8 Product- or Reactant-Favored Reactions and Thermodynamics

236



c h a p t er 5 Principles of Chemical Reactivity: Energy and Chemical Reactions



A CLOSER LOOK



Hess’s Law and Equation 5.6



Equation 5.6 is an application

of Hess’s law. To illustrate

this, let us look further at the decomposition

of calcium carbonate.

CaCO3(s) → CaO(s) + CO2(g)



∆rH° = ∆f H°[CaO(s)] + ∆f H°[CO2(g)]

− ∆f H°[CaCO3(s)]



That is, the change in enthalpy for the

reaction is equal to the enthalpies of formation of products (CO2 and CaO) minus

the enthalpy of formation of the reactant



∆rH° = ?



Because enthalpy is a state function, the

change in enthalpy for this reaction is independent of the route from reactants to

products. We can imagine an alternate route

from reactant to products that involves first

converting the reactant (CaCO3) to elements in their standard states, then recombining these elements to give the reaction

products. Notice that the enthalpy changes

for these processes are the enthalpies of

formation of the reactants and products in

the equation above:



(CaCO3), which is, of course, what one does

when using Equation 5.6 for this calculation.

The relationship among these enthalpy

quantities is illustrated in the energy-level

diagram.



Energy level diagram for the decomposition of CaCO3(s)



Energy, q



CaCO3(s) → Ca(s) + C(s) + 3/2 O2(g)

−∆f H°[CaCO3(s)] = ∆rH°1

C(s) + O2(g) → CO2(g)



∆rH°2 + ∆rH°3 =

(−635.1 kJ) + (−393.5 kJ)



∆rH°1 =

−∆f H°[CaCO3(s)]

= +1207.6 kJ



∆f H°[CO2(g)] = ∆rH°2



CaO(s) + CO2(g)



Ca(s) + 1⁄2 O2(g) → CaO(s)

∆f H°[CaO(s)] = ∆rH°3

CaCO3(s) → CaO(s) + CO2(g)



3

O (g)

2 2



Ca(s) + C(s) +



∆rH°net = ∆rH°1 + ∆rH°2 + ∆r H°3

= + 179.0 kJ



∆rH°net



∆rH°net = ∆rH°1 + ∆rH°2 + ∆rH°3



CaCO3(s)



2.



Acetic acid is made by the reaction CH3OH(ℓ) + CO(g) n CH3CO2H(ℓ). Determine the

enthalpy change for this reaction from the enthalpies of the three reactions below.



(a)



2 CH3OH(ℓ) + 3 O2(g) n 2 CO2(g) + 4 H2O(ℓ)



∆rH°1



CH3CO2H(ℓ) + 2 O2(g) n 2 CO2(g) + 2 H2O(ℓ)



∆rH°2



2 CO(g) + O2(g) n 2 CO2(g)



∆rH°3



∆rH°1 + ∆rH°2 + ∆rH°3



(b) ∆rH°1 − ∆rH°2 + ∆rH°3



(c)



1/2 ∆rH°1 − ∆rH°2 + 1/2 ∆rH°3



(d) −1/2 ∆rH°1 + ∆rH°2 − 1/2 ∆rH°3



5.8 Product-orreactant-Favoredreactions

andThermodynamics

At the beginning of this chapter, we noted that thermodynamics would provide answers to four questions:

•

•

•

•



kotz_48288_05_0208-0251.indd 236



How do we measure and calculate the energy changes associated with physical

changes and chemical reactions?

What is the relationship between energy changes, heat, and work?

How can we determine whether a chemical reaction is product-favored or

reactant-favored at equilibrium?

How can we determine whether a chemical reaction or physical process will

occur spontaneously, that is, without outside intervention?



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237



5.8 Product- or Reactant-Favored Reactions and Thermodynamics







The first two questions were addressed in this chapter, but the other two important

questions still remain (for Chapter 19).

In Chapter 3, we learned that chemical reactions proceed toward equilibrium,

and spontaneous changes occur in a way that allows a system to approach equilibrium. Reactions in which reactants are largely converted to products when equilibrium is reached are said to be product-favored at equilibrium. Reactions in which only

small amounts of products are present at equilibrium are called reactant-favored at

equilibrium (◀ page 118).



The Fuel Controversy—Alcohol and Gasoline



It is clear that supplies of fossil fuels are declining and

their prices are increasing, just as the nations

of the earth have ever greater energy needs.

We will have more to say about this in the

Interchapter (Energy) that follows. Here,

however, let’s analyze the debate about

replacing gasoline with ethanol (C2H5OH).

As Matthew Wald said in the article “Is

Ethanol in for the Long Haul?” (Scientific

American, January 2007), “The U.S. has gone

on an ethanol binge.” In 2005, the U.S.

Congress passed an energy bill stating that

ethanol production should be 7.5 billion gallons a year by 2012, up from about 5 billion

gallons in 2005. The goal is to at least partially

replace gasoline with ethanol.

Is a goal of replacing gasoline completely with ethanol reasonable? This is a

lofty goal, given that present gasoline consumption in the U.S. is about 140 billion

gallons annually. Again, according to

Matthew Wald, “Even if 100 percent of the

U.S. corn supply was distilled into ethanol, it

would supply only a small fraction of the

fuel consumed by the nation’s vehicles.”

Wald’s thesis in his article, which is supported by numerous scientific studies, is

that if ethanol is to be pursued as an alternative to gasoline, more emphasis would

have to be placed on deriving ethanol from

sources other than corn, such as cellulose

from cornstalks and various grasses.

Beyond this, there are other problems

associated with ethanol. One is that it cannot be distributed through a pipeline system as gasoline can. Any water in the pipeline is miscible with ethanol, which causes

the fuel value to decline.

Finally, even E85 fuel—a blend of 85%

ethanol and 15% gasoline—cannot be used

in most current vehicles because relatively

few vehicles as yet have engines designed

for fuels with a high ethanol content (socalled “flexible fuel” engines). The number

of these vehicles would need to be increased



kotz_48288_05_0208-0251.indd 237



in order for E85 to have a significant effect

on our gasoline usage.

