CHAPTER 6 ENERGY RELATIONSHIPS IN CHEMICAL REACTIONS

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CHAPTER 6
ENERGY RELATIONSHIPS IN
CHEMICAL REACTIONS
6.1
The system is the specific part of the universe that is of interest to us. The surroundings are the rest of the
universe outside the system. An open system can exchange mass and energy, usually in the form of heat with
its surroundings. A closed system allows the transfer of energy (heat) but not mass. An isolated system does
not allow the transfer of either mass or energy. Thermal energy is the energy associated with the random
motion of atoms and molecules. Chemical energy is stored within the structural units of chemical substances.
Potential energy is energy available by virtue of an object’s position. Kinetic energy is the energy produced
by a moving object. The law of conservation of energy states that the total quantity of energy in the universe
is assumed constant.
6.2
Heat is the transfer of thermal energy between two bodies that are at different temperatures. Thermal energy
is the energy associated with the random motion of atoms and molecules.
6.3
The units of energy commonly employed in chemistry are the Joule (J) and the kilojoule (kJ).
6.4
No, the kinetic energy of motion is converted to heat through the friction between the brakes, wheels, tires,
and the road.
6.5
Turning on a flashlight converts chemical energy to electrical energy to electromagnetic energy, which
includes visible light and infrared (heat) radiation.
6.6
(a)
(b)
(c)
(d)
6.7
Thermochemistry is the study of heat change in chemical reactions. An exothermic process is any process
that gives off heatthat is, transfers thermal energy to the surroundings. In an endothermic process, heat has
to be supplied to the system by the surroundings.
6.8
The law of conservation of energy.
6.9
The combustion of methane and the freezing of water are exothermic processes. The decomposition of
limestone (CaCO3) and the vaporization of water are endothermic processes.
6.10
To decompose a substance, bonds must be broken (an endothermic process). In combination reactions,
bonds are formed (an exothermic process).
6.11
The first law of thermodynamics is based on the law of conservation of energy. The sign conventions for q
and w are as follows: q is positive for an endothermic process and negative for an exothermic process, and w
is positive for work done on the system by the surroundings and negative for work done by the system on the
surroundings.
Mechanical energy to potential energy to kinetic energy.
Chemical energy to electrical energy to electromagnetic energy.
Mechanical energy to potential energy to kinetic energy.
Chemical energy to thermal energy
130
CHAPTER 6: ENERGY RELATIONSHIPS IN CHEMICAL REACTIONS
6.12
State functions are properties that are determined by the state of the system, regardless of how that condition
was achieved. Energy and temperature are state functions. Work and heat are not state functions.
6.13
(a) Yes. (b) q > 0. Heat absorbed by the gas from the surroundings enables the gas to expand at constant
temperature. (c) U = 0. Note that the internal energy of an ideal gas depends only on temperature.
Because there is no change in temperature, there is no change in internal energy of the gas.
6.14
In (a) and (c), work is done by the system on the surroundings. In (b), work is done by the surroundings on
the system. In (d), no work is done.
6.15
Recall that the work in gas expansion is equal to the product of the external, opposing pressure and the
change in volume.
(a)
w  PV
w  (0)(5.4  1.6)L  0
(b)
w  PV
w  (0.80 atm)(5.4  1.6)L  3.0 Latm
To convert the answer to joules, we write
w   3.0 L  atm 
(c)
101.3 J
  3.0  102 J
1 L  atm
w  PV
w  (3.7 atm)(5.4  1.6)L  14 Latm
To convert the answer to joules, we write
w   14 L  atm 
6.16
(a)
101.3 J
  1.4  103 J
1 L  atm
Because the external pressure is zero, no work is done in the expansion.
w  PV  (0)(89.3  26.7)mL
w  0
(b)
The external, opposing pressure is 1.5 atm, so
w  PV  (1.5 atm)(89.3  26.7)mL
w   94 mL  atm 
0.001 L
  0.094 L  atm
1 mL
To convert the answer to joules, we write:
w   0.094 L  atm 
101.3 J
  9.5 J
1 L  atm
CHAPTER 6: ENERGY RELATIONSHIPS IN CHEMICAL REACTIONS
(c)
131
The external, opposing pressure is 2.8 atm, so
w  PV  (2.8 atm)(89.3  26.7)mL
w  (1.8  102 mL  atm) 
0.001 L
  0.18 L  atm
1 mL
To convert the answer to joules, we write:
w   0.18 L  atm 
101.3 J
  18 J
1 L  atm
6.17
An expansion implies an increase in volume, therefore w must be 325 J (see the defining equation for
pressure-volume work.) If the system absorbs heat, q must be 127 J. The change in energy (internal
energy) is:
U  q  w  127 J  325 J  198 J
6.18
Strategy: Compression is work done on the gas, so what is the sign for w? Heat is released by the gas to
the surroundings. Is this an endothermic or exothermic process? What is the sign for q?
Solution: To calculate the energy change of the gas (U), we need Equation (6.1) of the text. Work of
compression is positive and because heat is given off by the gas, q is negative. Therefore, we have:
U  q  w  26 J  74 J  48 J
As a result, the energy of the gas increases by 48 J.
6.19
We first find the number of moles of hydrogen gas formed in the reaction:
50.0 g Sn 
1 mol H 2
1 mol Sn

 0.421 mol H 2
118.7 g Sn 1 mol Sn
The next step is to find the volume occupied by the hydrogen gas under the given conditions. This is the
change in volume.
V 
nRT
(0.421 mol)(0.0821 L  atm / K  mol)(298 K)

 10.3 L H 2
P
1.00 atm
The pressure-volume work done is then:
w   PV   (1.00 atm)(10.3 L)   10.3 L  atm 
6.20
101.3 J
  1.04  103 J
1 L  atm
Strategy: The work done in gas expansion is equal to the product of the external, opposing pressure and
the change in volume.
w  PV
We assume that the volume of liquid water is zero compared to that of steam. How do we calculate the
volume of the steam? What is the conversion factor between Latm and J?
132
CHAPTER 6: ENERGY RELATIONSHIPS IN CHEMICAL REACTIONS
Solution: First, we need to calculate the volume that the water vapor will occupy (Vf).
Using the ideal gas equation:
VH 2O 
nH 2O RT
P
L  atm 

(1 mol)  0.0821
(373 K)
mol  K 

=
 31 L
(1.0 atm)
It is given that the volume occupied by liquid water is negligible. Therefore,
V  Vf  Vi  31 L  0 L  31 L
Now, we substitute P and V into Equation (6.3) of the text to solve for w.
w  PV  (1.0 atm)(31 L)  31 Latm
The problems asks for the work done in units of joules. The following conversion factor can be obtained
from Appendix 1 of the text.
1 Latm  101.3 J
Thus, we can write:
w   31 L  atm 
101.3 J
  3.1  103 J
1 L  atm
Check: Because this is gas expansion (work is done by the system on the surroundings), the work done has
a negative sign.
6.21
Enthalpy is a thermodynamic quantity used to describe heat changes taking place at constant pressure. The
enthalpy of reaction, H, is the difference between the enthalpies of the products and the enthalpies of the
reactants. At constant pressure, the heat of reaction is equal to the enthalpy change of the same reaction.
6.22
The amount of heat absorbed or released in a reaction will depend on the physical states of each substance.
6.23
This is an exothermic process. When four moles of NH3(g) react with 5 moles of O2(g) to produce four
moles of NO(g) and six moles of H2O(g), 904 kJ of thermal energy is released.
6.24
(a) 2905.6 kJ
6.25
The equation as written shows that 805.6 kJ of heat is released when two moles of CuS react. We want to
calculate the amount of heat released when 1 g of CuS reacts.
(c) 1276.8 kJ
(b) +1452.8 kJ
The heat evolved per gram of CuS roasted is:
heat evolved =
6.26
805.6 kJ
1 mol CuS

 4.213 kJ / g CuS
2 mol CuS 95.62 g CuS
Strategy: The thermochemical equation shows that for every 2 moles of NO2 produced, 114.6 kJ of heat
are given off (note the negative sign). We can write a conversion factor from this information.
114.6 kJ
2 mol NO2
4
How many moles of NO2 are in 1.26  10 g of NO2? What conversion factor is needed to convert between
grams and moles?
CHAPTER 6: ENERGY RELATIONSHIPS IN CHEMICAL REACTIONS
133
4
Solution: We need to first calculate the number of moles of NO2 in 1.26  10 g of the compound. Then,
we can convert to the number of kilojoules produced from the exothermic reaction. The sequence of
conversions is:
grams of NO2  moles of NO2  kilojoules of heat generated
Therefore, the heat change is:
(1.26  104 g NO2 ) 
1 mol NO2
114.6 kJ

