Calculating an Enthalpy Change
Using Enthalpy Data to Determine the Mass of Products
(Student textbook page 299)
11. Pentane reacts with an excess of oxygen to produce carbon dioxide and water vapour.
What is the enthalpy change of the reaction per mole of each of the following gases?
The enthalpy of combustion for pentane, C5H12(ℓ), is –3509.0 kJ/mol.
a. oxygen
b. carbon dioxide
c. water
What Is Required?
You need to calculate the enthalpy change per mole for O2(g), CO2(g), and H2O(g)
during the burning of pentane.
What Is Given?
You know that pentane is burned in an excess of oxygen, so complete combustion
occurs.
o
You know that the enthalpy of combustion for pentane C5H12(ℓ): DH comb
= –3509.0
kJ/mol.
Plan Your Strategy
Act on Your Strategy
Write the balanced chemical C5H12(ℓ)+ 8O2(g) Ѝ 5CO2(g) + 6H2O(g)
o
equation for the complete
= –3509.0 kJ/mol
DH comb
combustion of pentane.
o
a. Use the mole ratio in the
nC5H12 DH comb
(per
mole
O
)
H
D
=
´
r
2
balanced chemical equation
nO2
nC5H12
to calculate the enthalpy
1 mol C5 H12
-3509.0 kJ
change per mole of O2 (g).
´
=
8 mol O 2
1 mol C5 H12
= -438.62 kJ
o
b. Use the mole ratio in the
nC5H12 DH comb
(per
mole
CO
)
H
D
=
´
r
2
balanced chemical equation
nOC2
nC5H12
to calculate the enthalpy
1 mol C5 H12
-3509.0 kJ
change per mole of CO2 (g).
´
=
5 mol CO2 1 mol C5 H12
= -701.80 kJ
12 MHR ● Chemistry 12 Solutions Manual 978-0-07-106042-4
c. Use the mole ratio in the
balanced chemical equation
to calculate the enthalpy
change per mole of H2O(g).
DH r (per mole H 2 O) =
=
nC5H12
nH2O
o
DH comb
´
nC5H12
1 mol C5 H12
6 mol H 2 O
= -584.83 kJ
´
-3509.0 kJ
1 mol C5 H12
Check Your Solution
The enthalpy per mol is inversely related to the number of moles. This is a reasonable
result. The number of significant digits in each answer agrees with the given data.
Unit 3 Part B ● MHR 13
12. What is the enthalpy change when 4.608 g of ethanol, C2H5OH(ℓ), undergoes
complete combustion?
C2H5OH(ℓ) + 3O2(g) Ѝ2CO2(g) + 3H2O(ℓ) + 13 668 kJ
What Is Required?
You need to determine the enthalpy change when a given mass of ethanol undergoes
complete combustion.
What Is Given?
You know the mass of ethanol: methanol = 4.608 g
You know the balanced chemical equation for the reaction:
C2H5OH(ℓ) + 3O2(g) Ѝ2CO2(g) + 3H2O(ℓ) + 13 668 kJ
Plan Your Strategy
Determine the amount in moles, n, of ethanol
by using its mass and molar mass. Use the
m
formula n =
.
M
Act on Your Strategy
m
nC2 H5OH =
M
4.608 g
=
46.08 g /mol
= 0.1000 mol
o
Use the formula ∆H = n∆ H comb
to determine
the enthalpy change.
°
DH = nDH comb
(0.1000 mol )( - 1366.8 kJ/ mol )
= -136.7 kJ
Check Your Solution
The given mass is less than the mass of 1 mol of C2H5OH(ℓ) and the enthalpy change
is less that the enthalpy change per mol of C2H5OH(ℓ). This is a reasonable result and
shows the correct number of significant digits.
14 MHR ● Chemistry 12 Solutions Manual 978-0-07-106042-4
13. Determine the thermal energy released by the combustion of each of the following
samples of hydrocarbons to CO2(g) and H2O(ℓ) in an open system.
a. 56.78 g of hexane, C6H14(ℓ)
b. 1.36 kg of octane, C8H18(ℓ)
c. 2.344 × 104 g of heptane, C7H16(ℓ)
What Is Required?
You need to calculate the thermal energy released during combustion of each sample
of gas.
What Is Given?