For more information, see the references

in Wald’s Scientific American article.



Questions:

For the purposes of this analysis, let us use

octane (C8H18) as a substitute for the complex mixture of hydrocarbons in gasoline.

Data you will need for this question (in addition to Appendix L) are:

∆f H° [C8H18(ℓ)] = −250.1 kJ/mol

Density of ethanol = 0.785 g/mL

Density of octane = 0.699 g/mL



1. Calculate ∆rH° for the combustion of

ethanol and octane, and compare the

values per mole and per gram. Which

provides more energy per mole? Which

provides more energy per gram?



2. Compare the energy produced per liter

of the two fuels. Which produces more

energy for a given volume (something

useful to know when filling your gas

tank)?

3. What mass of CO2, a greenhouse gas, is

produced per liter of fuel (assuming

complete combustion)?

4. Now compare the fuels on an energyequivalent basis. What volume of ethanol

would have to be burned to get the same

energy as 1.00 L of octane? When you

burn enough ethanol to have the same

energy as a liter of octane, which fuel produces more CO2?

5. On the basis of this analysis and assuming the same price per liter, which fuel

will propel your car further? Which will

produce less greenhouse gas?

Answers to these questions are available in

Appendix N.



© GIPhotoStock Z/Alamy



CASE STUDY



Ethanol available at a service station. E85 fuel is a blend of 85% ethanol and 15% gasoline.

Be aware that you can only use E85 in vehicles designed for the fuel. In an ordinary vehicle, the

ethanol leads to deterioration of seals in the engine and fuel system.



11/18/10 3:03 PM



238



c h a p t er 5   Principles of Chemical Reactivity: Energy and Chemical Reactions



Let us look back at the many chemical reactions that we have seen. For example, all combustion reactions are exothermic, and the oxidation of iron (Figure 5.14) is clearly exothermic.

4 Fe(s) + 3 O2(g)  →  2 Fe2O3(s)

 2 mol Fe2O3   Ϫ825.5 kJ 

∆rH° ϭ 2 ∆ f H°[Fe2O3(s)] ϭ 

ϭ Ϫ1651.0 kJ/mol-rxn

 1 mol-rxn   1 mol Fe2O3 



© Cengage Learning/Charles D. Winters



The reaction has a negative value for ∆rH°, and it is also product-favored at

equilibrium.

Conversely, the decomposition of calcium carbonate is endothermic.

CaCO3(s)  →  CaO(s) + CO2(g)   ∆rH° = +179.0 kJ/mol-rxn



Figure 5.14   The productfavored oxidation of iron.  Iron

powder, sprayed into a bunsen burner

flame, is rapidly oxidized. The reaction

is exothermic and is product-favored.



  and 

Sign in at www.cengage.com/owl to:

• View tutorials and simulations, develop

problem-solving skills, and complete

online homework assigned by your

professor.

• For quick review and exam prep,

download Go Chemistry mini lecture

modules from OWL (or purchase them

at www.cengagebrain.com)

Access How Do I Solve It? tutorials

on how to approach problem solving

using concepts in this chapter.



The decomposition of CaCO3 proceeds to an equilibrium that favors the reactants;

that is, it is reactant-favored at equilibrium.

Are all exothermic reactions product-favored at equilibrium and all endothermic reactions reactant-favored at equilibrium? From these examples, we might formulate that idea as a hypothesis that can be tested by experiment and by examination of other examples. You would find that in most cases, product-favored reactions have

negative values of ∆rH°, and reactant-favored reactions have positive values of ∆rH°. But

this is not always true; there are exceptions.

Clearly, a further discussion of thermodynamics must be tied to the concept of

equilibrium. This relationship, and the complete discussion of the third and fourth

questions, will be presented in Chapter 19.



chapter goals revisited

Now that you have completed this chapter, you should ask whether you have met the chapter

goals. In particular, you should be able to:

Assess the transfer of energy as heat associated with changes in temperature and

changes of state



a. Describe the nature of energy transfers as heat (Section 5.1).

b. Recognize and use the language of thermodynamics: the system and its surroundings; exothermic and endothermic reactions (Section 5.1). Study

Questions: 1, 3, 59.

c. Use specific heat capacity in calculations of energy transfer as heat and of

temperature changes (Section 5.2). Study Questions: 5, 7, 9, 11, 13, 15.

d. Understand the sign conventions in thermodynamics.

e. Use enthalpy (heat) of fusion and enthalpy (heat) of vaporization to calculate

the energy transferred as heat in changes of state (Section 5.3). Study

Questions: 17, 19, 21, 23, 83.

Understand and apply the first law of thermodynamics



a. Understand the basis of the first law of thermodynamics (Section 5.4).

b. Recognize how energy transferred as heat and work done on or by a system

contribute to changes in the internal energy of a system (Section 5.4).

Define and understand state functions (enthalpy, internal energy)



a. Recognize state functions whose values are determined only by the state of the

system and not by the pathway by which that state was achieved (Section 5.4).

Describe how energy changes are measured



a. Recognize that when a process is carried out under constant pressure conditions, the energy transferred as heat is the enthalpy change, ∆H (Section 5.5).

Study Questions: 25, 26, 27, 28, 48.

b. Describe how to measure the quantity of energy transferred as heat in a reaction by calorimetry (Section 5.6). Study Questions: 29, 30, 31, 32, 34–40.



kotz_48288_05_0208-0251.indd 238



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▲ more challenging  blue-numbered questions answered in Appendix R







239



Calculate the energy evolved or required for physical changes and chemical reactions

using tables of thermodynamic data.



a. Apply Hess’s law to find the enthalpy change, ∆rH°, for a reaction (Section

5.7). Study Questions: 41–44, 73, 79, and Go Chemistry Module 10.

b. Know how to draw and interpret energy level diagrams (Section 5.7). Study

Questions: 53, 54, 73, 74, 79, 101, 105.

c. Use standard molar enthalpies of formation, ∆f H°, to calculate the enthalpy

change for a reaction, ∆rH° (Section 5.7). Study Questions: 47, 49, 51, 55, 56.