  1.57  104 kJ
46.01 g NO 2 2 mol NO2
4
This is an exothermic reaction. The amount of heat given off is 1.57 × 10 kJ.
6.27
We can calculate U using Equation (6.10) of the text.
U  H − RTn
We initially have 2.0 moles of gas. Since our products are 2.0 moles of H2 and 1.0 mole of O2, there is a net
gain of 1 mole of gas (2 reactant  3 product). Thus, n  1. Looking at the equation given in the problem,
it requires 483.6 kJ to decompose 2.0 moles of water (H  483.6 kJ). Substituting into the above equation:
3
U  483.6  10 J/mol − (8.314 J/molK)(398 K)(1)
5
2
U  4.80  10 J/mol  4.80  10 kJ/mol
6.28
We initially have 6 moles of gas (3 moles of chlorine and 3 moles of hydrogen). Since our product is 6
moles of hydrogen chloride, there is no change in the number of moles of gas. Therefore there is no volume
change; V  0.
w  PV  (1 atm)(0 L)  0
U  H  PV
PV  0, so
U  H

H  3H rxn
 3(184.6 kJ/mol)  553.8 kJ/mol

We need to multiply H rxn
by three, because the question involves the formation of 6 moles of HCl;
whereas, the equation as written only produces 2 moles of HCl.
U  H  553.8 kJ/mol
6.29
The specific heat (s) of a substance is the amount of heat required to raise the temperature of one gram of the
substance by one degree Celsius. The heat capacity (C) of a substance is the amount of heat required to raise
the temperature of a given quantity of the substance by one degree Celsius. Units of specific heat are J/gC,
and units of heat capacity are J/C. Specific heat is an intensive property; whereas, heat capacity is an
extensive property.
6.30
Calorimetry is the measurement of heat changes. Constant-volume and constant-pressure are two types of
calorimetry. We need to know the amount of heat absorbed per degree Celsius change (heat capacity) of the
calorimeter so that the heat change of the reaction can be determined. The heat capacity of the calorimeter is
determined by calibrating it by burning a substance with an accurately know heat of combustion.
134
CHAPTER 6: ENERGY RELATIONSHIPS IN CHEMICAL REACTIONS
6.31
Choice (d) will take place when the two metals are brought into contact. Heat will flow from Cu to Al
because Cu is at a higher temperature. The definition of heat is the transfer of thermal energy between two
bodies that are at different temperatures.
6.32
Specific heat of a substance is the amount of heat required to raise the temperature of one gram of the
substance one degree Celsius. Comparing two substances of equal mass, the substance with a larger specific
heat will require that more heat be applied to raise its temperature a given amount. Therefore, under the same
heating conditions, it will take longer for metal A to reach a temperature of 21°C.
6.33
Specific heat 
6.34
q  mCusCut  (6.22  10 g)(0.385 J/gC)(324.3C  20.5C)  7.28  10 J  728 kJ
6.35
See Table 6.2 of the text for the specific heat of Hg.
C
85.7 J/ C

 0.237 J / g  C
m
362 g
3
5
3
q  mst  (366 g)(0.139 J/g·C)(12.0  77.0)C  3.31  10 J  3.31 kJ
6.36
Strategy: We know the masses of gold and iron as well as the initial temperatures of each. We can look up
the specific heats of gold and iron in Table 6.2 of the text. Assuming no heat is lost to the surroundings, we
can equate the heat lost by the iron sheet to the heat gained by the gold sheet. With this information, we can
solve for the final temperature of the combined metals.
Solution: Treating the calorimeter as an isolated system (no heat lost to the surroundings), we can write:
or
qAu  qFe  0
qAu  qFe
The heat gained by the gold sheet is given by:
qAu  mAusAut  (10.0 g)(0.129 J/gC)(tf  18.0)C
where m and s are the mass and specific heat, and t  tfinal  tinitial.
The heat lost by the iron sheet is given by:
qFe  mFesFet  (20.0 g)(0.444 J/gC)(tf  55.6)C
Substituting into the equation derived above, we can solve for tf.
qAu  qFe
(10.0 g)(0.129 J/gC)(tf  18.0)C  (20.0 g)(0.444 J/gC)(tf  55.6)C
1.29 tf  23.2  8.88 tf  494
10.2 tf  517
tf  50.7C
Check: Must the final temperature be between the two starting values?
CHAPTER 6: ENERGY RELATIONSHIPS IN CHEMICAL REACTIONS
6.37
135
The heat gained by the calorimeter is:
q  Cpt
q  (3024 J/C)(1.126C)  3.405  103 J
The amount of heat given off by burning Mg in kJ/g is:
(3.405  103 J) 
1 kJ
1

 24.76 kJ/g Mg
1000 J 0.1375 g Mg
The amount of heat given off by burning Mg in kJ/mol is:
24.76 kJ 24.31 g Mg

 601.9 kJ/mol Mg
1 g Mg
1 mol Mg
If the reaction were endothermic, what would happen to the temperature of the calorimeter and the water?
6.38

Strategy: The neutralization reaction is exothermic. 56.2 kJ of heat are released when 1 mole of H reacts

with 1 mole of OH . Assuming no heat is lost to the surroundings, we can equate the heat lost by the
reaction
to the heat gained by the combined solution. How do we calculate the heat released during the reaction? Are


we reacting 1 mole of H with 1 mole of OH ? How do we calculate the heat absorbed by the combined
solution?
Solution: Assuming no heat is lost to the surroundings, we can write:
or
qsoln  qrxn  0
qsoln  qrxn
First, let's set up how we would calculate the heat gained by the solution,
qsoln  msolnssolnt
where m and s are the mass and specific heat of the solution and t  tf  ti.
We assume that the specific heat of the solution is the same as the specific heat of water, and we assume that
the density of the solution is the same as the density of water (1.00 g/mL). Since the density is 1.00 g/mL,
the mass of 400 mL of solution (200 mL  200 mL) is 400 g.
Substituting into the equation above, the heat gained by the solution can be represented as:
2
qsoln  (4.00  10 g)(4.184 J/gC)(tf  20.48C)
Next, let's calculate qrxn, the heat released when 200 mL of 0.862 M HCl are mixed with 200 mL of 0.431 M
Ba(OH)2. The equation for the neutralization is:
2HCl(aq)  Ba(OH)2(aq) 
 2H2O(l)  BaCl2(aq)
There is exactly enough Ba(OH)2 to neutralize all the HCl. Note that 2 mole HCl  1 mole Ba(OH)2, and
that the concentration of HCl is double the concentration of Ba(OH)2. The number of moles of HCl is:
(2.00  102 mL) 
0.862 mol HCl
 0.172 mol HCl
1000 mL
136
CHAPTER 6: ENERGY RELATIONSHIPS IN CHEMICAL REACTIONS

The amount of heat released when 1 mole of H is reacted is given in the problem (56.2 kJ/mol). The

amount of heat liberated when 0.172 mole of H is reacted is:
qrxn  0.172 mol 
56.2  103 J
  9.67  103 J
1 mol
Finally, knowing that the heat lost by the reaction equals the heat gained by the solution, we can solve for the
final temperature of the mixed solution.
qsoln  qrxn
2
3
(4.00  10 g)(4.184 J/gC)(tf  20.48C)  (9.67  10 J)
3
4
3
(1.67  10 )tf  (3.43  10 )  9.67  10 J
tf  26.3C
6.39
Substances are said to be in the standard state at 1 atmosphere of pressure.
6.40
By convention, the standard enthalpy of formation of any element in its most stable form is zero. The
standard enthalpy of formation of a compound is the heat change when 1 mole of the compound is formed
from its elements at a pressure of 1 atm.
6.41
The standard enthalpy of reaction, H rxn , is defined as the enthalpy of a reaction carried out at 1 atmosphere

pressure.
6.42

H rxn
= nHf(products)  mHf(reactants), where m and n denote the stoichiometric coefficients (in
moles) for the reactants and products, Hf is the standard enthalpy of formation, and  (sigma) means “the
sum of.”
6.43
Hess’s law can be stated as follows: When reactants are converted to products, the change in enthalpy is the
same whether the reaction takes place in one step or in a series of steps. The law enables us to determine the
standard enthalpy of formation of a compound from its elements by an indirect route when direct
combination of the elements is not feasible. Using Hess’s law, the standard enthalpy change for the reaction
of interest can be easily calculated.
6.44
See the example for CH4 given in Section 6.6 of the text. To determine the standard enthalpy of formation of
methane, the heat of combustion of methane along with the heats of combustion of carbon and hydrogen are
used.
6.45
CH4(g) and H(g). All the other choices are elements in their most stable form ( H f  0 ). The most stable
form of hydrogen is H2(g).
6.46
The standard enthalpy of formation of any element in its most stable form is zero. Therefore, since
H f (O2 )  0, O2 is the more stable form of the element oxygen at this temperature.
CHAPTER 6: ENERGY RELATIONSHIPS IN CHEMICAL REACTIONS
6.47
H2O(l)  H2O(g)
137
Endothermic

