HEAT PROBLEMS
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Name
Period ________
Date
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LECTURE PROBLEMS
Internal Energy
1. Inside a flexible container, a reaction occurs that releases 3.98 kJ of heat. It also releases
a gas, expanding the bag from 1.2 L to 14.8 L. Calculate the internal energy, in kJ, of the
system.
Heat Equation Problems
2. What mass of copper (specific heat = 0.356 J/g°C) is used if 533 J of energy are used to
induce a temperature change from 23.0°C to 84.2°C?
3. It takes 459 J to heat a 35.5 gram piece of niobium from 23.8C to 48.1C.
a. What is the specific heat of niobium? Explain its rate of heating and rate of cooling.
b. What is the molar heat capacity of niobium?
Conservation of Energy / Calorimetry
4. To take a break from studying chemistry, you rent the video of the movie version of the
book Fahrenheit 451, which starred Oscar Werner. The setting (in England) is an
Orwellian society where books are banned and all information is disseminated by a large
TV screen in each home. Fire departments respond not to put out fires, but to burn
books, which combust at a temperature of 451F (hence the name of the film, which also
equates to 233C). In the middle of the film, your mind wanders. You imagine the fire
department using the burning books to heat 600 mL of water for their afternoon tea. How
much will the water temperature rise from burning one copy of the 500-page book
Fahrenheit 451 if the heat of combustion is 382 Joules per page?
5. You grab an unknown piece of metal (with tongs!) that is 45.2 grams and initially at 24.5C.
It is dropped into 38.1 grams of water initially at 10.3C. The temperature finally gets to
11.5C. What was the specific heat of the metal you used?
Molar Enthalpy
6. 3.52 grams of potassium iodate are reacted, giving off heat over a water bath containing 450.
grams of water. The water bath undergoes a temperature change from 19.9C to 43.4C. What is
the molar heat (kJ/mol) associated with the formation of potassium iodate?
7. Given the following data, calculate the molar heat of combustion (kJ/mol burned) for wax and
write an appropriate chemical equation with the proper heat value on the correct side of the
equation. The chemical formula for wax is C25H52.
Volume of water = 100. mL
Initial water temp. = 22°C
Final water temp. = 45°C
Initial mass of wax = 3.60 g
Final mass of wax = 3.30 g
BOOK PROBLEMS
Lecture 1
8. Consider the following statements: “Heat is a form of energy, and energy is conserved. The heat
lost by a system must be equal to the amount of heat gained by the surroundings. Therefore, heat
is conserved.” Indicate everything you think is correct in these statements. Correct the incorrect
statements and explain.
(Zumdahl, 8th edition, Ch. 6, 5)
9. A fire is started in a fireplace by striking a match and lighting crumpled paper under some logs.
Explain all the energy transfers in this scenario using the terms exothermic, endothermic, system,
surroundings, potential energy, and kinetic energy in the discussion
(Zumdahl, 8th edition, Ch. 6, 3)
10. Consider the accompanying energy diagram.
a. Does this diagram represent an increase or decrease in the internal energy of the
system?
b. What sign is given to ∆E for this process?
c. If there is no work associated with the process, is it exothermic or endothermic?
(Brown and Lemay, 12th edition, 5.3)
11. The contents of the closed box in each of the following illustrations represent a system, and the
arrows show the changes to the system during some process. The lengths of the arrows show
the relative magnitudes of q and w.
a. Which of these processes is endothermic?
b. For which of these processes, if any, is ∆E < 0?
c. For which process, if any, does the system experience a net gain in internal energy?
(Brown and Lemay, 12th edition, 5.4)
12. Calculate ∆E for each of the following:
a. q = - 47 kJ, w = +88 kJ
b. q = +82 kJ, w = - 47 kJ
c. q = + 47 kJ, w = 0
d. In which of these cases do the surroundings do work on the system?
(Zumdahl, 8th edition, Ch. 6, 31)
13. A sample of an ideal gas at 15.0 atm and 10.0 L is allowed to expand against a constant external
pressure of 2.00 atm at a constant temperature. At the same time, 4.5 kJ of heat are transferred
from the surroundings to the system. Calculate the internal energy, in terms of kJ, for the gas
expansion
(HINT – Boyle’s Law applies).
(Zumdahl, 8th edition, Ch. 6, 35)
Lecture 2
14. Objects placed together eventually reach the same temperature. When you go into a cool room
and touch a piece of metal, it feels colder than a piece of plastic in the same room. Explain.
(Zumdahl, 8th edition, Ch. 6, 1)
15. Which substance in the table below requires the smallest amount of energy to increase the
temperature of 50.0 g of the substance by 10 K? Calculate the energy needed for this
temperature change.
SPECIFIC HEATS OF SOME SUBSTANCES AT 298 K
Elements
Compounds
Specific heat (J/g•K)
Specific heat (J/g•K)
Substance
Substance
N2 (g)
1.04
H2O (l)
4.18
Al (s)
0.90
CH4 (g)
2.20
Fe (s)
0.45
CO2 (g)
0.84
Hg (l)
0.14
CaCO3 (s)
0.82
(Brown and Lemay, 12th edition, 5.52)
16. The specific heat capacity of silver is 0.24 J/g•°C.
a. Calculate the energy required to raise the temperature of 150.0 g Ag from 273 K to 298 K.
b. Calculate the energy required to raise the temperature of 1.0 mole of Ag 1.0°C (called the
molar heat capacity of silver).
c. It takes 1.25 kJ of energy to heat a sample of pure silver from 12.0°C to 15.2°C. Calculate
the mass of the sample of silver.
(Zumdahl, 8th edition, Ch. 6, 52)
17. To a sample of water at 23.4°C in a constant-pressure calorimeter of negligible heat capacity is
added a 12.1-g piece of aluminum whose temperature is 81.7°C. If the final temperature of the
water is 24.9°C, calculate the mass of water in the calorimeter.
(Chang, 11th edition, 6.36)
18. When a 4.25-g sample of solid ammonium nitrate dissolves in 60.0 g of water in a coffee cup
calorimeter, the temperature drops from 22.0°C to 16.9°C. Calculate the ∆H (in kJ/mol NH4NO3)
for the dissolving process: NH4NO3 (s)  NH4+ (aq) + NO3- (aq). Assume that the specific heat of
the solution is the same as that of pure water. Use the appropriate sign to indicate an
endothermic/exothermic reaction.
(Brown and Lemay, 12th edition, 5.56)
19. Consider the dissolution of CaCl2:
CaCl2 (s)  Ca2+ (aq) + 2 Cl- (aq)
∆H = - 81.5 kJ/mol
An 11.0-g sample of CaCl2 is dissolved in 125 g of water, with both substances at 25.0°C.
Calculate the final temperature of the solution assuming no heat loss to the surroundings and
assuming the solution has a specific heat capacity of 4.18 J/g•°C.
(Zumdahl, 8th edition, Ch. 6, 65)
20. A 1.800-g sample of phenol (C6H5OH) was burned in a bomb calorimeter whose total heat
capacity is 11.66 kJ/°C. The temperature of the calorimeter increased from 20.94°C to 26.37°C.
a. Write a balanced chemical equation for the bomb calorimeter reaction.
b. What is the heat of combustion per gram of phenol? Per mole of phenol?
(Brown and Lemay, 12th edition, 5.58)