ(aq); Ksp ϭ [Bi3ϩ]2[S2Ϫ]3

Self-Check EXERCISE 17.6 Write the balanced equation for the reaction describing the dissolving of

each of the following solids in water. Also write the Ksp expression for each

solid.

a. BaSO4(s)

b. Fe(OH)3(s)

c. Ag3PO4(s)

See Problems 17.57 and 17.58. ■

EXAMPLE 17.9

Calculating Solubility Products

Copper(I) bromide, CuBr, has a measured solubility of 2.0 ϫ 10Ϫ4 mol/L at

25 °C. That is, when excess CuBr(s) is placed in 1.0 L of water, we can determine that 2.0 ϫ 10Ϫ4 mole of the solid dissolves to produce a saturated solution. Calculate the solid’s Ksp value.

SOLUTION

Where Are We Going?

We want to determine the Ksp value for solid CuBr at 25 °C.

What Do We Know?

• The solubility of CuBr at 25 °C is 2.0 ϫ 10Ϫ4 M.

• CuBr(s) 4

3 Cuϩ(aq) ϩ BrϪ(aq)

• Ksp ϭ [Cuϩ][BrϪ]

How Do We Get There?

We can calculate the value of Ksp if we know [Cuϩ] and [BrϪ], the equilibrium

concentrations of the ions. We know that the measured solubility of CuBr is

2.0 ϫ 10Ϫ4 mol/L. This means that 2.0 ϫ 10Ϫ4 mole of solid CuBr dissolves

per 1.0 L of solution to come to equilibrium. The reaction is

CuBr(s) S Cu ϩ (aq) ϩ Br Ϫ (aq)

so

2.0 ϫ 10 Ϫ4 mol/L CuBr(s) S

2.0 ϫ 10 Ϫ4 mol/L Cu ϩ (aq) ϩ 2.0 ϫ 10 Ϫ4 mol/L Br Ϫ (aq)

We can now write the equilibrium concentrations

[Cu ϩ ] ϭ 2.0 ϫ 10 Ϫ4 mol/L

and

[Br Ϫ ] ϭ 2.0 ϫ 10 Ϫ4 mol/L

These equilibrium concentrations allow us to calculate the value of Ksp for

CuBr.

Ksp ϭ [Cu ϩ ][BrϪ] ϭ (2.0 ϫ 10 Ϫ4)(2.0 ϫ 10Ϫ4)

ϭ 4.0 ϫ 10 Ϫ8

The units for Ksp values are omitted.

570 Chapter 17 Equilibrium

Self-Check EXERCISE 17.7 Calculate the Ksp value for barium sulfate, BaSO4, which has a solubility of

3.9 ϫ 10Ϫ5 mol/L at 25 °C.

See Problems 17.59 through 17.62. ■

Solubilities must be expressed

in mol/L in Ksp calculations.

EXAMPLE 17.10

We have seen that the known solubility of an ionic solid can be used to

calculate its Ksp value. The reverse is also possible: the solubility of an ionic

solid can be calculated if its Ksp value is known.

Calculating Solubility from Ksp Values

The Ksp value for solid AgI(s) is 1.5 ϫ 10Ϫ16 at 25 °C. Calculate the solubility

of AgI(s) in water at 25 °C.

SOLUTION

Where Are We Going?

We want to determine the solubility of AgI at 25 °C.

What Do We Know?

• AgI(s) 4

3 Agϩ(aq) ϩ IϪ(aq)

• At 25 °C, Ksp ϭ [Agϩ][ IϪ] ϭ 1.5 ϫ 10Ϫ16

How Do We Get There?

Because we do not know the solubility of this solid, we will assume that x

moles per liter dissolves to reach equilibrium. Therefore,

x

mol

mol Ϫ

mol

AgI(s) S x

Agϩ(aq) ϩ x

I (aq)

L

L

L

and at equilibrium,

mol

L

mol

[IϪ] ϭ x

L

[Agϩ] ϭ x

Substituting these concentrations into the equilibrium expression gives

Ksp ϭ 1.5 ϫ 10 Ϫ16 ϭ [Ag ϩ ][I Ϫ ] ϭ (x)(x) ϭ x2

Thus

x2 ϭ 1.5 ϫ 10Ϫ16

x ϭ 21.5 ϫ 10Ϫ16 ϭ 1.2 ϫ 10Ϫ8 mol/L

The solubility of AgI(s) is 1.2 ϫ 10Ϫ8 mol/L.