You know the mass of hexane, C6H14(ℓ): m = 56.78 g
You know the mass of octane, C8H18(ℓ): m = 1.36 kg
You know the mass of heptane, C7H16(ℓ): m = 2.344 × 104 g
From Table 5.4 (student textbook page 295), you know the heat of combustion for
each gas:
o
for hexane = –4163.2 kJ/mol
DH comb
o
DH comb for octane = –5470.3 kJ/mol
o
for heptane = –4817.0 kJ/mol
DH comb
Plan Your Strategy
Use the molar mass of each gas and
m
the formula n =
to calculate the
M
amount in moles of each sample.
a. nC6 H14
Act on Your Strategy
m
=
M
56.78 g
=
86.20 g /mol
= 0.65870 mol
b. nC8H18 =
=
m
M
1.36 ´ 103 g
114.26 g /mol
= 11.9026 mol
c. nC7 H16 =
=
m
M
2.344 ´ 104 g
100.23 g /mol
= 233.8621 mol
Unit 3 Part B ● MHR 15
°
Use the formula DH r = nDH comb
to
calculate the thermal energy
released by the combustion of each
sample.
°
a. DH r = nC6H14 DH comb
= ( 0.65870 mol ) ( –4163.2 kJ/ mol )
= -2742.17 kJ
= -2742 kJ
°
b. DH r = nC H DH comb
8 18
= (11.9026 mol ) ( -5470.3 kJ/ mol )
= -65 110.792 kJ
= -6.51´104 kJ
°
c. DH r = nC H DH comb
7 16
= ( 233.8611 mol ) ( –4817.0 kJ/ mol )
= -1 126 513.8 kJ
= -1.126 ´106 kJ
Check Your Solution
Check that the given data has been substituted correctly. The answers seem reasonable
and show the correct number of significant digits.
16 MHR ● Chemistry 12 Solutions Manual 978-0-07-106042-4
14. What is the enthalpy change for the combustion of a 1.00 g sample of methane,
CH4(g), under standard conditions?
What Is Required?
You need to determine the enthalpy change when a given mass of methane, CH4(g),
undergoes combustion.
What Is Given?
You know the mass of methane, CH4(g): m = 1.00 g
From Table 5.4 (student textbook page 295), you know the heat of combustion for
o
methane: DH comb
= –890.8 kJ/mol
Plan Your Strategy
Use the molar mass of methane and the
m
formula n =
to calculate the amount
M
in of moles, n, of CH4(g).
°
Use the formula DH r = nDH comb
to
calculate the thermal energy released
by the combustion of the sample.
Act on Your Strategy
nCH4 =
=
m
M
1.00 g
16.05 g /mol
= 0.062305 mol
°
DH r = nCH4 DH comb
= ( 0.062305 mol ) ( -890.8 kJ/ mol )
= -55.5 kJ
Check Your Solution
The enthalpy change would be expected to be small for a small mass of methane. The
answer is reasonable and shows the correct number of significant digits.
Unit 3 Part B ● MHR 17
15. Naphthalene, C10H8(s), is an organic compound used in the manufacture of dyes,
plastics, and insecticides, especially insecticides that combat moths. What mass of this
compound will release 500.0 kJ of thermal energy?
C10H8(s) + 12O2 → 10CO2(g) + 4H2O(ℓ) + 5156 kJ
What Is Required?
You need to calculate the mass of naphthalene, C10H8(s), that can be combusted to
release a given amount of thermal energy.
What Is Given?
You know the balanced thermochemical equation for the combustion of naphthalene,
C10H8(s).
Plan Your Strategy
Use the mole ratio in the balanced
thermochemical equation to
determine the amount in moles, n, of
C10H8(s) that were combusted to
produce 500.0 kJ of thermal energy.
Use the molar mass of naphthalene
and the formula m = n ´ M to
determine the mass, m, of C10H8(s).
Act on Your Strategy
nC10 H8
1 mol C10 H8
=
5156 kJ
500.0 kJ
(1 mol C10 H8 ) ( 500.0 kJ )
nC10 H8 =
5156 kJ
= 0.096974 mol
mC10 H8 = n ´ M
= 0.096974 mol ´128.18 g/ mol
= 12.43 g
Check Your Solution
The mass of naphthalene seems reasonable and the answer shows the correct number
of significant digits.
