**Chapter
16: Theories of Energy Changes Problems**

**
**

1. 100 g
of ethanol at 25°C is heated until it reaches 50°C. How much heat does the
ethanol gain? **(Note: the **specific heat capacity of ethanol is 2.46 J/g^{o}C)

**
2. S**tudents
added ice to 120.0 g of water, resulting in a drop of temperature from 25.5 °C
to 17.4 °C. Calculate the heat lost by the water.

**
3.
**Beaker
A contains 50 g of liquid at room temperature. The beaker is heated until the
liquid gains 10°C. Beaker B contains 100 g of the same liquid at room
temperature. This beaker is also heated until the liquid gains 10°C. In which
beaker does the liquid absorb the most heat? Explain.

**
4. T**he
sign of the heat value (q) tells you whether a substance has lost or gained heat
energy. Consider the following descriptions. Write each heat value, and give it
the appropriate sign (+/-) to indicate whether heat was lost from or gained by
the system.

**
(a)
**In
Part A of the ThoughtLab (p.631), the ice absorbed the heat that was lost by the
water. When ice was added to 60.0 g of water, it absorbed 4.22 kJ of heat. When
ice was added to 120.0 g of water, it absorbed 4.6 kJ of heat.

**
(b)
**When
2.0 L of water was heated over a campfire, the water gained 487 kJ of energy.

**
(c)
**A
student baked a cherry pie and put it outside on a cold winter day. There was a
change of 290 kJ of heat energy in the pie.

**
5.
**Solve
the equation *q *= *mc*Δ*T *for the following quantities.

**
(a)
***
m ***
(b)
***
c ***
(c)
**Δ*T*

**
6.
**You
know that Δ*T *= *T*_{f} − *T*_{i}. Combine this
equation with the heat equation, *q *= *mc*Δ*T*, to solve for the
following quantities.

**(a) **
*T*_{i} (in terms of *q*, *m*, *c*, and *T*_{f}
) **(b) ***T*_{f} (in terms of *q*, *m*,
*c*, and *T*_{i} )

**
7.
**How
much heat is required to raise the temperature of 789 g of liquid ammonia, from
25.0°C to 82.7°C?

**
8.
**A
solid substance has a mass of 250.00 g. It is cooled by 25.00°C and loses
4937.50 J of heat. What is its specific heat capacity? Refer to the table to
identify the substance.

**
9.
**A
piece of metal with a mass of 14.9 g is heated to 98.0°C. When the metal is
placed in 75.0 g of water at 20.0°C, the temperature of the water rises by
28.5°C. What is the specific heat capacity of the metal? Assume all heat
released by metal is absorbed by the water.

**
10.
**A
piece of gold (*c *= 0.129 J/g°C) with mass of 45.5 g and a temperature of
80.5°C is dropped into 192 g of water at 15.0°C. What is the final temperature
of the water? (**Hint: **Use the equation *q*_{w} = −*q*_{g}
.)

**
11.
**A
bathtub contains 100.0 kg of water.

**
(a)
**What
is the heat capacity, *C*, of the water in the bathtub?

**
(b)
**How
much heat is transferred to the surroundings as the water in the bathtub cools
from 60.0°C to 20.0°C? Use your answer from (a) in your calculations.

**
(c)
**
Calculate the heat transferred in (b) using a different method.

**
12.
**A
teacup contains 0.100 kg of water.

**
(a)
**What
is the heat capacity, *C*, of the water in the teacup?

**
(b)
**How
much heat is transferred to the surroundings as the water in the teacup cools
from 60.0°C to 20.0°C? Use your answer from (a) in your calculations.

**
(c)
**
Calculate the heat transferred in (b) using a different method.

**
13.
**A ring
of pure gold with a mass of 18.8 g is tossed into a fire, and then removed with
a pair of tongs. The initial temperature of the ring was 23.2°C and the final
temperature of the ring is 55.8°C.

