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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?
11/18/10 3:03 PM
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
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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.
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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)
11/18/10 3:03 PM
240
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
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▲ 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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242
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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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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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.
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