18 MHR ● Chemistry 12 Solutions Manual 978-0-07-106042-4
16. What mass, in kilograms, of methanol must be combusted to generate 5.39 × 105 kJ of
thermal energy?
What Is Required?
You need to determine the mass, in kilograms, of methanol that must be combusted to
produce a given amount of thermal energy.
What Is Given?
You know the amount of energy produced: ∆Hr = –5.39 × 105 kJ
You know that the fuel to be burned is methanol.
From Table 5.4 (student textbook page 295), you know that the heat of combustion of
o
methanol DH comb
= –726.1 kJ/mol.
Plan Your Strategy
Act on Your Strategy
o
comb
Use the heat of combustion, DH
, of
methanol, CH3OH(ℓ), and the formula
°
to determine the amount
DH r = nDH comb
in moles of CH3OH(ℓ) that was
combusted.
Convert the amount in moles of
CH3OH(ℓ) to mass, m, using the molar
mass of methanol and the formula
m = n´ M .
°
DH r = nDH comb
-5.39 ´ 105 kJ = n(–726.1 kJ/mol)
-5.39 ´ 105 kJ
n=
-726.1 kJ /mol
= 742.32 mol
mCH3OH = n ´ M
= 742.32 mol ´ 32.05 g/ mol
= 23 791 g
= 23.8 kg
Check Your Solution
The mass of methanol seems reasonable for this large amount of energy to be given
off during combustion. The number of significant digits in the answer is correct.
Unit 3 Part B ● MHR 19
17. Answer the questions for the combustion of propene, C3H6(g), using the following
equation:
2C3H6(g) + 9O2(g) → 6CO2(g) + 6H2O(ℓ) + 4116.0 kJ
a. Determine the standard molar enthalpy of combustion of propene.
b. What is the maximum amount of thermal energy available from the combustion of
5.00 g of C3H6(g)?
What Is Required?
a. You need to determine the standard molar enthalpy of combustion for propene
C3H6(g):
b. You need to calculate the amount of thermal energy released when a given mass of
C3H6(g) burns.
What Is Given?
a. You know the balanced thermochemical equation for the combustion of 2 mol of
C3H6(g).
b. You know the mass of propene: mC H = 5.00 g
3
6
Plan Your Strategy
a. Rewrite the thermochemical equation
for the combustion for 1 mol of C3H6(g).
The quantity of heat shown in this
equation is the standard heat of
combustion.
b. Use the molar mass of propene and
m
the formula n =
to calculate the
M
amount in moles, n, of C3H6(g).
Act on Your Strategy
9
C3H6(g) + O2(g) →
2
3CO2(g) + 3H2O(ℓ) + 2058.0 kJ
o
DH comb
= -2058.0 kJ/mol
n=
nC3H 6 =
m
M
5.00 g
42.09 g /mol
= 0.118 79 mol
°
comb
Use the formula DH r = nDH to
calculate the amount of heat given off.
°
DH r = nDH comb
= ( 0.118 79 mol ) ( -2058.0 kJ/ mol ) =
= 244.469 kJ
The thermal energy released is 244 kJ.
Check Your Solution
a. The answer has the correct number of significant digits.
b. The answer seems reasonable since the mass burned is less than 1 mol. The correct
number of significant digits is shown.
20 MHR ● Chemistry 12 Solutions Manual 978-0-07-106042-4
18. When 0.050 mol of a hydrocarbon undergoes complete combustion, 110.95 kJ of heat
is given off.
a. What is the enthalpy of combustion for this hydrocarbon?
b. Refer to Table 5.4 (student textbook page 295) and identify the hydrocarbon.
What Is Required?
a. You need to determine the enthalpy of combustion of a hydrocarbon.
b. You need to identify the hydrocarbon.
What Is Given?
You know the amount in moles of hydrocarbon: n = 0.050 mol
You know the amount of heat energy given off: Q = –110.95 kJ
Plan Your Strategy
a. Calculate the amount of energy
given off from the complete
combustion of 1 mol of hydrocarbon.
a.
Act on Your Strategy
0.050 mol
1
=
o
-110.95 kJ DH comb
-110.95 kJ
0.050 mol
= -2219 kJ/mol
o
DH comb
=
b. Refer to Table 5.4.