Key Equations

Equation 5.1 (page 212)  The energy transferred as heat when the temperature of a

substance changes. Calculated from the specific heat capacity (C), mass (m), and

change in temperature (∆T).

q(J) = C(J/g ⋅ K) × m(g) × ∆T(K)



Equation 5.2 (page 212)  Temperature changes are always calculated as final temperature minus initial temperature.

∆T = Tfinal − Tinitial



Equation 5.3 (page 214)  If no energy is transferred between a system and its surroundings and if energy is transferred within the system only as heat, the sum of

the thermal energy changes within the system equals zero.

q1 + q2 + q3 + . . . = 0



Equation 5.4 (page 220)  The first law of thermodynamics: The change in internal

energy (∆U) in a system is the sum of the energy transferred as heat (q) and the

energy transferred as work (w).

∆U = q + w



Equation 5.5 (page 221)  P –V work (w) at constant pressure is the product of pressure (P) and change in volume (∆V)

w = −P × ∆V



Equation 5.6 (page 234)  This equation is used to calculate the standard enthalpy

change of a reaction (∆rH °) when the enthalpies of formation (∆f H°) of all of the

reactants and products are known. The parameter n is the stoichiometric coefficient

of each product or reactant in the balanced chemical equation.

∆rH° = Σn∆fH°(products) − Σn∆fH°(reactants)



Study Questions

  Interactive versions of these questions are

assignable in OWL

▲ denotes challenging questions.

Blue-numbered questions have answers in Appendix R and

fully worked solutions in the Student Solutions Manual.



Practicing Skills

Energy: Some Basic Principles

(See Section 5.1.)

1. Define the terms system and surroundings. What does it

mean to say that a system and its surroundings are in

thermal equilibrium?



kotz_48288_05_0208-0251.indd 239



2. What determines the directionality of energy transfer as

heat ?

3. Identify whether the following processes are exothermic

or endothermic.

(a)combustion of methane

(b)melting of ice

(c)raising the temperature of water from 25 °C to 100 °C

(d)heating CaCO3(s) to form CaO(s) and CO2(g)

4. Identify whether the following processes are exothermic

or endothermic.

(a)the reaction of Na(s) and Cl2(g)

(b)cooling and condensing gaseous N2 to form

liquid N2

(c)cooling a soft drink from 25 °C to 0 °C

(d)heating HgO(s) to form Hg(ℓ) and O2(g)



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c h a p t er 5   Principles of Chemical Reactivity: Energy and Chemical Reactions



Specific Heat Capacity

(See Section 5.2 and Examples 5.1 and 5.2.)



Changes of State

(See Section 5.3 and Examples 5.3 and 5.4.)



5. The molar heat capacity of mercury is 28.1 J/mol ∙ K.

What is the specific heat capacity of this metal in J/g ∙ K?



17. How much energy is evolved as heat when 1.0 L of

water at 0 °C solidifies to ice? (The heat of fusion of

water is 333 J/g.)



6. The specific heat capacity of benzene (C6H6) is

1.74 J/g ∙ K. What is its molar heat capacity (in

J/mol ∙ K)?

7. The specific heat capacity of copper metal is

0.385 J/g ∙ K. How much energy is required to heat

168 g of copper from −12.2 °C to +25.6 °C?

8. How much energy as heat is required to raise the

temperature of 50.00 mL of water from 25.52 °C to

28.75 °C? (Density of water at this temperature =

0.997 g/mL.)

9. The initial temperature of a 344-g sample of iron is

18.2 °C. If the sample absorbs 2.25 kJ of energy as heat,

what is its final temperature?

10. After absorbing 1.850 kJ of energy as heat, the temperature of a 0.500-kg block of copper is 37 °C. What was its

initial temperature?

11. A 45.5-g sample of copper at 99.8 °C was dropped into a

beaker containing 152 g of water at 18.5 °C. What was the

final temperature when thermal equilibrium was reached?

12. A 182-g sample of gold at some temperature was added

to 22.1 g of water. The initial water temperature was

25.0 °C, and the final temperature was 27.5 °C. If the

specific heat capacity of gold is 0.128 J/g ∙ K, what was

the initial temperature of the gold sample?

13. One beaker contains 156 g of water at 22 °C, and a

second beaker contains 85.2 g of water at 95 °C. The

water in the two beakers is mixed. What is the final

water temperature?

14. When 108 g of water at a temperature of 22.5 °C is

mixed with 65.1 g of water at an unknown temperature,

the final temperature of the resulting mixture is

47.9 °C. What was the initial temperature of the second

sample of water?

15. A 13.8-g piece of zinc was heated to 98.8 °C in boiling

water and then dropped into a beaker containing 45.0 g

of water at 25.0 °C. When the water and metal came to

thermal equilibrium, the temperature was 27.1 °C. What

is the specific heat capacity of zinc?



18. The energy required to melt 1.00 g of ice at 0 °C is 333

J. If one ice cube has a mass of 62.0 g and a tray contains 16 ice cubes, what quantity of energy is required

to melt a tray of ice cubes to form liquid water at 0 °C?

19. How much energy is required to vaporize 125 g of

benzene, C6H6, at its boiling point, 80.1 °C? (The heat

of vaporization of benzene is 30.8 kJ/mol.)

20. Chloromethane, CH3Cl, arises from microbial fermentation and is found throughout the environment. It is also

produced industrially, is used in the manufacture of

various chemicals, and has been used as a topical anesthetic. How much energy is required to convert 92.5 g

of liquid to a vapor at its boiling point, −24.09 °C?

(The heat of vaporization of CH3Cl is 21.40 kJ/mol.)

21. The freezing point of mercury is −38.8 °C. What quantity of energy, in joules, is released to the surroundings

if 1.00 mL of mercury is cooled from 23.0 °C to −38.8

°C and then frozen to a solid? (The density of liquid

mercury is 13.6 g/cm3. Its specific heat capacity is 0.140

J/g ∙ K and its heat of fusion is 11.4 J/g.)