H rxn
 H f [H 2 O( g )]  H f [H 2 O(l )]  0

H f [H 2O( l )] is more negative since H rxn
 0.
You could also solve the problem by realizing that H2O(l) is the stable form of water at 25C, and therefore
will have the more negative H f value.
6.48
(a)
Br2(l) is the most stable form of bromine at 25C; therefore, H f [Br2 (l )]  0. Since Br2(g) is less
stable than Br2(l), H f [Br2 ( g )]  0.
(b)
I2(s) is the most stable form of iodine at 25C; therefore, H f [I2 ( s )]  0. Since I2(g) is less stable
than I2(s), H f [I2 ( g )]  0.
6.49
2H2O2(l)  2H2O(l)  O2(g)
H2O2(l) has a tendency to decompose because H2O(l) has a more negative H f than H2O2(l).
6.50
Strategy: What is the reaction for the formation of Ag2O from its elements? What is the Hf value for an
element in its standard state?
Solution: The balanced equation showing the formation of Ag2O(s) from its elements is:
2Ag(s) 
1
2
O2(g) 
 Ag2O(s)
Knowing that the standard enthalpy of formation of any element in its most stable form is zero, and using
Equation (6.18) of the text, we write:

H rxn
  nH f (products)   mH f (reactants)

H rxn
 [H f (Ag 2 O)]  [2H f (Ag) 
1 H  (O )]
f
2
2

H rxn
 [H f (Ag 2 O)]  [0  0]

H f (Ag 2O)  H rxn

In a similar manner, you should be able to show that H f (CaCl 2 )  H rxn
for the reaction
Ca(s)  Cl2(g) 
 CaCl2(s)
6.51
H   [H f (CaO)  H f (CO2 )]  H f (CaCO3 )
H  [(1)(635.6 kJ/mol)  (1)(393.5 kJ/mol)]  (1)(1206.9 kJ/mol)  177.8 kJ/mol
138
CHAPTER 6: ENERGY RELATIONSHIPS IN CHEMICAL REACTIONS
6.52
Strategy: The enthalpy of a reaction is the difference between the sum of the enthalpies of the products and
the sum of the enthalpies of the reactants. The enthalpy of each species (reactant or product) is given by the
product of the stoichiometric coefficient and the standard enthalpy of formation, Hf , of the species.
Solution: We use the Hf values in Appendix 2 and Equation (6.18) of the text.

H rxn
  nH f (products)   mH f (reactants)
(a)


HCl(g)  H (aq)  Cl (aq)

H rxn
 H f (H  )  H f (Cl )  H f (HCl)

74.9 kJ/mol  0  H f (Cl )  (1)(92.3 kJ/mol)
H f (Cl  )   167.2 kJ/mol
(b)
The neutralization reaction is:

and,

H (aq)  OH (aq)  H2O(l)

H rxn
 H f [H 2 O(l )]  [H f (H  )  H f (OH  )]
H f [H 2 O(l )]   285.8 kJ/mol (See Appendix 2 of the text.)

H rxn
 (1)(285.8 kJ/mol)  [(1)(0 kJ/mol)  (1)(229.6 kJ/mol)]  56.2 kJ/mol
6.53
(a)
H   2H f (H 2 O)  2H f (H 2 )  H f (O 2 )
H  (2)(285.8 kJ/mol)  (2)(0)  (1)(0)  571.6 kJ/mol
(b)
H   4H f (CO 2 )  2H f (H 2 O)  2H f (C2 H 2 )  5H f (O 2 )
H  (4)(393.5 kJ/mol)  (2)(285.8 kJ/mol)  (2)(226.6 kJ/mol)  (5)(0)  2599 kJ/mol
6.54
(a)
H  = [2H f (CO2 )  2H f (H 2 O)]  [H f (C2 H 4 )  3H f (O2 )] ]
H  [(2)(393.5 kJ/mol)  (2)(285.8 kJ/mol)]  [(1)(52.3 kJ/mol)  (3)(0)]
H  1410.9 kJ/mol
(b)
H  = [2H f (H 2 O)  2H f (SO2 )]  [2H f (H 2S)  3H f (O 2 )]
H  [(2)(285.8 kJ/mol)  (2)(296.1 kJ/mol)]  [(2)(20.15 kJ/mol)  (3)(0)]
H  1123.5 kJ/mol
6.55
The given enthalpies are in units of kJ/g. We must convert them to units of kJ/mol.
(a)
22.6 kJ 32.04 g

  724 kJ/mol
1g
1 mol
(b)
29.7 kJ 46.07 g

  1.37  103 kJ/mol
1g
1 mol
CHAPTER 6: ENERGY RELATIONSHIPS IN CHEMICAL REACTIONS
(c)
6.56
33.4 kJ 60.09 g

  2.01  103 kJ/mol
1g
1 mol

H rxn
  nH f (products)   mH f (reactants)
The reaction is:
H2(g) 
 H(g)  H(g)
and,

H rxn
 [H f (H)  H f (H)]  H f (H 2 )
H f (H 2 )  0

H rxn
 436.4 kJ/mol  2H f (H)  (1)(0)
H f (H) 
6.57
436.4 kJ/mol
 218.2 kJ/mol
2
H   6H f (CO 2 )  6H f (H 2 O)  [H f (C6 H12 )  9H f (O 2 )]
H  (6)(393.5 kJ/mol)  (6)(285.8 kJ/mol)  (1)(151.9 kJ/mol)  (l)(0)
 3924 kJ/mol
Why is the standard heat of formation of oxygen zero?
6.58
The equation as written shows that 879 kJ of heat is released when two moles of ZnS react. We want to
calculate the amount of heat released when 1 g of ZnS reacts.
Let H be the heat change per gram of ZnS roasted. We write:
H  
879 kJ
1 mol ZnS

  4.51 kJ/g ZnS
2 mol ZnS 97.46 g ZnS
This is an exothermic reaction. The amount of heat evolved per gram of ZnS roasted is 4.51 kJ/g ZnS.
6.59
4
This is an exothermic reaction. The amount of heat given off when 1.26 × 10 g of NH3 are produced is:
(1.26  104 g NH3 ) 
6.60
1 mol NH3
92.6 kJ

 3.43  104 kJ
17.03 g NH3 2 mol NH3

H rxn
  nH f (products)   mH f (reactants)
The balanced equation for the reaction is:
CaCO3(s) 
 CaO(s)  CO2(g)

H rxn
 [H f (CaO)  H f (CO 2 )]  H f (CaCO3 )

H rxn
 [(1)(635.6 kJ/mol)  (1)(393.5 kJ/mol)]  (1)(1206.9 kJ/mol)  177.8 kJ/mol
139
140
CHAPTER 6: ENERGY RELATIONSHIPS IN CHEMICAL REACTIONS
The enthalpy change calculated above is the enthalpy change if 1 mole of CO2 is produced. The problem
asks for the enthalpy change if 66.8 g of CO2 are produced. We need to use the molar mass of CO2 as a
conversion factor.
H   66.8 g CO 2 
6.61
1 mol CO 2
177.8 kJ

 2.70  102 kJ
44.01 g CO 2 1 mol CO 2
H (kJ/mol)
Reaction
S(rhombic)  O2(g)  SO2(g)
SO2(g)  S(monoclinic)  O2(g)
S(rhombic)  S(monoclinic)
296.06
296.36

H rxn
 0.30 kJ/mol
Which is the more stable allotropic form of sulfur?
6.62
Strategy: Our goal is to calculate the enthalpy change for the formation of C2H6 from is elements C and
H2. This reaction does not occur directly, however, so we must use an indirect route using the information
given in the three equations, which we will call equations (a), (b), and (c).
Solution: Here is the equation for the formation of C2H6 from its elements.