**
(a)
**What
is the heat capacity of the ring?

**
(b)
**How
much heat did the ring absorb from the fire?

**
14. **
Because humans are about 85% water, the specific heat capacity of a human is
sometimes approximated as 0.85 times the specific heat capacity of water.

**
(a)
**Using
the above approximation, what is the heat capacity of a human that has a mass of
68.0 kg?

**
(b)
**How
much heat is required to raise the temperature of a 68.0 kg human by 1.00°C?

**
15.
**Write
a balanced thermochemical equation to represent the standard molar enthalpy of
formation of each of the following substances. Include the heat term within the
equation.

**
(a)
**H_{2}O
_{(g)} **(b) **CaCl_{2(s)} **(c) **CH_{4}
_{(g)} **(d) **C_{6}H_{6 (l)}

**
(e)
**Repeat
(c) and (d), showing the standard molar enthalpy of formation in a different
way.

**
16.
**Draw
an enthalpy diagram to represent the standard molar enthalpy formation of sodium
chloride.

**
17.
**Write
a balanced thermochemical equation to represent the standard molar enthalpy of
combustion of each of the following alkanes (see Table 16.3). Remember: the
products and reactants must be in their standard states. **
(a) **ethane **(b) **propane **(c) **
butane **(d) **pentane

**
18.
**Draw
an enthalpy diagram to represent the standard molar enthalpy of the combustion
of heptane (see Table 16.3). Remember: the products and reactants must be in
their standard states.

**
19. (a)
**
Hydrogen
gas and oxygen gas react to form 0.534 g of *liquid *water. How much heat
is released to the surroundings?

**
(b)
**
Hydrogen gas and oxygen gas react to form 0.534 g of *gaseous*water. How
much heat is released?

**
20.
**Carbon
and oxygen react to form carbon dioxide. At STP, the carbon dioxide has a volume
of 78.2 L. How much heat was released to the surroundings during the reaction?

**
21.
**
Determine the heat released by the combustion of each of the following samples
of hydrocarbons.

**
(a)
**56.78
g pentane, C_{5}H_{12 (l)} **(b) **1.36 kg octane, C_{8}H_{18
(l) }**(c) **2.344 × 10^{4} g hexane, C_{6}H_{14
(l)}

**
22.
**How
much heat is released by the combustion of 5.34 mL of methane, CH_{4(g)},
at STP?

**
23.
**What
mass of methanol, CH_{3}OH _{(l)}, is formed from its elements
if 2.34 × 10^{4} kJ of energy is released during the process?

**
24.
**An ice
cube with a mass of 8.2 g is placed in some lemonade. The ice cube melts
completely. How much heat does the ice cube absorb from the lemonade as it
melts?

**
25.
**A
teacup contains 0.100 kg of water at its freezing point. The water freezes
solid.

**
(a)
**How
much heat is released to the surroundings?

**
(b) **
How much heat would be required to melt the ice in the teacup?

**
26.
**A
sample of liquid mercury vaporizes. The mercury is at its boiling point and has
a mass of 0.325 g.

**
(a)
**Is
heat absorbed from the surroundings or released to the surroundings?

**
(b)
**How
much heat is absorbed or released to the surroundings by the process?

**
27.
**The
molar enthalpy of solution for sodium chloride, NaCl, is 3.9 kJ/mol.

**
(a)
**Write
a thermochemical equation to represent the dissolution of sodium chloride.

**
(b)
**
Suppose you dissolve 25.3 g of sodium chloride in a glass of water at room
temperature. How much heat is absorbed or released by the process?

**
(c)
**Do you
expect the glass containing the salt solution to feel warm or cool? Explain your
answer.

**
28.
**What
mass of diethyl ether, C_{4}H_{10}O, can be vaporized by adding
80.7 kJ of heat?

**
29.
**3.97 ×
10^{4} J of heat is required to vaporize 100 g of benzene, C_{6}H_{6}.
What is the molar enthalpy of vaporization of benzene?