22. What quantity of energy, in joules, is required to raise

the temperature of 454 g of tin from room temperature, 25.0 °C, to its melting point, 231.9 °C, and then

melt the tin at that temperature? (The specific heat

capacity of tin is 0.227 J/g ∙ K, and the heat of fusion

of this metal is 59.2 J/g.)

23. Ethanol, C2H5OH, boils at 78.29 °C. How much energy,

in joules, is required to raise the temperature of 1.00 kg

of ethanol from 20.0 °C to the boiling point and then

to change the liquid to vapor at that temperature? (The

specific heat capacity of liquid ethanol is 2.44 J/g ∙ K,

and its enthalpy of vaporization is 855 J/g.)

24. A 25.0-mL sample of benzene at 19.9 °C was cooled to

its melting point, 5.5 °C, and then frozen. How much

energy was given off as heat in this process? (The density

of benzene is 0.80 g/mL, its specific heat capacity is

1.74 J/g ∙ K, and its heat of fusion is 127 J/g.)



16. A 237-g piece of molybdenum, initially at 100.0 °C, was

dropped into 244 g of water at 10.0 °C. When the

system came to thermal equilibrium, the temperature

was 15.3 °C. What is the specific heat capacity of

molybdenum?



kotz_48288_05_0208-0251.indd 240



11/18/10 3:03 PM



▲ more challenging  blue-numbered questions answered in Appendix R







Enthalpy Changes

(See Section 5.5 and Example 5.5.)

25. Nitrogen monoxide, a gas recently found to be involved

in a wide range of biological processes, reacts with

oxygen to give brown NO2 gas.

2 NO(g) + O2(g)  →  2 NO2(g)

∆rH°= −114.1 kJ/mol-rxn

Is this reaction endothermic or exothermic? What is the

enthalpy change if 1.25 g of NO is converted completely

to NO2?

26. Calcium carbide, CaC2, is manufactured by the reaction

of CaO with carbon at a high temperature. (Calcium

carbide is then used to make acetylene.)

CaO(s) + 3 C(s)  →  CaC2(s) + CO(g)

∆rH°= +464.8 kJ/mol-rxn

Is this reaction endothermic or exothermic? What is the

enthalpy change if 10.0 g of CaO is allowed to react

with an excess of carbon?

27. Isooctane (2,2,4-trimethylpentane), one of the many

hydrocarbons that make up gasoline, burns in air to

give water and carbon dioxide.

2 C8H18(ℓ) + 25 O2(g)  →  16 CO2(g) + 18 H2O(ℓ)

∆rH°= −10,922 kJ/mol-rxn

What is the enthalpy change if you burn 1.00 L of

isooctane (d = 0.69 g/mL)?

28. Acetic acid, CH3CO2H, is made industrially by the reaction of methanol and carbon monoxide.



241



30. You mix 125 mL of 0.250 M CsOH with 50.0 mL of

0.625 M HF in a coffee-cup calorimeter, and the temperature of both solutions rises from 21.50 °C before

mixing to 24.40 °C after the reaction.

CsOH(aq) + HF(aq)  →  CsF(aq) + H2O(ℓ)

What is the enthalpy of reaction per mole of CsOH?

Assume the densities of the solutions are all 1.00 g/mL,

and the specific heat capacities of the solutions are

4.2 J/g ∙ K.

31. A piece of titanium metal with a mass of 20.8 g is

heated in boiling water to 99.5 °C and then dropped

into a coffee-cup calorimeter containing 75.0 g of water

at 21.7 °C. When thermal equilibrium is reached, the

final temperature is 24.3 °C. Calculate the specific heat

capacity of titanium.

32. A piece of chromium metal with a mass of 24.26 g is

heated in boiling water to 98.3 °C and then dropped

into a coffee-cup calorimeter containing 82.3 g of water

at 23.3 °C. When thermal equilibrium is reached, the

final temperature is 25.6 °C. Calculate the specific heat

capacity of chromium.

33. Adding 5.44 g of NH4NO3(s) to 150.0 g of water in a

coffee-cup calorimeter (with stirring to dissolve the salt)

resulted in a decrease in temperature from 18.6 °C to

16.2 °C. Calculate the enthalpy change for dissolving

NH4NO3(s) in water, in kJ/mol. Assume the solution

(whose mass is 155.4 g) has a specific heat capacity of

4.2 J/g ∙ K. (Cold packs take advantage of the fact that

dissolving ammonium nitrate in water is an endothermic process.)



What is the enthalpy change for producing 1.00 L of

acetic acid (d = 1.044 g/mL) by this reaction?

Calorimetry

(See Section 5.6 and Examples 5.6 and 5.7.)

29. Assume you mix 100.0 mL of 0.200 M CsOH with

50.0 mL of 0.400 M HCl in a coffee-cup calorimeter.

The following reaction occurs:

CsOH(aq) + HCl(aq)  →  CsCl(aq) + H2O(ℓ)

The temperature of both solutions before mixing was

22.50 °C, and it rises to 24.28 °C after the acid–base

reaction. What is the enthalpy change for the reaction

per mole of CsOH? Assume the densities of the solutions are all 1.00 g/mL and the specific heat capacities

of the solutions are 4.2 J/g ∙ K.



kotz_48288_05_0208-0251.indd 241



© Cengage Learning/Charles D. Winters



CH3OH(ℓ) + CO(g)  →  CH3CO2H(ℓ)

∆rH°= −134.6 kJ/mol-rxn



A cold pack uses the endothermic enthalpy of a solution of

ammonium nitrate.



34. You should use care when dissolving H2SO4 in water

because the process is highly exothermic. To measure the

enthalpy change, 5.2 g of concentrated H2SO4(ℓ) was

added (with stirring) to 135 g of water in a coffee-cup

calorimeter. This resulted in an increase in temperature

from 20.2 °C to 28.8 °C. Calculate the enthalpy change

for the process H2SO4(ℓ)  →  H2SO4(aq), in kJ/mol.