H rxn
 ?
 C2H6(g)
2C(graphite)  3H2(g) 
Looking at this reaction, we need two moles of graphite as a reactant. So, we multiply Equation (a) by two to
obtain:
(d)

H rxn
 2(393.5 kJ/mol)   787.0 kJ/mol
2C(graphite)  2O2(g) 
 2CO2(g)
Next, we need three moles of H2 as a reactant. So, we multiply Equation (b) by three to obtain:
(e)
3H2(g) 
3
2

H rxn
 3(285.8 kJ/mol)   857.4 kJ/mol
O2(g) 
 3H2O(l)
Last, we need one mole of C2H6 as a product. Equation (c) has two moles of C2H6 as a reactant, so we need
to reverse the equation and divide it by 2.
(f)
2CO2(g)  3H2O(l) 
 C2H6(g) 
7
2
O2(g)

H rxn

1 (3119.6
2
kJ/mol)  1559.8 kJ/mol
Adding Equations (d), (e), and (f) together, we have:
H (kJ/mol)
Reaction
(d)
2C(graphite)  2O2(g) 
 2CO2(g)
(e)
3H2(g) 
(f)
 C2H6(g) 
2CO2(g)  3H2O(l) 
3
2
787.0
O2(g) 
 3H2O(l)
857.4
7
2
2C(graphite)  3H2(g) 
 C2H6(g)
O2(g)
1559.8
H  84.6 kJ/mol
CHAPTER 6: ENERGY RELATIONSHIPS IN CHEMICAL REACTIONS
6.63
141
H (kJ/mol)
Reaction
CO2(g)  2H2O(l)  CH3OH(l) 
3
2
O2(g)
726.4
C(graphite)  O2(g)  CO2(g)
2H2(g)  O2(g)  2H2O(l)
C(graphite)  2H2(g) 
1
2
393.5
2(285.8)

H rxn
  238.7 kJ/mol
O2(g)  CH3OH(l)

. In this case, the
We have just calculated an enthalpy at standard conditions, which we abbreviate H rxn
reaction in question was for the formation of one mole of CH3OH from its elements in their standard state.

that we calculated is also, by definition, the standard heat of formation H f of
Therefore, the H rxn
CH3OH (238.7 kJ/mol).
6.64
The second and third equations can be combined to give the first equation.
2Al(s) 
3
2
O2(g ) 
 Al2O3(s)
3
2
 2Fe(s) 
Fe2O3(s) 
H  1669.8 kJ/mol
H  822.2 kJ/mol
O2(g)
2Al(s)  Fe2O3(s) 
 2Fe(s)  Al2O3(s)
H  847.6 kJ/mol
6.65
In a chemical reaction the same elements and the same numbers of atoms are always on both sides of the
equation. This provides a consistent reference which allows the energy change in the reaction to be
interpreted in terms of the chemical or physical changes that have occurred. In a nuclear reaction the same
elements are not always on both sides of the equation and no common reference point exists.
6.66
Rearrange the equations as necessary so they can be added to yield the desired equation.
6.67
2B 
 A
H1
 C
A 
H2
2B 
 C
H  H2  H1
The reaction corresponding to standard enthalpy of formation, H f , of AgNO2(s) is:
Ag(s) 
1
2
N2(g)  O2(g)  AgNO2(s)
Rather than measuring the enthalpy directly, we can use the enthalpy of formation of AgNO3(s) and the

H rxn
provided.
AgNO3(s)  AgNO2(s) 

H rxn
 H f (AgNO2 ) 
1
2
O2(g)
1 H  (O )
f
2
2
 H f (AgNO3 )
78.67 kJ/mol  H f (AgNO2)  0  (123.02 kJ/mol)
H f (AgNO 2 )   44.35 kJ/mol
142
CHAPTER 6: ENERGY RELATIONSHIPS IN CHEMICAL REACTIONS
6.68
(a)

H rxn
  nH f (products)   mH f (reactants)

H rxn
 [4H f (NH3 )  H f (N 2 )]  3H f (N 2 H 4 )

H rxn
 [(4)(46.3 kJ/mol)  (0)]  (3)(50.42 kJ/mol)   336.5 kJ/mol
(b)
The balanced equations are:
(1)
N2H4(l)  O2(g) 
 N2(g)  2H2O(l)
(2)
4NH3(g)  3O2(g) 
 2N2(g)  6H2O(l)
The standard enthalpy change for equation (1) is:

H rxn
 H f (N 2 )  2H f [H 2 O(l )]  {H f [N 2 H 4 (l )]  H f (O2 )}

ΔH rxn
 [(1)(0)  (2)(285.8 kJ/mol)]  [(1)(50.42 kJ/mol)  (1)(0)]  622.0 kJ/mol
The standard enthalpy change for equation (2) is:

H rxn
 [2H f (N 2 )  6H f (H 2 O)]  [4H f (NH3 )  3H f (O2 )]

ΔH rxn
 [(2)(0)  (6)(285.8 kJ/mol)]  [(4)(46.3 kJ/mol)  (3)(0)]  1529.6 kJ/mol

We can now calculate the enthalpy change per kilogram of each substance. H rxn
above is in units of
kJ/mol. We need to convert to kJ/kg.

N 2 H 4 (l ): H rxn

1 mol N 2 H 4
622.0 kJ
1000 g


  1.941  104 kJ / kg N 2 H 4
1 mol N 2 H 4 32.05 g N 2 H 4
1 kg

NH3 ( g ): H rxn

1 mol NH3
1529.6 kJ
1000 g


  2.245  104 kJ / kg NH3
4 mol NH3 17.03 g NH3
1 kg
Since ammonia, NH3, releases more energy per kilogram of substance, it would be a better fuel.
6.69
We initially have 8 moles of gas (2 of nitrogen and 6 of hydrogen). Since our product is 4 moles of
ammonia, there is a net loss of 4 moles of gas (8 reactant  4 product). The corresponding volume loss is
V 
nRT
(4.0 mol)(0.0821 L  atm / K  mol)(298 K)

 98 L
P
1 atm
w   PV   (1 atm)(98 L)  98 L  atm 
H  U  PV
or
101.3 J
 9.9  103 J  9.9 kJ
1 L  atm
U  H  PV
Using H as 185.2 kJ  (2  92.6 kJ), (because the question involves the formation of 4 moles of ammonia,
not 2 moles of ammonia for which the standard enthalpy is given in the question), and PV as 9.9 kJ (for
which we just solved):
U  185.2 kJ  9.9 kJ  175.3 kJ
CHAPTER 6: ENERGY RELATIONSHIPS IN CHEMICAL REACTIONS
6.70
143
The reaction is, 2Na(s)  Cl2(g)  2NaCl(s). First, let's calculate H for this reaction using H f values
in Appendix 2.

H rxn
 2H f (NaCl)  [2H f (Na)  H f (Cl2 )]

H rxn
 2(411.0 kJ/mol)  [2(0)  0]   822.0 kJ/mol
This is the amount of heat released when 1 mole of Cl2 reacts (see balanced equation). We are not reacting
1 mole of Cl2, however. From the volume and density of Cl2, we can calculate grams of Cl2. Then, using the
molar mass of Cl2 as a conversion factor, we can calculate moles of Cl2. Combining these two calculations
into one step, we find moles of Cl2 to be:
2.00 L Cl2 
1.88 g Cl2
1 mol Cl2

 0.0530 mol Cl2
1 L Cl2
70.90 g Cl2

Finally, we can use the H rxn
calculated above to find the heat change when 0.0530 mole of Cl2 reacts.
0.0530 mol Cl2 
822.0 kJ
  43.6 kJ
1 mol Cl2
This reaction is exothermic. The amount of heat released is 43.6 kJ.
6.71
(a)

Although we cannot measure H rxn
for this reaction, the reverse process, is the combustion of

glucose. We could easily measure H rxn
for this combustion in a bomb calorimeter.
C6H12O6(s)  6O2(g) 
 6CO2(g)  6H2O(l)
(b)

We can calculate H rxn
using standard enthalpies of formation.