Self-Check EXERCISE 17.8 The Ksp value for lead chromate, PbCrO4, is 2.0 ϫ 10Ϫ16 at 25 °C. Calculate its

solubility at 25 °C.

See Problems 17.69 and 17.70. ■

Chapter Review

C H A P T E R

17

REVIEW

F

Key Terms

equilibrium

constant (17.5)

equilibrium

position (17.5)

homogeneous

equilibria (17.6)

heterogeneous

equilibria (17.6)

Le Châtelier’s

principle (17.7)

solubility product

(Ksp) (17.9)

collision model (17.1)

activation energy

(Ea) (17.2)

catalyst (17.2)

enzyme (17.2)

equilibrium (17.3)

chemical

equilibrium (17.3)

law of chemical

equilibrium (17.5)

equilibrium

expression (17.5)

Summary

1. Chemical reactions can be described by the collision

model, which assumes that molecules must collide to

react. In terms of this model, a certain threshold energy, called the activation energy (Ea), must be overcome for a collision to form products.

2. A catalyst is a substance that speeds up a reaction

without being consumed. A catalyst operates by providing a lower-energy pathway for the reaction in

question. Enzymes are biological catalysts.

3. When a chemical reaction is carried out in a closed

vessel, the system achieves chemical equilibrium, the

state where the concentrations of both reactants and

products remain constant over time. Equilibrium is a

highly dynamic state; reactants are converted continually into products, and vice versa, as molecules collide with each other. At equilibrium, the rates of the

forward and reverse reactions are equal.

4. The law of chemical equilibrium is a general description of the equilibrium condition. It states that for a

reaction of the type

aA ϩ bB 4

3 cC ϩ dD

the equilibrium expression is given by

571

[C]c [D]d

[A]a [B]b

where K is the equilibrium constant.

5. For each reaction system at a given temperature,

there is only one value for the equilibrium constant,

but there are an infinite number of possible equilibrium positions. An equilibrium position is defined as

a particular set of equilibrium concentrations that

VP

directs you to the Chemistry in Focus feature in the chapter

indicates visual problems

interactive versions of these problems are assignable in OWL

satisfy the equilibrium expression. A specific equilibrium position depends on the initial concentrations.

The amount of a pure liquid or a pure solid is never

included in the equilibrium expression.

6. Le Châtelier’s principle allows us to predict the effects

of changes in concentration, volume, and temperature on a system at equilibrium. This principle states

that when a change is imposed on a system at equilibrium, the equilibrium position will shift in a direction that tends to compensate for the imposed

change.

7. The principle of equilibrium can also be applied

when an excess of a solid is added to water to form a

saturated solution. The solubility product (Ksp) is an

equilibrium constant defined by the law of chemical

equilibrium. Solubility is an equilibrium position,

and the Ksp value of a solid can be determined by

measuring its solubility. Conversely, the solubility of

a solid can be determined if its Ksp value is known.

Active Learning Questions

These questions are designed to be considered by groups of

students in class. Often these questions work well for introducing a particular topic in class.

1. Consider an equilibrium mixture of four chemicals

(A, B, C, and D, all gases) reacting in a closed flask according to the following equation:

AϩB4

3CϩD

a. You add more A to the flask. How does the concentration of each chemical compare to its original concentration after equilibrium is reestablished? Justify your answer.

b. You have the original set-up at equilibrium, and

add more D to the flask. How does the concentration of each chemical compare to its original concentration after equilibrium is reestablished? Justify your answer.

VP 2. The boxes shown on the following page represent a

set of initial conditions for the reaction:

+

+

K = 25

Draw a quantitative molecular picture that shows

what this system looks like after the reactants are

572 Chapter 17 Equilibrium

mixed in one of the boxes and the system reaches

+

3 2HI, consider two possi3. For the reaction H2 ϩ I2 4

bilities: (a) you add 0.5 mole of each reactant, allow

the system to come to equilibrium, and then add

1 mol H2, and allow the system to reach equilibrium

again, or (b) you add 1.5 mol H2 and 0.5 mol I2 and

allow the system to come to equilibrium. Will the final equilibrium mixture be different for the two procedures? Explain.