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c h a p t er 5   Principles of Chemical Reactivity: Energy and Chemical Reactions



35. Sulfur (2.56 g) was burned in a constant volume calorimeter with excess O2(g). The temperature increased

from 21.25 °C to 26.72 °C. The bomb has a heat

capacity of 923 J/K, and the calorimeter contained

815 g of water. Calculate ∆U per mole of SO2 formed

for the reaction



© Cengage Learning/Charles D. Winters



S8(s) + 8 O2(g)  →  8 SO2(g)



38. A 0.692-g sample of glucose, C6H12O6, was burned in a

constant volume calorimeter. The temperature rose

from 21.70 °C to 25.22 °C. The calorimeter contained

575 g of water, and the bomb had a heat capacity of

650 J/K. What is ∆U per mole of glucose?

39. An “ice calorimeter” can be used to determine the

specific heat capacity of a metal. A piece of hot metal is

dropped onto a weighed quantity of ice. The energy

transferred from the metal to the ice can be determined from the amount of ice melted. Suppose you

heated a 50.0-g piece of silver to 99.8 °C and then

dropped it onto ice. When the metal’s temperature had

dropped to 0.0 °C, it is found that 3.54 g of ice had

melted. What is the specific heat capacity of silver?

40. A 9.36-g piece of platinum was heated to 98.6 °C in a

boiling water bath and then dropped onto ice. (See

Study Question 39.) When the metal’s temperature had

dropped to 0.0 °C, it was found that 0.37 g of ice had

melted. What is the specific heat capacity of platinum?

Hess’s Law

(See Section 5.7 and Example 5.8.)



Sulfur burns in oxygen with a bright blue flame to give SO2(g).



36. Suppose you burned 0.300 g of C(s) in an excess of

O2(g) in a constant volume calorimeter to give CO2(g).

C(s) + O2(g)  →  CO2(g)

The temperature of the calorimeter, which contained

775 g of water, increased from 25.00 °C to 27.38 °C.

The heat capacity of the bomb is 893 J/K. Calculate

∆U per mole of carbon.

37. Suppose you burned 1.500 g of benzoic acid,

C6H5CO2H, in a constant volume calorimeter and

found that the temperature increased from 22.50 °C

to 31.69 °C. The calorimeter contained 775 g of water,

and the bomb had a heat capacity of 893 J/K. Calculate

∆U per mole of benzoic acid.



41. The enthalpy changes for the following reactions can be

measured:

CH4(g) + 2 O2(g)  →  CO2(g) + 2 H2O(g)

∆rH ° = −802.4 kJ/mol-rxn

CH3OH(g) + 3⁄2 O2(g)  →  CO2(g) + 2 H2O(g)

∆rH° = −676 kJ/mol-rxn

(a)Use these values and Hess’s law to determine the

enthalpy change for the reaction

CH4(g) + 1⁄2 O2(g)  →  CH3OH(g)

(b)Draw an energy-level diagram that shows the relationship between the energy quantities involved in

this problem.

42. The enthalpy changes of the following reactions can be

measured:

C2H4(g) + 3 O2(g)  →  2 CO2(g) + 2 H2O(ℓ)

∆rH° = −1411.1 kJ/mol-rxn

C2H5OH(ℓ) + 3 O2(g)  →  2 CO2(g) + 3 H2O(ℓ)

∆rH° = −1367.5 kJ/mol-rxn

(a)Use these values and Hess’s law to determine the

enthalpy change for the reaction

C2H4(g) + H2O(ℓ)  →  C2H5OH(ℓ)



Benzoic acid, C6H5CO2H, occurs naturally in many berries. Its

heat of combustion is well known, so it is used as a standard to

calibrate calorimeters.



kotz_48288_05_0208-0251.indd 242



(b)Draw an energy level diagram that shows the relationship between the energy quantities involved in

this problem.



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▲ more challenging  blue-numbered questions answered in Appendix R







43. Enthalpy changes for the following reactions can be

determined experimentally:

N2(g) + 3 H2(g)  →  2 NH3(g)

∆rH° = −91.8 kJ/mol-rxn

4 NH3(g) + 5 O2(g)  →  4 NO(g) + 6 H2O(g)

∆rH° = −906.2 kJ/mol-rxn

H2(g) + 1⁄2 O2(g)  →  H2O(g)

∆rH° = −241.8 kJ/mol-rxn

Use these values to determine the enthalpy change for

the formation of NO(g) from the elements (an enthalpy

change that cannot be measured directly because the

reaction is reactant-favored).

⁄2 N2(g) + 1⁄2 O2(g)  →  NO(g)   ∆rH° = ?



1



44. You wish to know the enthalpy change for the formation of liquid PCl3 from the elements.

P4(s) + 6 Cl2(g)  →  4 PCl3(ℓ)   ∆rH° = ?

The enthalpy change for the formation of PCl5 from

the elements can be determined experimentally, as can

the enthalpy change for the reaction of PCl3(ℓ) with

more chlorine to give PCl5(s):

P4(s) + 10 Cl2(g)  →  4 PCl5(s)

∆rH° = −1774.0 kJ/mol-rxn

PCl3(ℓ) + Cl2(g)  →  PCl5(s)

∆rH° = −123.8 kJ/mol-rxn

Use these data to calculate the enthalpy change for the

formation of 1.00 mol of PCl3(ℓ) from phosphorus and

chlorine.

Standard Enthalpies of Formation

(See Section 5.7 and Example 5.9.)

45. Write a balanced chemical equation for the formation

of CH3OH(ℓ) from the elements in their standard

states. Find the value for ∆f H° for CH3OH(ℓ) in

Appendix L.

46. Write a balanced chemical equation for the formation

of CaCO3(s) from the elements in their standard states.

Find the value for ∆f H° for CaCO3(s) in Appendix L.

47. (a)Write a balanced chemical equation for the formation of 1 mol of Cr2O3(s) from Cr and O2 in their

standard states. (Find the value for ∆f H° for

Cr2O3(s) in Appendix L.)