**
30.
**1.451
kg of water at 25.2°C is added to a kettle and the water is completely
vaporized.

**
(a)
**Draw a
heating curve for this process.

**
(b)
**How
much heat is required for the vaporization of all the water?

**
31.
**A
metal bucket containing 532.1 g of ice at 0.00°C is placed on a wood-burning
stove. The ice is melted and then heated to 45.21°C.

**
(a)
**Draw a
heating curve for this process.

**
(b)
**How
much heat is required to melt the ice and warm the water to 45.21°C?

**
32.
**A
sample of liquid mercury having a mass of 0.0145 g cools from 35.1°C and forms
solid mercury at −38.8°C. The melting point of mercury is −38.8°C and its
specific heat capacity is 0.140 J/g°C.

**
(a)
**Draw a
cooling curve for this process.

**
(b)
**How
much heat is released during this process?

**
33.
**A
sample of 36.8 g of ethanol gas at 300.0°C is cooled to liquid ethanol at
25.5°C. The specific heat capacity of ethanol gas is 1.43 J/g°C, and the
specific heat capacity of liquid ethanol is 2.45 J/g°C. The boiling point of
ethanol is 78.5°C.

**
(a)
**Draw a
cooling curve for this process.

**
(b)
**
Calculate the heat released during this process.

**
34.
**
Calculate the total heat released when 200 g of water vapour at 300.0°C is
cooled until it reaches −20.0°C. The specific heat capacity of ice is 2.02
J/g°C. The specific heat capacity of water vapour is 1.99 J/g°C.

__
Section Review1__

**
1.**
In your own words, state the first law of thermodynamics. Then express the first
law of thermodynamics as an equation.

**
2.**
Define the term “heat.”

**
3.**
What are three important factors to consider when measuring heat transfer?

**
4.**
In Part B of the ThoughtLab on page 631, 60.0 g of water was in beaker 2. The
initial temperature of the water was 35.0°C, and the final temperature was
16.9°C.

**
(a)
**
Calculate the heat that was lost by the water in beaker 2.

**
(b)
**Where
did the heat go?

**
5.**
When iron nails are hammered into wood, friction causes the nails to heat up.

**
(a)
**
Calculate the heat that is gained by a 5.2 g iron nail as it changes from 22.0°C
to 38.5°C.

**
(b)
**
Calculate the heat that is gained by a 10.4 g iron nail as it changes from
22.0°C to 38.5°C.

**
(c)
**
Calculate the heat that is gained by the 5.2 g nail if its temperature changes
from 22.0°C to 55.0°C.

**
6(a)
**
A 23.9 g
silver spoon is put in a cup of hot chocolate. It takes 0.343 kJ of energy to
change the temperature of the spoon from 24.5°C to 85.0°C. What is the specific
heat capacity of solid silver?

**
(b)
**What
is the heat capacity, *C*, of the silver spoon?

**
7.**
The specific heat capacity of aluminum is 0.902 J/g°C. The specific heat
capacity of copper is 0.389 J/g°C. The same amount of heat is transferred to
equal masses of these two metals. Which metal increases more in temperature?
Explain your answer.

**
8.**
You have prepared some hot chocolate to take with you on a hike. You are about
to fill your Thermos™ bottle with the hot chocolate when your friend stops you.
Your friend suggests you rinse the inside of the bottle with hot water before
filling the bottle with hot chocolate.

**
(a)
**
Explain in detail why rinsing the bottle with hot water will help keep your hot
chocolate hot.

**
(b)
**A
Thermos™ bottle has a vacuum between its inner layer and its outer layer.
Explain why the vacuum insulation helps to keep cold drinks cold and hot drinks
hot.

**
(c)
**What
kind of system (open, closed, or insulated) is hot chocolate inside a sealed
Thermos™ bottle? Explain your answer.