4. Given the reaction A ϩ B 4

3 C ϩ D, consider the following situations:

a. You have 1.3 M A and 0.8 M B initially.

b. You have 1.3 M A, 0.8 M B, and 0.2 M C initially.

c. You have 2.0 M A and 0.8 M B initially.

9. What do you suppose happens to the Ksp value of a

solid as the temperature of the solution changes?

Consider both increasing and decreasing temperatures, and explain your answer.

10. Consider an equilibrium mixture consisting of

H2O(g), CO(g), H2(g), and CO2(g) reacting in a closed

vessel according to the equation

H2O(g) ϩ CO(g) 4

3 H2(g) ϩ CO2(g)

a. You add more H2O to the flask. How does the new

equilibrium concentration of each chemical compare to its original equilibrium concentration

after equilibrium is reestablished? Justify your

b. You add more H2 to the flask. How does the concentration of each chemical compare to its original concentration after equilibrium is reestablished? Justify your answer.

11. Equilibrium is microscopically dynamic but macroscopically static. Explain what this means.

12. In Section 17.3 of your text, it is mentioned that equilibrium is reached in a “closed system.” What is

meant by the term “closed system,” and why is it necessary for a system to reach equilibrium? Explain why

equilibrium is not reached in an open system.

7. The value of the equilibrium constant, K, is dependent on which of the following? (There may be more

a.

b.

c.

d.

the initial concentrations of the reactants

the initial concentrations of the products

the temperature of the system

the nature of the reactants and products

Energy

Order the preceding situations in terms of increasing VP 13. Explain why the development

of a vapor pressure above a

equilibrium concentration of D and explain your orliquid in a closed container

der. Give the order in terms of increasing equilibrium

represents an equilibrium.

concentration of B and explain.

What are the opposing

5. Consider the reaction A ϩ B 4

3 C ϩ D. A friend asks

processes? How do we

the following: “I know we have been told that if a

recognize when the sysmixture of A, B, C, and D is in equilibrium and more

tem has reached a state

A is added, more C and D will form. But how can

of equilibrium.

more C and D form if we do not add more B?” What

VP 14. Consider the figure below in answering the following

do you tell your friend?

questions.

6. Consider the following statements: “Consider the reaction A( g) ϩ B(g) 4

3 C(g), for which at equilibrium

[A] ϭ 2 M, [B] ϭ 1 M, and [C] ϭ 4 M. To a 1-L con1

tainer of the system at equilibrium you add 3 moles

of B. A possible equilibrium condition is [A] ϭ 1 M,

[B] ϭ 3 M, and [C] ϭ 6 M, because in both cases, K ϭ

2.” Indicate everything you think is correct in these

2

statements, and everything that is incorrect. Correct

the incorrect statements, and explain.

Products

Reactants

Reaction progress

Explain.

8. You are browsing through the Handbook of Hypothetical Chemistry when you come across a solid that is reported to have a Ksp value of zero in water at 25 °C.

What does this mean?

a. What does a catalyst do to a chemical reaction?

b. Which of the pathways in the figure is the catalyzed reaction pathway? How do you know?

c. What is represented by the double-headed arrow?

Chapter Review

Questions and Problems

17.1 How Chemical Reactions Occur

QUESTIONS

1. For a chemical reaction to take place, some or all

chemical bonds in the reactants must break, and new

chemical bonds must form among the participating

atoms to create the products. Write a simple chemical

equation of your own choice, and list the bonds that

must be broken and the bonds that must form for the

reaction to take place.

2. For the simple reaction

CH4( g) ϩ 4Cl2( g) S CCl4(l ) ϩ 4HCl( g)

list the types of bonds that must be broken and the

types of bonds that must form for the chemical reaction to take place.

17.2 Conditions That Affect Reaction Rates

QUESTIONS

3. How do chemists envision reactions taking place in

terms of the collision model for reactions? Give an example of a simple reaction and how you might envision the reaction’s taking place by means of a collision between the molecules.

4. In Figure 17.3, the height of the reaction hill is indicated as Ea. What does the symbol Ea stand for, and

what does it represent in terms of a chemical reaction?

5. How does a catalyst work to speed up a chemical

reaction?

6. What are enzymes and why are they important?

17.3 The Equilibrium Condition

QUESTIONS

7. How does equilibrium represent the balancing of opposing processes? Give an example of an “equilibrium” encountered in everyday life, showing how the

processes involved oppose each other.