(b)What is the enthalpy change if 2.4 g of chromium is

oxidized to Cr2O3(s)?

48. (a)Write a balanced chemical equation for the formation of 1 mol of MgO(s) from the elements in their

standard states. (Find the value for ∆f H° for MgO(s)

in Appendix L.)

(b)What is the standard enthalpy change for the reaction of 2.5 mol of Mg with oxygen?



kotz_48288_05_0208-0251.indd 243



243



49. Use standard enthalpies of formation in Appendix L to

calculate enthalpy changes for the following:

(a)1.0 g of white phosphorus burns, forming P4O10(s)

(b)0.20 mol of NO(g) decomposes to N2(g) and O2(g)

(c)2.40 g of NaCl(s) is formed from Na(s) and excess

Cl2(g)

(d)250 g of iron is oxidized with oxygen to Fe2O3(s)

50. Use standard enthalpies of formation in Appendix L to

calculate enthalpy changes for the following:

(a)0.054 g of sulfur burns, forming SO2(g)

(b)0.20 mol of HgO(s) decomposes to Hg(ℓ) and O2(g)

(c)2.40 g of NH3(g) is formed from N2(g) and excess

H2(g)

(d)1.05 × 10−2 mol of carbon is oxidized to CO2(g)

51. The first step in the production of nitric acid from

ammonia involves the oxidation of NH3.

4 NH3(g) + 5 O2(g)  →  4 NO(g) + 6 H2O(g)

(a)Use standard enthalpies of formation to calculate

the standard enthalpy change for this reaction.

(b)How much energy is evolved or absorbed as heat in

the oxidation of 10.0 g of NH3?

52. The Romans used calcium oxide, CaO, to produce a

strong mortar to build stone structures. Calcium oxide

was mixed with water to give Ca(OH)2, which reacted

slowly with CO2 in the air to give CaCO3.

Ca(OH)2(s) + CO2(g)  →  CaCO3(s) + H2O(g)

(a)Calculate the standard enthalpy change for this

reaction.

(b)How much energy is evolved or absorbed as heat if

1.00 kg of Ca(OH)2 reacts with a stoichiometric

amount of CO2?

53. The standard enthalpy of formation of solid barium

oxide, BaO, is −553.5 kJ/mol, and the standard enthalpy

of formation of barium peroxide, BaO2, is −634.3 kJ/mol.

(a)Calculate the standard enthalpy change for the following reaction. Is the reaction exothermic or

endothermic?

2 BaO2(s)  →  2 BaO(s) + O2(g)

(b)Draw an energy level diagram that shows the relationship between the enthalpy change of the decomposition of BaO2 to BaO and O2 and the enthalpies

of formation of BaO(s) and BaO2(s).

54. An important step in the production of sulfuric acid is

the oxidation of SO2 to SO3.

SO2(g) + 1⁄2 O2(g)  →  SO3(g)

Formation of SO3 from the air pollutant SO2 is also a

key step in the formation of acid rain.

(a)Use standard enthalpies of formation to calculate

the enthalpy change for the reaction. Is the reaction

exothermic or endothermic?

(b)Draw an energy level diagram that shows the relationship between the enthalpy change for the oxidation of SO2 to SO3 and the enthalpies of formation

of SO2(g) and SO3(g).



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244



c h a p t er 5   Principles of Chemical Reactivity: Energy and Chemical Reactions



55. The enthalpy change for the oxidation of naphthalene,

C10H8, is measured by calorimetry.

C10H8(s) + 12 O2(g)  →  10 CO2(g) + 4 H2O(ℓ)

∆rH° = −5156.1 kJ/mol-rxn

Use this value, along with the standard enthalpies of

formation of CO2(g) and H2O(ℓ), to calculate the

enthalpy of formation of naphthalene, in kJ/mol.

56. The enthalpy change for the oxidation of styrene, C8H8,

is measured by calorimetry.

C8H8(ℓ) + 10 O2(g)  →  8 CO2(g) + 4 H2O(ℓ)

∆rH° = −4395.0 kJ/mol-rxn

Use this value, along with the standard enthalpies of

formation of CO2(g) and H2O(ℓ), to calculate the

enthalpy of formation of styrene, in kJ/mol.



General Questions

These questions are not designated as to type or location in the

chapter. They may combine several concepts.

57. The following terms are used extensively in thermodynamics. Define each and give an example.

(a)exothermic and endothermic

(b)system and surroundings

(c)specific heat capacity

(d)state function

(e)standard state

(f) enthalpy change, ∆H

(g)standard enthalpy of formation

58. For each of the following, tell whether the process is

exothermic or endothermic. (No calculations are

required.)

(a)H2O(ℓ)  →  H2O(s)

(b)2 H2(g) + O2(g)  →  2 H2O(g)

(c)H2O(ℓ, 25 °C)  →  H2O(ℓ, 15 °C)

(d)H2O(ℓ)  →  H2O(g)

59. For each of the following, define a system and its surroundings, and give the direction of energy transfer

between system and surroundings.

(a)Methane burns in a gas furnace in your home.

(b)Water drops, sitting on your skin after a swim,

evaporate.

(c)Water, at 25 °C, is placed in the freezing compartment of a refrigerator, where it cools and eventually

solidifies.

(d)Aluminum and Fe2O3(s) are mixed in a flask sitting

on a laboratory bench. A reaction occurs, and a

large quantity of energy is evolved as heat.

60. What does the term standard state mean? What are the

standard states of the following substances at 298 K:

H2O, NaCl, Hg, CH4?

61. Use Appendix L to find the standard enthalpies of

formation of oxygen atoms, oxygen molecules (O2), and

ozone (O3). What is the standard state of oxygen? Is the

formation of oxygen atoms from O2 exothermic? What

is the enthalpy change for the formation of 1 mol of

O3 from O2?



kotz_48288_05_0208-0251.indd 244



62. You have a large balloon containing 1.0 mol of gaseous

water vapor at 80 °C. How will each step affect the

internal energy of the system?

(a)The temperature of the system is raised to 90 °C.

(b)The vapor is condensed to a liquid, at 40 °C.