= - 2.2 ´103 kJ/mol
b. From Table 5.4, the hydrocarbon is
propane.
Check Your Solution
The answer is reasonable for 1 mol and shows the correct number of significant digits.
Unit 3 Part B ● MHR 21
19. What mass of butane, C4H10(g), must undergo complete combustion to produce 1.00 MJ
of heat according to the following equation?
C4H10(g) +
13
O2(g) →4CO2(g) + 5H2O(ℓ) + 2877.6 kJ
2
What Is Required?
You need to calculate the mass of butane, C4H10(g), that must be burned to produce a
given amount of heat.
What Is Given?
You know amount of heat energy produced: ∆H= 1.00 MJ
From the balanced thermochemical equation, you know the heat of combustion per
mol of butane, C4H10(g).
Plan Your Strategy
Convert 1.00 MJ to kJ.
Use the mole ratio in the
balanced thermochemical
equation to calculate the amount
in moles, n, of butane, C4H10(g),
that is combusted.
Act on Your Strategy
1.00 MJ = 1.00 × 103 kJ
Convert the amount in moles of
C4H10(g) to mass, m, using the
molar mass of butane and the
formula m = n ´ M .
mC4H10
-2877.6 kJ - 1.00 ´ 103 kJ
=
nC4H10
1 mol C4 H10
nC4 H10 =
(1 mol C4 H10 ) ( - 1.00 ´ 103
kJ )
-2877.6 kJ
= 0.34751 mol
= n´ M
= 0.34751 mol ´ 58.14 g/ mol
= 20.2 g
Check Your Solution
Since the given amount of heat energy is less than the heat of combustion per mol. the
mass burned should be less than the mass of 1 mol. the answer is reasonable. The
answer has the correct number of significant digits.
22 MHR ● Chemistry 12 Solutions Manual 978-0-07-106042-4
20. The standard molar heat of combustion of propan-2-ol, CH3CH(OH)CH3(ℓ), is
–2006 kJ/mol.
a. Write the thermochemical equation for the combustion of 1 mol of this compound
to form carbon dioxide and water.
b. How much heat is given off when 25.00 g of water is produced?
What Is Required?
a. You need to determine the amount of heat given off when a given mass of water is
produced during the burning of propan-2-ol, CH3CH(OH)CH3(ℓ).
b. You need to determine the amount of heat given off when 25.00 g of water is
produced.
What Is Given?
o
You know standard heat of combustion of CH3CH(OH)CH3(ℓ): DH comb
= –2006
kJ/mol
You know the chemical formula for propan-2-ol, CH3CH(OH)CH3(ℓ).
You know that the products of complete combustion are CO2(g) and H2O(ℓ).
Plan Your Strategy
a. Write a balanced chemical equation
showing propanol-2-ol and oxygen,
O2(g), as reactants and carbon dioxide,
CO2(g), and water, H2O(ℓ), as
products. Divide each coefficient by a
factor so that 1 mol of propan-2-ol is
shown in the balanced chemical
equation. Since the standard molar heat
of combustion is a negative number,
you know the reaction is exothermic.
b. Use the molar mass of water and the
m
formula n =
to determine the
M
amount in moles, n, of H2O(ℓ).
Use the mole ratio in the balanced
chemical equation to calculate the
amount of heat given off.
Act on Your Strategy
9
CH3CH(OH)CH3(ℓ) + O2(g) →
2
3CO2(g) + 4H2O(ℓ) + 2006 kJ
n=
nH2O =
m
M
25.00 g
18.02 g /mol
= 1.387 34 mol
-2006 kJ
x
=
4 mol H 2O(( ) 1.387 34 mol H 2 O( )
x = –695.8 kJ
Unit 3 Part B ● MHR 23
Check Your Solution
a. The balanced equation shows 1 mol of propan-2-ol. The heat term is on the right
side of the equation since a combustion reaction is exothermic.
1
b. The amount of heat given off is about the heat of combustion for
4
CH3CH(OH)CH3(ℓ). Since the balanced thermochemical equation shows 4 mol of
H2O(ℓ) produced, the answer is reasonable and shows the correct number of
significant digits.
24 MHR ● Chemistry 12 Solutions Manual 978-0-07-106042-4