H rxn
 H f [C6 H12 O6 ( s )]  6H f [O 2 ( g )]  {6H f [CO 2 ( g )]  6H f [H 2 O(l )]}

H rxn
 [(1)(1274.5 kJ/mol)  0]  [(6)(393.5 kJ/mol)  (6)(285.8 kJ/mol)]  2801.3 kJ/mol

H rxn
has units of kJ/1 mol glucose. We want the H change for 7.0  10
calculate how many moles of glucose are in 7.0  10
following strategy to solve the problem.
14
14
kg glucose. We need to
kg glucose. You should come up with the
kg glucose  g glucose  mol glucose  kJ (H)
H   (7.0  1014 kg) 
1 mol C6 H12 O6
1000 g
2801.3 kJ


 1.1  1019 kJ
1 kg
180.16 g C6 H12 O6 1 mol C6 H12 O6
6.72
The initial and final states of this system are identical. Since enthalpy is a state function, its value depends
only upon the state of the system. The enthalpy change is zero.
6.73
From the balanced equation we see that there is a 1:2 mole ratio between hydrogen and sodium. The number
of moles of hydrogen produced is:
0.34 g Na 
1 mol H 2
1 mol Na

 7.4  103 mol H 2
22.99 g Na 2 mol Na
144
CHAPTER 6: ENERGY RELATIONSHIPS IN CHEMICAL REACTIONS
Using the ideal gas equation, we write:
V 
nRT
(7.4  103 mol)(0.0821 L  atm / K  mol)(273 K)

 0.17 L H 2
P
(1 atm)
V  0.17 L
w   PV   (1.0 atm)(0.17 L)   0.17 L  atm 
6.74
H(g)  Br(g) 
 HBr(g)
101.3 J
  17 J
1 L  atm

H rxn
 ?
Rearrange the equations as necessary so they can be added to yield the desired equation.
H(g) 


Br(g) 
1
2
H2(g) 
1
2
1
2
1
2
H2(g)
Br2(g)
Br2(g) 
 HBr(g)
H(g)  Br(g) 
 HBr(g)
6.75

H rxn

1 ( 436.4
2
kJ/mol)   218.2 kJ/mol

H rxn

1 (192.5
2
kJ/mol)   96.25 kJ/mol

H rxn

1 (72.4
2
kJ/mol)   36.2 kJ/mol
H  350.7 kJ/mol
Using the balanced equation, we can write:

H rxn
 [2H f (CO 2 )  4H f (H 2 O)]  [2H f (CH3OH)  3H f (O 2 )]
1452.8 kJ/mol  (2)(393.5 kJ/mol)  (4)(285.8 kJ/mol)  (2) H f (CH3OH)  (3)(0 kJ/mol)
477.4 kJ/mol  (2) H f (CH3OH)
H f (CH3OH)  238.7 kJ/mol
6.76
qsystem  0  qmetal  qwater  qcalorimeter
qmetal  qwater  qcalorimeter  0
mmetalsmetal(tfinal  tinitial)  mwaterswater(tfinal  tinitial)  Ccalorimeter(tfinal  tinitial)  0
All the needed values are given in the problem. All you need to do is plug in the values and solve for smetal.
(44.0 g)(smetal)(28.4  99.0)C  (80.0 g)(4.184 J/gC)(28.4  24.0)C  (12.4 J/C)(28.4  24.0)C  0
3
3
(3.11  10 )smetal (gC)  1.53  10 J
smetal  0.492 J/gC
6.77
The original volume of ammonia is:
(a)
V 
nRT
(1.00 mol)(0.0821 L  atm / K  mol)(298 K)

 1.75 L NH3
P
14.0 atm
T2 
P2V2T1
(1 atm)(23.5 L)(298 K)

 286 K
(14.0 atm)(1.75 L)
PV
1 1
CHAPTER 6: ENERGY RELATIONSHIPS IN CHEMICAL REACTIONS
(b)
145
t  (286  298)C  12C
q  mst  (17.03 g)(0.0258 J/gC)(12C)  5.27 J
w   PV   (1 atm)(23.5  1.75)L   21.75 L  atm 
3
101.3 J
  2.20  103 J
1 L  atm
3
U  q  w  5.27 J  (2.20  10 J)  2.21  10 J  2.21 kJ
6.78
A good starting point would be to calculate the standard enthalpy for both reactions.
Calculate the standard enthalpy for the reaction:
C(s) 
1
2
O2(g) 
 CO(g)
This reaction corresponds to the standard enthalpy of formation of CO, so we use the value of 110.5 kJ/mol
(see Appendix 2 of the text).
Calculate the standard enthalpy for the reaction:
 CO(g)  H2(g)
C(s)  H2O(g) 

H rxn
 [H f (CO)  H f (H 2 )]  [H f (C)  H f (H 2 O)]

H rxn
 [(1)(110.5 kJ/mol)  (1)(0)]  [(1)(0)  (1)(241.8 kJ/mol)]  131.3 kJ/mol
The first reaction, which is exothermic, can be used to promote the second reaction, which is endothermic.
Thus, the two gases are produced alternately.
6.79
As energy consumers, we are interested in the availability of usable energy.
6.80
First, calculate the energy produced by 1 mole of octane, C8H18.
C8H18(l) 
25
2
O2(g) 
 8CO2(g)  9H2O(l)

H rxn
 8H f (CO2 )  9H f [H 2 O(l )]  [H f (C8 H18 ) 
25 H  (O )]
f
2
2

H rxn
 [(8)(393.5 kJ/mol)  (9)(285.8 kJ/mol)]  [(1)(249.9 kJ/mol)  ( 25
)(0)]
2
 5470 kJ/mol

The problem asks for the energy produced by the combustion of 1 gallon of octane. H rxn
above has units
of kJ/mol octane. We need to convert from kJ/mol octane to kJ/gallon octane. The heat of combustion for
1 gallon of octane is:
H  
5470 kJ
1 mol octane
2660 g


  1.274  105 kJ / gal
1 mol octane 114.22 g octane
1 gal
The combustion of hydrogen corresponds to the standard heat of formation of water:
H2(g) 
1
2
O2(g) 
 H2O(l)

Thus, H rxn
is the same as H f for H2O(l), which has a value of 285.8 kJ/mol. The number of moles of
5
hydrogen required to produce 1.274  10 kJ of heat is:
nH 2  (1.274  105 kJ) 
1 mol H 2
 445.8 mol H 2
285.8 kJ
146
CHAPTER 6: ENERGY RELATIONSHIPS IN CHEMICAL REACTIONS
Finally, use the ideal gas law to calculate the volume of gas corresponding to 445.8 moles of H2 at 25C and
1 atm.
L  atm 

(445.8 mol)  0.0821
(298 K)
nH 2 RT
mol  K 

 1.09  104 L
=
VH 2 
(1 atm)
P
That is, the volume of hydrogen that is energy-equivalent to 1 gallon of gasoline is over 10,000 liters at
1 atm and 25C!
6.81
C2H6(l) 
The combustion reaction is:
7
2
O2(g) 
 2CO2(g)  3H2O(l)
The heat released during the combustion of 1 mole of ethane is:

H rxn
 [2H f (CO2 )  3H f (H 2 O)]  [H f (C2 H6 ) 
7 H  (O )]
f
2
2

H rxn
 [(2)(393.5 kJ/mol)  (3)(285.8 kJ/mol)]  [(1)(84.7 kJ/mol  ( 72 )(0)]
 1559.7 kJ/mol
The heat required to raise the temperature of the water to 98C is:
5
q  mH2O sH 2O t  (855 g)(4.184 J/gC)(98.0  25.0)C  2.61  10 J  261 kJ
The combustion of 1 mole of ethane produces 1559.7 kJ; the number of moles required to produce 261 kJ is:
261 kJ 
1 mol ethane
 0.167 mol ethane
1559.7 kJ
The volume of ethane is:
nRT
=
Vethane 
P
6.82
L  atm 

(0.167 mol)  0.0821
(296 K)
mol  K 

 4.10 L

1 atm 

752
mmHg


760 mmHg 

The heat gained by the liquid nitrogen must be equal to the heat lost by the water.
qN 2   qH 2O
If we can calculate the heat lost by the water, we can calculate the heat gained by 60.0 g of the nitrogen.
Heat lost by the water  qH2O = mH 2O sH2O t
2
4
q H 2O  (2.00  10 g)(4.184 J/gC)(41.0  55.3)C  1.20  10 J
The heat gained by 60.0 g nitrogen is the opposite sign of the heat lost by the water.
qN 2   qH 2O
qN 2  1.20  104 J
The problem asks for the molar heat of vaporization of liquid nitrogen. Above, we calculated the amount of
heat necessary to vaporize 60.0 g of liquid nitrogen. We need to convert from J/60.0 g N2 to J/mol N2.
H vap 
1.20  104 J 28.02 g N 2