8. How do chemists define a state of chemical equilibrium?

9. When writing a chemical equation for a reaction that

comes to equilibrium, how do we indicate symbolically that the reaction is reversible?

10. How do chemists recognize a system that has reached

a state of chemical equilibrium? When writing chemical equations, how do we indicate reactions that

come to a state of chemical equilibrium?

17.4 Chemical Equilibrium: A Dynamic Condition

QUESTIONS

11. What does it mean to say that a state of chemical or

physical equilibrium is dynamic?

573

12. Figure 17.8 shows a plot of the rates of the forward

and reverse reactions versus the time for the reaction

H2O(g) ϩ CO(g) 4

3 H2(g) ϩ CO2(g). What is the significance of the portion of the plot where the two

curves join together to form a single curve as time

increases?

17.5 The Equilibrium Constant: An Introduction

QUESTIONS

13. In general terms, what does the equilibrium constant

for a reaction represent? What is the algebraic form of

the equilibrium constant for a typical reaction? What

do square brackets indicate when we write an equilibrium constant?

14. There is only one value of the equilibrium constant

for a particular system at a particular temperature,

but there are an infinite number of equilibrium positions. Explain.

PROBLEMS

15. Write the equilibrium expression for each of the following reactions.

a. C2H6(g) ϩ Cl2(g) 4

3 C2H5Cl(s) ϩ HCl(g)

b. 4NH3(g) ϩ 5O2(g) 4

3 4NO( g) ϩ 6H2O(g)

c. PCl5(g) 4

3 PCl3(g) ϩ Cl2(g)

16. Write the equilibrium expression for each of the following reactions.

a. H2(g) ϩ CO2(g) 4

3 H2O(g) ϩ CO(g)

b. 2N2O(g) ϩ O2(g) 4

3 4NO( g)

c. CO(g) ϩ 2H2(g) 4

3 CH3OH(g)

17. Write the equilibrium expression for each of the following reactions.

a. NO2(g) ϩ ClNO(g) 4

3 ClNO2(g) ϩ NO(g)

b. Br2(g) ϩ 5F2(g) 4

3 2BrF5(g)

c. 4NH3(g) ϩ 6NO(g) 4

3 5N2(g) ϩ 6H2O(g)

18. Write the equilibrium expression for each of the following reactions.

a. CO(g) ϩ 2H2(g) 4

3 CH3OH(g)

b. 2NO2(g) 4

3 2NO( g) ϩ O2(g)

c. P4(g) ϩ 6Br2(g) 4

3 4PBr3(g)

19. Suppose that for the reaction

3 PCl3(g) ϩ Cl2(g)

PCl5(g) 4

it is determined, at a particular temperature, that the

equilibrium concentrations are [PCl5(g)] ϭ 0.0711 M,

[PCl3(g)] ϭ 0.0302 M, and [Cl2(g)] ϭ 0.0491 M. Calculate the value of K for the reaction at this temperature.

20. Suppose that for the reaction

3 CO( g) ϩ Cl2(g)

COCl2(g) 4

it is determined, at a particular temperature, that

the equilibrium concentrations are [COCl2( g)] ϭ

0.00103 M, [CO( g)] ϭ 0.0345 M, and [Cl2( g)] ϭ

0.0219 M. Calculate the value of K for the reaction

at this temperature.

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

574 Chapter 17 Equilibrium

21. At high temperatures, elemental nitrogen and oxygen react with each other to form nitrogen monoxide.

3 2NO( g)

N2( g) ϩ O2( g) 4

Suppose the system is analyzed at a particular temperature, and the equilibrium concentrations are found

to be [N2] ϭ 0.041 M, [O2] ϭ 0.0078 M, and [NO] ϭ

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

22. Suppose that for the reaction

2N2O(g) ϩ O2(g) 4

3 4NO( g)

it is determined, at a particular temperature, that the

equilibrium concentrations are [NO(g)] ϭ 0.00341 M,

[N2O(g)] ϭ 0.0293 M, and [O2(g)] ϭ 0.0325 M. Calculate the value of K for the reaction at this temperature.

17.6 Heterogeneous Equilibria

QUESTIONS

23. What is a homogeneous equilibrium system? Give an

example of a homogeneous equilibrium reaction.