63. Determine whether energy as heat is evolved or

required, and whether work was done on the system

or whether the system does work on the surroundings,

in the following processes at constant pressure:

(a) Liquid water at 100 °C is converted to steam at 100 °C.

(b)Dry ice, CO2(s), sublimes to give CO2(g).

64. Determine whether energy as heat is evolved or

required, and whether work was done on the system or

whether the system does work on the surroundings, in

the following processes at constant pressure:

(a)Ozone, O3, decomposes to form O2.

(b)Methane burns:

CH4(g) + 2 O2(g) n CO2(g) + 2 H2O(ℓ)

65. Use standard enthalpies of formation to calculate the

enthalpy change that occurs when 1.00 g of SnCl4(ℓ)

reacts with excess H2O(ℓ) to form SnO2(s) and

HCl(aq).

66. Which evolves more energy on cooling from 50 °C to

10 °C: 50.0 g of water or 100. g of ethanol (Cethanol =

2.46 J/g ∙ K)?

67. You determine that 187 J of energy as heat is required to

raise the temperature of 93.45 g of silver from 18.5 °C to

27.0 °C. What is the specific heat capacity of silver?

68. Calculate the quantity of energy required to convert

60.1 g of H2O(s) at 0.0 °C to H2O(g) at 100.0 °C. The

enthalpy of fusion of ice at 0 °C is 333 J/g; the enthalpy

of vaporization of liquid water at 100 °C is 2256 J/g.

69. You add 100.0 g of water at 60.0 °C to 100.0 g of ice at

0.00 °C. Some of the ice melts and cools the water to

0.00 °C. When the ice and water mixture reaches

thermal equilibrium at 0 °C, how much ice has melted?

70. ▲ Three 45-g ice cubes at 0 °C are dropped into

5.00 × 102 mL of tea to make iced tea. The tea was

initially at 20.0 °C; when thermal equilibrium was

reached, the final temperature was 0 °C. How much of

the ice melted, and how much remained floating in the

beverage? Assume the specific heat capacity of tea is the

same as that of pure water.

71. ▲ Suppose that only two 45-g ice cubes had been added

to your glass containing 5.00 × 102 mL of tea (see Study

Question 70). When thermal equilibrium is reached, all

of the ice will have melted, and the temperature of the

mixture will be somewhere between 20.0 °C and 0 °C.

Calculate the final temperature of the beverage. (Note:

The 90 g of water formed when the ice melts must be

warmed from 0 °C to the final temperature.)



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▲ more challenging  blue-numbered questions answered in Appendix R







72. You take a diet cola from the refrigerator and pour

240 mL of it into a glass. The temperature of the beverage is 10.5 °C. You then add one ice cube (45 g).

Which of the following describes the system when

thermal equilibrium is reached?

(a)The temperature is 0 °C, and some ice remains.

(b)The temperature is 0 °C, and no ice remains.

(c)The temperature is higher than 0 °C, and no ice

remains.



245



76. Camping stoves are fueled by propane (C3H8), butane

[C4H10(g), ∆fH° = −127.1 kJ/mol], gasoline, or ethanol

(C2H5OH). Calculate the enthalpy of combustion per

gram of each of these fuels. [Assume that gasoline is

represented by isooctane, C8H18(ℓ), with ∆f H° =

−259.3 kJ/mol.] Do you notice any great differences

among these fuels? How are these differences related to

their composition?



Determine the final temperature and the amount of ice

remaining, if any.



© Cengage Learning/Charles D. Winters



73. ▲ The standard molar enthalpy of formation of diborane, B2H6(g), cannot be determined directly because

the compound cannot be prepared by the reaction of

boron and hydrogen. It can be calculated from other

enthalpy changes, however. The following enthalpy

changes can be measured.

4 B(s) + 3 O2(g)  →  2 B2O3(s)

∆rH° = −2543.8 kJ/mol-rxn

H2(g) + 1⁄2 O2(g)  →  H2O(g) ∆rH° = −241.8 kJ/mol-rxn

B2H6(g) + 3 O2(g)  →  B2O3(s) + 3 H2O(g)

∆rH° = −2032.9 kJ/mol-rxn

(a)Show how these equations can be added together to

give the equation for the formation of B2H6(g) from

B(s) and H2(g) in their standard states. Assign enthalpy changes to each reaction.

(b)Calculate ∆fH° for B2H6(g).

(c)Draw an energy level diagram that shows how the

various enthalpies in this problem are related.

(d)Is the formation of B2H6(g) from its elements

exo- or endothermic?

74. Chloromethane, CH3Cl, a compound found throughout

the environment, is formed in the reaction of chlorine

atoms with methane.

CH4(g) + 2 Cl(g)  →  CH3Cl(g) + HCl(g)

(a)Calculate the enthalpy change for the reaction of

CH4(g) and Cl atoms to give CH3Cl(g) and HCl(g).

Is the reaction exo- or endothermic?

(b)Draw an energy level diagram that shows how the

various enthalpies in this problem are related.

75. When heated to a high temperature, coke (mainly

carbon, obtained by heating coal in the absence of air)

and steam produce a mixture called water gas, which can

be used as a fuel or as a starting place for other reactions. The equation for the production of water gas is



A camping stove that uses butane as a fuel.



77. Methanol, CH3OH, a compound that can be made relatively inexpensively from coal, is a promising substitute

for gasoline. The alcohol has a smaller energy content

than gasoline, but, with its higher octane rating, it burns

more efficiently than gasoline in combustion engines. (It

has the added advantage of contributing to a lesser

degree to some air pollutants.) Compare the enthalpy of

combustion per gram of CH3OH and C8H18 (isooctane),

the latter being representative of the compounds in

gasoline. (∆f H° = −259.2 kJ/mol for isooctane.)