 5.60  103 J/mol  5.60 kJ/mol
60.0 g N 2
1 mol N 2
CHAPTER 6: ENERGY RELATIONSHIPS IN CHEMICAL REACTIONS
6.83
147
The reaction is:
2CO  2NO  2CO2  N2
The limiting reagent is CO (NO is in excess).
H   [2H f (CO2 )  H f (N 2 )]  [2H f (CO)  2H f (NO)]
H  [(2)(393.5 kJ/mol)  (1)(0)]  [(2)(110.5 kJ/mol)  (2)(90.4 kJ/mol)]  747 kJ/mol
6.84
Recall that the standard enthalpy of formation ( Hf ) is defined as the heat change that results when 1 mole

of a compound is formed from its elements at a pressure of 1 atm. Only in choice (a) does H rxn
 H f .
In choice (b), C(diamond) is not the most stable form of elemental carbon under standard conditions;
C(graphite) is the most stable form.
6.85
(a)
No work is done by a gas expanding in a vacuum, because the pressure exerted on the gas is zero.
(b)
w  PV
w  (0.20 atm)(0.50  0.050)L  0.090 Latm
Converting to units of joules:
w   0.090 L  atm 
(c)
101.3 J
  9.1 J
L  atm
The gas will expand until the pressure is the same as the applied pressure of 0.20 atm. We can calculate
its final volume using the ideal gas equation.
nRT
V 

P
L  atm 

(0.020 mol)  0.0821
(273  20)K
 K 
mol

 2.4 L
0.20 atm
The amount of work done is:
w  PV  (0.20 atm)(2.4  0.050)L  0.47 Latm
Converting to units of joules:
w   0.47 L  atm 
6.86
(a)
101.3 J
  48 J
L  atm
The more closely packed, the greater the mass of food. Heat capacity depends on both the mass and
specific heat.
C  ms
The heat capacity of the food is greater than the heat capacity of air; hence, the cold in the freezer will
be retained longer.
(b)
Tea and coffee are mostly water; whereas, soup might contain vegetables and meat. Water has a higher
heat capacity than the other ingredients in soup; therefore, coffee and tea retain heat longer than soup.
148
CHAPTER 6: ENERGY RELATIONSHIPS IN CHEMICAL REACTIONS
6.87
The balanced equation is:
C6H12O6(s) 
 2C2H5OH(l)  2CO2(g)

H rxn
 [2H f (C2 H5 OH)  2H f (CO 2 )]  H f (C6 H12 O6 )

H rxn
 [(2)(276.98 kJ/mol)  (2)(393.5 kJ/mol)]  (1)(1274.5 kJ/mol)  66.5 kJ/mol
6.88
4Fe(s)  3O2(g)  2Fe2O3(s). This equation represents twice the standard enthalpy of formation of Fe2O3.
From Appendix 2, the standard enthalpy of formation of Fe2O3  822.2 kJ/mol. So, H for the given
reaction is:

H rxn
 (2)(822.2 kJ/mol)   1644 kJ/mol
Looking at the balanced equation, this is the amount of heat released when four moles of Fe react. But, we
are reacting 250 g of Fe, not 4 moles. We can convert from grams of Fe to moles of Fe, then use H as a
conversion factor to convert to kJ.
250 g Fe 
1 mol Fe
1644 kJ

  1.84  103 kJ
55.85 g Fe 4 mol Fe
3
The amount of heat produced by this reaction is 1.84 × 10 kJ.
6.89
One conversion factor needed to solve this problem is the molar mass of water. The other conversion factor
is given in the problem. It takes 44.0 kJ of energy to vaporize 1 mole of water.
1 mol H 2 O
44.0 kJ
You should come up with the following strategy to solve the problem.
4000 kJ  mol H2O  g H2O
? g H 2O  4000 kJ 
6.90
1 mol H 2 O 18.02 g H 2 O

= 1.64  103 g H 2O
44.0 kJ
1 mol H 2 O
The heat required to raise the temperature of 1 liter of water by 1C is:
4.184
J
1g
1000 mL


 1C  4184 J/L
g  C 1 mL
1L
Next, convert the volume of the Pacific Ocean to liters.
3
3
 1000 m   100 cm 
1L
(7.2  10 km )  
 7.2  1020 L
 
 
3
 1 km   1 m  1000 cm
8
3
The amount of heat needed to raise the temperature of 7.2  10
(7.2  1020 L) 
4184 J
 3.0  1024 J
1L
20
L of water is:
CHAPTER 6: ENERGY RELATIONSHIPS IN CHEMICAL REACTIONS
149
Finally, we can calculate the number of atomic bombs needed to produce this much heat.
(3.0  1024 J) 
6.91
1 atomic bomb
1.0  1015 J
 3.0  109 atomic bombs  3.0 billion atomic bombs
First calculate the final volume of CO2 gas:

1 mol 
19.2 g 
 (0.0821 L  atm / K  mol)(295 K)
44.01
g
nRT

V =
=
= 10.6 L
0.995 atm
P
w  PV  (0.995 atm)(10.6 L)  10.5 Latm
w   10.5 L  atm 
101.3 J
  1.06  103 J   1.06 kJ
1 L  atm
The expansion work done is 1.06 kJ.
6.92
Strategy: The heat released during the reaction is absorbed by both the water and the calorimeter. How do
we calculate the heat absorbed by the water? How do we calculate the heat absorbed by the calorimeter?
How much heat is released when 1.9862 g of benzoic acid are reacted? The problem gives the amount of
heat that is released when 1 mole of benzoic acid is reacted (3226.7 kJ/mol).
Solution: The heat of the reaction (combustion) is absorbed by both the water and the calorimeter.
qrxn  (qwater  qcal)
If we can calculate both qwater and qrxn, then we can calculate qcal. First, let's calculate the heat absorbed by
the water.
qwater  mwaterswatert
4
qwater  (2000 g)(4.184 J/gC)(25.67  21.84)C  3.20  10 J  32.0 kJ
Next, let's calculate the heat released (qrxn) when 1.9862 g of benzoic acid are burned. Hrxn is given in
units of kJ/mol. Let’s convert to qrxn in kJ.
1 mol benzoic acid
3226.7 kJ
qrxn  1.9862 g benzoic acid 

  52.48 kJ
122.12 g benzoic acid 1 mol benzoic acid
And,
qcal  qrxn  qwater
qcal  52.48 kJ  32.0 kJ  20.5 kJ
To calculate the heat capacity of the bomb calorimeter, we can use the following equation:
qcal  Ccalt
Ccal 
6.93
(a)
qcal
20.5 kJ

 5.35 kJ/ C
t
(25.67  21.84)C
We carry an extra significant figure throughout this calculation to avoid rounding errors. The number
of moles of water present in 500 g of water is:
moles of H 2 O  500 g H 2 O 
1 mol H 2 O
 27.75 mol H 2 O
18.02 g H 2 O
150
CHAPTER 6: ENERGY RELATIONSHIPS IN CHEMICAL REACTIONS
From the equation for the production of Ca(OH)2, we have 1 mol H2O  1 mol CaO  1 mol Ca(OH)2.
Therefore, the heat generated by the reaction is:
27.75 mol Ca(OH)2 
65.2 kJ
  1.809  103 kJ
1 mol Ca(OH)2
Knowing the specific heat and the number of moles of Ca(OH)2 produced, we can calculate the
temperature rise using Equation (6.12) of the text. First, we need to find the mass of Ca(OH)2 in
27.75 moles.
27.75 mol Ca(OH) 2 
74.10 g Ca(OH)2
 2.056  103 g Ca(OH)2
1 mol Ca(OH)2
From Equation (6.12) of the text, we write:
q  mst
Rearranging, we get
t 
t 
q
ms
1.809  106 J
(2.056  103 g)(1.20 J/g C)
 733C
and the final temperature is
t  tfinal  tinitial
tfinal  733C  25C  758C
A temperature of 758C is high enough to ignite wood.
(b)
The reaction is:
CaO(s)  H2O(l)  Ca(OH)2(s)

H rxn
 H f [Ca(OH) 2 ]  [H f (CaO)  H f (H 2 O)]

H rxn
is given in the problem (65.2 kJ/mol). Also, the H f values of CaO and H2O are given.
Thus, we can solve for H f of Ca(OH)2.
65.2 kJ/mol  H f [Ca(OH)2 ]  [(1)(635.6 kJ/mol  (1)(285.8 kJ/mol)]
H f [Ca(OH)2 ]   986.6 kJ/mol
6.94
First, let’s calculate the standard enthalpy of reaction.