What is a heterogeneous equilibrium system? Write

two chemical equations that represent heterogeneous equilibria.

24. Explain why the position of a heterogeneous equilibrium does not depend on the amounts of pure solid

or pure liquid reactants or products present.

PROBLEMS

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

a. P4(s) ϩ 6F2(g) 4

3 4PF3(g)

b. Xe(g) ϩ 2F2(g) 4

3 XeF4(s)

c. 2SiO(s) ϩ 4Cl2(g) 4

3 2SiCl4(l) ϩ O2(g)

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

a. Fe(s) ϩ H2O(g) 4

3 FeO(s) ϩ H2(g)

b. 4Al(s) ϩ 3O2(g) 4

3 2Al2O3(s)

c. CH4(g) ϩ 4Cl2(g) 4

3 CCl4(l) ϩ 4HCl(g)

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

a. C(s) ϩ H2O(g) 4

3 H2(g) ϩ CO(g)

b. H2O(l) 4

3 H2O(g)

c. 4B(s) ϩ 3O2(g) 4

3 2B2O3(s)

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

a. CS2(g) ϩ 3Cl2(g) 4

3 CCl4(l) ϩ S2Cl2(g)

b. Xe(g) ϩ 3F2(g) 4

3 XeF6(s)

c. 4Fe(s) ϩ 3O2(g) 4

3 2Fe2O3(s)

17.7 Le Châtelier’s Principle

QUESTIONS

29. In your own words, describe what Le Châtelier’s principle tells us about how we can change the position

of a reaction system at equilibrium.

30. Consider the reaction

2CO( g) ϩ O2( g) 4

3 2CO2( g)

Suppose the system is already at equilibrium, and

then an additional mole of CO(g) is injected into the

system at constant temperature. Does the amount of

CO2(g) in the system increase or decrease? Does the

value of K for the reaction change?

31. For an equilibrium involving gaseous substances,

what effect, in general terms, is realized when the volume of the system is decreased?

32. What is the effect on the equilibrium position if an

endothermic reaction is carried out at a higher temperature? Does the net amount of product increase or

decrease? Does the value of the equilibrium constant

change if the temperature is increased?

PROBLEMS

33. For the reaction system

C(s) ϩ H2O(g) 4

3 H2(g) ϩ CO(g)

which has already reached a state of equilibrium, predict the effect that each of the following changes will

have on the position of the equilibrium. Tell whether

the equilibrium will shift to the right, will shift to the

left, or will not be affected.

a. The pressure of hydrogen is increased by injecting

an additional mole of hydrogen gas into the reaction vessel.

b. Carbon monoxide gas is removed as it forms by

use of a chemical absorbent or “scrubber.”

c. An additional amount of solid carbon is added to

the reaction vessel.

34. For the reaction system

P4(s) ϩ 6F2(g) 4

3 4PF3(g)

which has already reached a state of equilibrium, predict the effect that each of the following changes will

have on the position of the equilibrium. Tell whether

the equilibrium will shift to the right, will shift to the

left, or will not be affected.

a. Additional fluorine gas is added to the system.

b. Additional phosphorus is added to the system.

c. Additional phosphorus trifluoride is added to the

system.

35. Suppose the reaction system

CH4( g) ϩ 2O2( g) 4

3 CO2( g) ϩ 2H2O(l )

has already reached equilibrium. Predict the effect of

each of the following changes on the position of the

equilibrium. Tell whether the equilibrium will shift

to the right, will shift to the left, or will not be affected.

a. Any liquid water present is removed from the system.

b. CO2 is added to the system by dropping a chunk of

dry ice into the reaction vessel.

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

Chapter Review

c. The reaction is performed in a metal cylinder fitted with a piston, and the piston is compressed to

decrease the total volume of the system.

d. Additional O2(g) is added to the system from a

cylinder of pure O2.

36. Consider the general reaction

2A(g) ϩ B(s) 4

3 C(g) ϩ 3D(g)

⌬H ϭ ϩ115 kJ/mol

which has already come to equilibrium. Predict

whether the equilibrium will shift to the left, will

shift to the right, or will not be affected if the changes

indicated below are made to the system.

a. Additional B(s) is added to the system.

b. C(g) is removed from the system as it forms.

c. The volume of the system is decreased by a factor

of 2.

d. The temperature is increased.