78. Hydrazine and 1,1-dimethylhydrazine both react spontaneously with O2 and can be used as rocket fuels.

N2H4(ℓ) + O2(g)  →  N2(g) + 2 H2O(g)





hydrazine



N2H2(CH3)2(ℓ) + 4 O2(g)  → 

1,1-dimethylhydrazine

2 CO2(g) + 4 H2O(g) + N2(g)

The molar enthalpy of formation of N2H4(ℓ) is

+50.6 kJ/mol, and that of N2H2(CH3)2(ℓ) is

+48.9 kJ/mol. Use these values, with other ∆f H° values,

to decide whether the reaction of hydrazine or

1,1-dimethylhydrazine with oxygen provides more

energy per gram.



C(s) + H2O(g)  →  CO(g) + H2(g)



NASA



(a)Use standard enthalpies of formation to determine

the enthalpy change for this reaction.

(b)Is the reaction exo- or endothermic?

(c)What is the enthalpy change if 1000.0 kg (1 metric

ton) of carbon is converted to water gas?



A control rocket in the Space Shuttle uses hydrazine as fuel.



kotz_48288_05_0208-0251.indd 245



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246



c h a p t er 5   Principles of Chemical Reactivity: Energy and Chemical Reactions



79. (a)  Calculate the enthalpy change, ∆rH°, for the formation of 1.00 mol of strontium carbonate (the material

that gives the red color in fireworks) from its elements.

Sr(s) + C(s) + 3⁄2 O2(g)  →  SrCO3(s)

The experimental information available is

Sr(s) + 1⁄2 O2(g) → SrO(s)   ∆f H° = −592 kJ/mol-rxn

SrO(s) + CO2(g) → SrCO3(s)  ∆rH° = −234 kJ/mol-rxn

C(graphite) + O2(g) → CO2(g)  ∆f H° = −394 kJ/mol-rxn

(b)Draw an energy level diagram relating the energy

quantities in this problem.

80. You drink 350 mL of diet soda that is at a temperature

of 5 °C.

(a)How much energy will your body expend to raise

the temperature of this liquid to body temperature

(37 °C)? Assume that the density and specific heat

capacity of diet soda are the same as for water.

(b)Compare the value in part (a) with the caloric content of the beverage. (The label says that it has a caloric content of 1 Calorie.) What is the net energy

change in your body resulting from drinking this

beverage? (1 Calone = 1000 kCal = 4184 J.)

(c)Carry out a comparison similar to that in part (b)

for a nondiet beverage whose label indicates a caloric content of 240 Calories.

81. ▲ Chloroform, CHCl3, is formed from methane and

chlorine in the following reaction.

CH4(g) + 3 Cl2(g)  →  3 HCl(g) + CHCl3(g)

Calculate ∆rH°, the enthalpy change for this reaction,

using the enthalpies of formation of CO2(g), H2O(ℓ),

and CHCl3(g) (∆f H° = −103.1 kJ/mol), and the

enthalpy changes for the following reactions:

CH4(g) + 2 O2(g)  →  2 H2O(ℓ) + CO2(g)

∆rH° = −890.4 kJ/mol-rxn

2 HCl(g)  →  H2(g) + Cl2(g)

∆rH° = +184.6 kJ/mol-rxn

82. Water gas, a mixture of carbon monoxide and hydrogen,

is produced by treating carbon (in the form of coke or

coal) with steam at high temperatures. (See Study Question 75.)

C(s) + H2O(g)  →  CO(g) + H2(g)



In the Laboratory

83. A piece of lead with a mass of 27.3 g was heated to

98.90 °C and then dropped into 15.0 g of water at

22.50 °C. The final temperature was 26.32 °C. Calculate

the specific heat capacity of lead from these data.

84. A 192-g piece of copper is heated to 100.0 °C in a

boiling water bath and then dropped into a beaker

containing 751 g of water (density = 1.00 g/cm3) at

4.0 °C. What was the final temperature of the copper

and water after thermal equilibrium was reached?

(CCu = 0.385 J/g ∙ K.)

85. Insoluble AgCl(s) precipitates when solutions of

AgNO3(aq) and NaCl(aq) are mixed.

AgNO3(aq) + NaCl(aq)  →  AgCl(s) + NaNO3(aq)

∆rH° = ?

To measure the energy evolved in this reaction, 250. mL

of 0.16 M AgNO3(aq) and 125 mL of 0.32 M NaCl(aq)

are mixed in a coffee-cup calorimeter. The temperature

of the mixture rises from 21.15 °C to 22.90 °C. Calculate

the enthalpy change for the precipitation of AgCl(s), in

kJ/mol. (Assume the density of the solution is 1.0 g/mL

and its specific heat capacity is 4.2 J/g ∙ K.)

86. Insoluble PbBr2(s) precipitates when solutions of

Pb(NO3)2(aq) and NaBr(aq) are mixed.

Pb(NO3)2(aq) + 2 NaBr(aq)  →  PbBr2(s) + 2 NaNO3(aq)

∆rH° = ?

To measure the enthalpy change, 200. mL of 0.75 M

Pb(NO3)2(aq) and 200. mL of 1.5 M NaBr(aq) are

mixed in a coffee-cup calorimeter. The temperature of

the mixture rises by 2.44 °C. Calculate the enthalpy

change for the precipitation of PbBr2(s), in kJ/mol.

(Assume the density of the solution is 1.0 g/mL, and its

specific heat capacity is 4.2 J/g ∙ K.)

87. The value of ∆U for the decomposition of 7.647 g of

ammonium nitrate can be measured in a bomb calorimeter. The reaction that occurs is

NH4NO3(s)  →  N2O(g) + 2 H2O(g)

The temperature of the calorimeter, which contains

415 g of water, increases from 18.90 °C to 20.72 °C. The

heat capacity of the bomb is 155 J/K. What is the value

of ∆U for this reaction, in kJ/mol?



© Cengage Learning/Charles D. Winters



Not all of the carbon available is converted to water gas

since some is burned to provide the heat for the endothermic reaction of carbon and water. What mass of

carbon must be burned (to CO2 gas) to provide the

energy to convert 1.00 kg of carbon to water gas?



The decomposition of ammonium nitrate is clearly exothermic.



kotz_48288_05_0208-0251.indd 246



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