H rxn
 2H f (CaSO4 )  [2H f (CaO)  2H f (SO2 )  H f (O2 )]
 (2)(1432.69 kJ/mol)  [(2)(635.6 kJ/mol)  (2)(296.1 kJ/mol)  0]
 1002 kJ/mol
CHAPTER 6: ENERGY RELATIONSHIPS IN CHEMICAL REACTIONS
This is the enthalpy change for every 2 moles of SO2 that are removed. The problem asks to calculate the
5
enthalpy change for this process if 6.6  10 g of SO2 are removed.
(6.6  105 g SO2 ) 
6.95
1 mol SO2
1002 kJ

  5.2  106 kJ
64.07 g SO2 2 mol SO2
First, we need to calculate the volume of the balloon.
V 
(a)
4 3
4
1000 L
r  (8 m)3  (2.1  103 m3 ) 
 2.1  106 L
3
3
3
1m
We can calculate the mass of He in the balloon using the ideal gas equation.


1 atm
 98.7 kPa 
 (2.1  106 L)
2


1.01325
10
kPa

PV

nHe 
 
 8.6  104 mol He
L  atm 
RT

 0.0821 mol  K  (273  18)K


mass He  (8.6  104 mol He) 
(b)
4.003 g He
 3.4  105 g He
1 mol He
Work done  PV


1 atm
   98.7 kPa 
 (2.1  106 L)
2



1.01325
10
kPa


 (2.0  106 L  atm) 
101.3 J
1 L  atm
8
Work done  2.0  10 J
6.96
(a)
The heat needed to raise the temperature of the water from 3C to 37C can be calculated using the
equation:
q  mst
First, we need to calculate the mass of the water.
4 glasses of water 
2.5  102 mL
1 g water

 1.0  103 g water
1 glass
1 mL water
3
The heat needed to raise the temperature of 1.0  10 g of water is:
3
5
2
q  mst  (1.0  10 g)(4.184 J/gC)(37  3)C  1.4  10 J  1.4  10 kJ
(b)
We need to calculate both the heat needed to melt the snow and also the heat needed to heat liquid
water form 0C to 37C (normal body temperature).
The heat needed to melt the snow is:
(8.0  102 g) 
1 mol
6.01 kJ

 2.7  102 kJ
18.02 g
1 mol
151
152
CHAPTER 6: ENERGY RELATIONSHIPS IN CHEMICAL REACTIONS
The heat needed to raise the temperature of the water from 0C to 37C is:
2
5
2
q  mst  (8.0  10 g)(4.184 J/gC)(37  0)C  1.2  10 J  1.2  10 kJ
The total heat lost by your body is:
2
2
2
(2.7  10 kJ)  (1.2  10 kJ)  3.9  10 kJ
6.97
The reaction we are interested in is the formation of ethanol from its elements.
2C(graphite) 
1
2
O2(g)  3H2(g) 
 C2H5OH(l)
Along with the reaction for the combustion of ethanol, we can add other reactions together to end up with the
above reaction.
Reversing the reaction representing the combustion of ethanol gives:
2CO2(g)  3H2O(l) 
 C2H5OH(l)  3O2 (g)
H  1367.4 kJ/mol
We need to add equations to add C (graphite) and remove CO2 and H2O from the reactants side of the
equation. We write:
 C2H5OH(l)  3O2(g)
2CO2(g)  3H2O(l) 
H  1367.4 kJ/mol
 2CO2(g)
2C(graphite)  2O2(g) 
H  2(393.5 kJ/mol)
3H2(g) 
3
2
O2(g) 
 3H2O(l)
2C(graphite) 
6.98
1
2
H  3(285.8 kJ/mol)
H f  277.0 kJ/mol
O2(g)  3H2(g) 
 C2H5OH(l)
Heat gained by ice  Heat lost by the soft drink
mice  334 J/g  msdssdt
mice  334 J/g  (361 g)(4.184 J/gC)(0  23)C
mice  104 g
6.99
The heat required to heat 200 g of water (assume d  1 g/mL) from 20C to 100C is:
q  mst
4
q  (200 g)(4.184 J/gC)(100  20)C  6.7  10 J
Since 50% of the heat from the combustion of methane is lost to the surroundings, twice the amount of heat
4
5
2
needed must be produced during the combustion: 2(6.7  10 J)  1.3  10 J  1.3  10 kJ.
Use standard enthalpies of formation (see Appendix 2) to calculate the heat of combustion of methane.
CH4(g)  2O2(g)  CO2(g)  2H2O(l)
H  890.3 kJ/mol
2
The number of moles of methane needed to produce 1.3  10 kJ of heat is:
(1.3  102 kJ) 
1 mol CH 4
 0.15 mol CH 4
890.3 kJ
CHAPTER 6: ENERGY RELATIONSHIPS IN CHEMICAL REACTIONS
153
The volume of 0.15 mole CH4 at 1 atm and 20C is:
V 
nRT
(0.15 mol)(0.0821 L  atm / K  mol)(293 K)

 3.6 L
P
1.0 atm
3
Since we have the volume of methane needed in units of liters, let's convert the cost of natural gas per 15 ft
to the cost per liter.
3
3
 1 ft   1 in  1000 cm3
$3.1  103






1L
1 L CH 4
15 ft 3  12 in   2.54 cm 
$1.30
The cost for 3.6 L of methane is:
3.6 L CH 4 
6.100
$3.1  103
 $0.011 or about 1.1¢
1 L CH 4
From Chapter 5, we saw that the kinetic energy (or internal energy) of 1 mole of a gas is
1 mole of an ideal gas, PV  RT. We can write:
internal energy 

3
RT . For
2
3
3
RT 
PV
2
2
3
5
3 3
(1.2  10 Pa)(5.5  10 m )
2
8
3
 9.9  10 Pam
3
1 Pam  1
N
m
2
3
m  1 Nm  1 J
8
Therefore, the internal energy is 9.9  10 J.
6
The final temperature of the copper metal can be calculated. (10 tons  9.072  10 g)
q  mCusCut
8
6
9.9  10 J  (9.072  10 g)(0.385 J/gC)(tf  21C)
6
(3.49  10 )tf  1.06  10
9
tf  304C
6.101
Energy must be supplied to break a chemical bond. By the same token, energy is released when a bond is
formed.
6.102
(a)
CaC2(s)  2H2O(l) 
 Ca(OH)2(s)  C2H2(g)
(b)
The reaction for the combustion of acetylene is:
2C2H2(g)  5O2(g) 
 4CO2(g)  2H2O(l)
154
CHAPTER 6: ENERGY RELATIONSHIPS IN CHEMICAL REACTIONS
We can calculate the enthalpy change for this reaction from standard enthalpy of formation values
given in Appendix 2 of the text.

H rxn
 [4 H f (CO 2 )  2H f (H 2 O)]  [2H f (C2 H 2 )  5H f (O2 )]

H rxn
 [(4)(393.5 kJ/mol)  (2)(285.8 kJ/mol)]  [(2)(226.6 kJ/mol)  (5)(0)]

H rxn
 2599 kJ/mol
Looking at the balanced equation, this is the amount of heat released when two moles of C2H2 are
reacted. The problem asks for the amount of heat that can be obtained starting with 74.6 g of CaC2.
From this amount of CaC2, we can calculate the moles of C2H2 produced.
74.6 g CaC2 
1 mol CaC2
1 mol C2 H 2

 1.16 mol C2 H 2
64.10 g CaC2 1 mol CaC2

Now, we can use the H rxn
calculated above as a conversion factor to determine the amount of heat
obtained when 1.16 moles of C2H2 are burned.
1.16 mol C2 H 2 
6.103
2599 kJ
 1.51  103 kJ
2 mol C2 H 2
When 1.034 g of naphthalene are burned, 41.56 kJ of heat are evolved. Let's convert this to the amount of
heat evolved on a molar basis. The molar mass of naphthalene is 128.2 g/mol.
q 
128.2 g C10 H8
41.56 kJ