37. Hydrogen gas and chlorine gas in the presence of

light react explosively to form hydrogen chloride

H2(g) ϩ Cl2(g) 4

3 2HCl( g)

The reaction is strongly exothermic. Would an increase in temperature for the system tend to favor or

disfavor the production of hydrogen chloride?

38. For the general reaction

A(g) ϩ B(g) ϩ heat 4

3 C(g)

would an increase in temperature tend to favor the

forward or the reverse process? Why?

39. The reaction

3 C2H2Br4( g)

C2H2( g) ϩ 2Br2( g) 4

is exothermic in the forward direction. Will an increase in temperature shift the position of the equilibrium toward reactants or products?

40. The reaction

4NO( g) ϩ 6H2O( g) 4

3 4NH3( g) ϩ 5O2( g)

is strongly endothermic. Will an increase in temperature shift the equilibrium position toward products

or toward reactants?

41. Plants synthesize the sugar dextrose according to the

following reaction by absorbing radiant energy from

the sun (photosynthesis).

6CO2( g) ϩ 6H2O( g) 4

3 C6H12O6(s) ϩ 6O2( g)

Will an increase in temperature tend to favor or discourage the production of C6H12O6(s)?

42. Consider the exothermic reaction

3 CH3OH(l)

CO(g) ϩ 2H2(g) 4

Predict three changes that could be made to the system that would increase the yield of product over

that produced by a system in which no change was

575

17.8 Applications Involving the Equilibrium

Constant

QUESTIONS

43. Suppose a reaction has the equilibrium constant K ϭ

1.3 ϫ 108. What does the magnitude of this constant

tell you about the relative concentrations of products

and reactants that will be present once equilibrium is

reached? Is this reaction likely to be a good source of

the products?

44. Suppose a reaction has the equilibrium constant K ϭ

1.7 ϫ 10Ϫ8 at a particular temperature. Will there be a

large or small amount of unreacted starting material

present when this reaction reaches equilibrium? Is

this reaction likely to be a good source of products at

this temperature?

PROBLEMS

45. For the reaction

Br2(g) ϩ 5F2(g) 4

3 2BrF5(g)

the system at equilibrium at a particular temperature is

analyzed, and the following concentrations are found:

[BrF5(g)] ϭ 1.01 ϫ 10Ϫ9 M, [Br2(g)] ϭ 2.41 ϫ 10Ϫ2 M,

and [F2(g)] ϭ 8.15 ϫ 10Ϫ2 M. Calculate the value of K

for the reaction at this temperature.

46. Consider the reaction

SO2(g) ϩ NO2(g) 4

3 SO3(g) ϩ NO(g)

Suppose it is found at a particular temperature that

the concentrations in the system at equilibrium are

as follows: [SO3(g)] ϭ 4.99 ϫ 10Ϫ5 M, [NO( g)] ϭ

6.31 ϫ 10Ϫ7 M, [SO2(g)] ϭ 2.11 ϫ 10Ϫ2 M, and

[NO2(g)] ϭ 1.73 ϫ 10Ϫ3 M. Calculate the value of K for

the reaction at this temperature.

47. For the reaction

2CO( g) ϩ O2( g) 4

3 2CO2( g)

it is found at equilibrium at a certain temperature

that the concentrations are [CO(g)] ϭ 2.7 ϫ 10Ϫ4 M,

[O2(g)] ϭ 1.9 ϫ 10Ϫ3 M, and [CO2(g)] ϭ 1.1 ϫ 10Ϫ1 M.

Calculate K for the reaction at this temperature.

48. For the reaction

CO2(g) ϩ H2(g) 4

3 CO(g) ϩ H2O(g)

the equilibrium constant, K, has the value 5.21 ϫ 10Ϫ3

at a particular temperature. If the system is analyzed at

equilibrium at this temperature, it is found that

[CO(g)] ϭ 4.73 ϫ 10Ϫ3 M, [H2O(g)] ϭ 5.21 ϫ 10Ϫ3 M,

and [CO2(g)] ϭ 3.99 ϫ 10Ϫ2 M. What is the equilibrium

concentration of H2(g) in the system?

49. The equilibrium constant for the reaction

3 2HF( g)

H2( g) ϩ F2( g) 4

has the value 2.1 ϫ 103 at a particular temperature.

When the system is analyzed at equilibrium at this

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

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