  5153 kJ/mol
1.034 g C10 H8
1 mol C10 H8
q has a negative sign because this is an exothermic reaction.
This reaction is run at constant volume (V  0); therefore, no work will result from the change.
w  PV  0
From Equation (6.4) of the text, it follows that the change in energy is equal to the heat change.
U  q  w  qv  5153 kJ/mol
To calculate H, we rearrange Equation (6.10) of the text.
U  H  RTn
H  U  RTn
To calculate H, n must be determined, which is the difference in moles of gas products and moles of gas
reactants. Looking at the balanced equation for the combustion of naphthalene:
C10H8(s)  12O2(g)  10CO2(g)  4H2O(l)
n  10  12  2
H  U  RTn
H   5153 kJ/mol  (8.314 J/mol  K)(298 K)(2) 
H  5158 kJ/mol
Is H equal to qp in this case?
1 kJ
1000 J
CHAPTER 6: ENERGY RELATIONSHIPS IN CHEMICAL REACTIONS
6.104
(a)
155
If no heat exchange occurs between the system and surroundings, then q  0 (called an adiabatic
process).
U  q  w  w
Because the system does work on the surroundings, w is a negative quantity, and there is a decrease in
the system's energy. In Section 5.6 of the text, we saw that the average kinetic energy of a gas is
directly proportional to the absolute temperature [Equation (5.15) of the text]. It follows that as the
energy of the system decreases, the temperature also decreases. It is this cooling effect (or the decrease
in the kinetic energy of the water molecules) that is responsible for the formation of snow.
(b)
This process is approximately adiabatic, so that q  0 and U  w. Because work is done on the gas
(system), w is positive, and there is an increase in the system's energy. As discussed in part (a) above,
the kinetic energy of a gas is directly proportional to the absolute temperature. Thus, the temperature of
the system increases, which we notice as a warming effect at the valve stem.
(c)
We assume that when the car is stopped, its kinetic energy is completely converted into heat (friction of
the brakes and friction between the tires and the road). Thus,
q 
1
mu 2
2
Thus the amount of heat generated must be proportional to the braking distance, d:
dq
du
2
2
2
Therefore, as u increases to 2u, d increases to (2u)  4u which is proportional to 4d.
6.105
Water has a larger specific heat than air. Thus cold, damp air can extract more heat from the body than cold,
dry air. By the same token, hot, humid air can deliver more heat to the body.
6.106
Since the humidity is very low in deserts, there is little water vapor in the air to trap and hold the heat
radiated back from the ground during the day. Once the sun goes down, the temperature drops dramatically.
40F temperature drops between day and night are common in desert climates. Coastal regions have much
higher humidity levels compared to deserts. The water vapor in the air retains heat, which keeps the
temperature at a more constant level during the night. In addition, sand and rocks in the desert have small
specific heats compared with water in the ocean. The water absorbs much more heat during the day
compared to sand and rocks, which keeps the temperature warmer at night.
6.107
Let's write balanced equations for the reactions between Mg and CO2, and Mg and H2O. Then, we can

for each reaction from H f values.
calculate H rxn
(1)
2Mg(s)  CO2(g)  2MgO(s)  C(s)
(2)
Mg(s)  2H2O(l)  Mg(OH)2(s)  H2(g)

is:
For reaction (1), H rxn

H rxn
 2H f [MgO( s )]  H f [C( s )]  {2H f [Mg( s )]  H f [CO2 ( g )]}

H rxn
 (2)(601.8 kJ/mol)  (1)(0)  [(2)(0)  (1)(393.5 kJ/mol)]   8.10  102 kJ/mol
156
CHAPTER 6: ENERGY RELATIONSHIPS IN CHEMICAL REACTIONS

For reaction (2), H rxn
is:

H rxn
 H f [Mg(OH)2 ( s )]  H f [H 2 ( g )]  {H f [Mg( s )]  2H f [H 2 O(l )]}

H rxn
 (1)(924.66 kJ/mol)  (1)(0)  [(1)(0)  (2)( 285.8 kJ/mol)]   353.1 kJ/mol
Both of these reactions are highly exothermic, which will promote the fire rather than extinguishing it.
6.108
First, we calculate H for the combustion of 1 mole of glucose using data in Appendix 2 of the text. We can
then calculate the heat produced in the calorimeter. Using the heat produced along with H for the
combustion of 1 mole of glucose will allow us to calculate the mass of glucose in the sample. Finally, the
mass % of glucose in the sample can be calculated.
C6H12O6(s)  6O2(g)  6CO2(g)  6H2O(l)

H rxn
 (6)(393.5 kJ/mol)  (6)(285.8 kJ/mol)  (1)(1274.5 kJ/mol)   2801 kJ/mol
The heat produced in the calorimeter is:
(3.134C)(19.65 kJ/C)  61.58 kJ
Let x equal the mass of glucose in the sample:
x g glucose 
1 mol glucose
2801 kJ

 61.58 kJ
180.16 g glucose 1 mol glucose
x  3.961 g
% glucose 
6.109
(a)
(b)
(c)
(d)
(e)
(f)
q






3.961 g
 100%  96.21%
4.117 g
w




0

U

0




H

0




In (b), the internal energy of an ideal gas depends only on temperature. Since temperature is held constant,
U  0. Also, H  0 because H  U  (PV)  U  (nRT)  0.
6.110
(a)
From the mass of CO2 produced, we can calculate the moles of carbon in the compound. From the mass of
H2O produced, we can calculate the moles of hydrogen in the compound.
1.419 g CO 2 
1 mol CO 2
1 mol C

 0.03224 mol C
44.01 g CO 2 1 mol CO 2
0.290 g H 2 O 
1 mol H 2 O
2 mol H

 0.03219 mol H
18.02 g H 2 O 1 mol H 2 O
The mole ratio between C and H is 1:1, so the empirical formula is CH.
CHAPTER 6: ENERGY RELATIONSHIPS IN CHEMICAL REACTIONS
(b)
157
The empirical molar mass of CH is 13.02 g/mol.
molar mass
76 g

 5.8  6
empirical molar mass
13.02 g
Therefore, the molecular formula is C6H6, and the hydrocarbon is benzene. The combustion reaction is:
2C6H6(l)  15O2(g)  12CO2(g)  6H2O(l)
17.55 kJ of heat is released when 0.4196 g of the hydrocarbon undergoes combustion. We can now

) for the above reaction in units of kJ/mol. Then, from the
calculate the enthalpy of combustion ( H rxn
enthalpy of combustion, we can calculate the enthalpy of formation of C6H6.
78.11 g C6 H6
17.55 kJ

 2 mol C6 H6   6534 kJ/mol
0.4196 g C6 H6
1 mol C6 H6

H rxn
 (12)H f (CO2 )  (6)H f (H 2 O)  (2)H f (C6 H 6 )
6534 kJ/mol  (12)(393.5 kJ/mol)  (6)(285.8 kJ/mol)  (2)H f (C6 H6 )
H f (C6 H6 )  49 kJ/mol
6.111
If the body absorbs all the heat released and is an isolated system, the temperature rise, t, is:
q  mst
t 
q
1.0  107 J

 48C
(50, 000 g)(4.184 J/g C)
ms
If the body temperature is to remain constant, the heat released by metabolic activity must be used for the
evaporation of water as perspiration, that is,
1 g H2O
 (1.0  104 kJ)  4.1  103 g H 2O
2.41 kJ
Assuming that the density of perspiration is 1 g/mL, this mass corresponds to a volume of 4.1 L. The actual
amount of perspiration is less than this because part of the body heat is lost to the surroundings by convection
and radiation.
6.112
AB
BC
CD
DA
w  0, because V  0
w  PV  (2 atm)(2  1)L  2 Latm
w  0, because V  0
w  PV  (1 atm)(1  2)L  1 Latm
The total work done  (2 Latm)  (1 Latm)  1 Latm
Converting to units of joules,
1 L  atm 
101.3 J
  101.3 J
1 L  atm
In a cyclic process, the change in a state function must be zero. We therefore conclude that work is not a
state function. Note that the total work done equals the area of the enclosure.
158
CHAPTER 6: ENERGY RELATIONSHIPS IN CHEMICAL REACTIONS
6.113
(a)
Heating water at room temperature to its boiling point.
(b)
Heating water at its boiling point.
(c)
A chemical reaction taking place in a bomb calorimeter (an isolated system) where there is no heat
exchange with the surroundings.
6.114
C (graphite)  C (diamond)
H  U  PV
ΔH  ΔU  PΔV
ΔH  ΔU  PΔV
The pressure is 50,000 atm. From the given densities, we can calculate the volume in liters occupied by one
mole of graphite and one mole of diamond. Taking the difference will give ΔV. We carry additional
significant figures throughout the calculations to avoid rounding errors.
1 cm3
1L
12.01 g graphite


 0.0053378 L/mol graphite
2.25 g graphite 1000 cm3
1 mol graphite
1 cm3
1L
12.01 g diamond


 0.0034119 L/mol diamond
3
3.52 g diamond 1000 cm
1 mol diamond
ΔH  ΔU  PΔV  (50,000 atm)(0.0034119 L/mol  0.0053378 L/mol)
H  U   96.295
L  atm 101.3 J

  9.75  103 J / mol
mol
1 L  atm

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