__
Section Review 2__

**
1.**
In your own words, explain why exothermic reactions have Δ*H *< 0.

**
2.**
Label each thermochemical equation with the most specific form(s) of Δ*H*.
Pay attention to the *sign *of Δ*H*.

**
(a)
**Ag
_{(s)} + 12 Cl_{2 (g)}
→
AgCl _{
(s)} + 127.0 kJ (at 25°C and 100 kPa)

**
(b)
**44.0
kJ + H_{2}O _{(l)} →
H_{2}O_{(g)}
(at 25°C and 100 kPa)

**
(c)
**C_{2}H_{4
(g)} + 3O_{2} _{(g)}
→
2CO_{2}
_{(g)} + 2H_{2}O _{(g)} + energy

**
3.**
A pot of water boils on a stove. The temperature of the liquid water remains at
100°C.

**
(a)
**What
type of energy change (kinetic or potential) is taking place within the water

**
(b)
**
Explain why the temperature of the water does not change as the water boils,
even though heat is continuously absorbed by the water from the stove element.

**
(c) **
How much heat is needed to boil 2.32 kg of water at 100°C?

**
4.**
A group of campers light a bonfire by touching the flame from a butane lighter
to some kindling. They roast marshmallows over the blaze. Describe the energy
transfers involved using the terms potential energy, kinetic energy,
temperature, system, surroundings, endothermic, exothermic, and combustion
reaction.

**
5.**
Acetylene, C_{2}H_{2}, undergoes complete combustion in oxygen.
Carbon dioxide and water are formed. The standard molar enthalpy of the complete
combustion of acetylene is 1.3 × 10^{3} kJ/mol.

**
(a)
**Write
a thermochemical equation for this reaction.

**
(b)
**Draw a
diagram to represent the thermochemical equation.

**
(c)
**How
much heat is released during the complete combustion of 2.17 g of acetylene?

**
6.**
Write an equation to represent each phase change in Table 16.4. Include the
enthalpy change in the equation.

**
7.**
When one mole of gaseous water forms from its elements, 241.8 kJ of energy is
released. In other words, when hydrogen burns in oxygen or air, it produces a
great deal of energy. Since the nineteenth century, scientists have been
researching the potential of hydrogen as a fuel. One way in which the energy of
the combustion of hydrogen has been successfully harnessed is as rocket fuel for
aircraft.

**
(a)
**Write
a thermodynamic equation for the combustion of hydrogen.

**
(b)
**
Suggest three reasons why hydrogen gas is a desirable rocket fuel.

**
(c)
**
Suggest challenges that engineers might have had to overcome in order to make
hydrogen a workable rocket fuel for aircraft.

**
8.**
Calcium oxide, CaO, reacts with carbon in the form of graphite.Calcium carbide,
CaC_{2}, and carbon monoxide, CO, are produced in an endothermic
reaction.

CaO_{(s)}
+ 3C_{(s)} + 462.3 kJ
→
CaC_{2(s)}
+ CO_{(g)}

**
(a)
**246.7
kJ of heat is absorbed by the system. What mass of calcium carbide is produced?

**
(b)
**How
much heat is absorbed by the system if 46.7 g of graphite reacts with excess
calcium oxide?

**
(c) **
1.38 × 10^{24} formula units of calcium oxide react with excess
graphite. How much energy is needed?

__
Section Review 3__

**
1.**
The portions of heating curves and cooling curves that represent changes of
state are horizontal (flat). Explain why this is the case.

**
2.**
Iron melts at 1535°C. Draw a cooling curve to show what happens when molten iron
at 1600°C cools to solid iron at 50°C. Label the axes and sections of your
cooling curve appropriately.

**
3.**
A pure gold chain with a mass of 10.23 g is heated until it forms liquid gold at
the melting point of 1064.2°C. The temperature of the chain is initially 21.0°C.
The enthalpy of freezing for gold is 12.5 kJ/mol.

**
(a)
**Draw a
heating curve to represent what happens to the gold.

**
(b)
**What
is the total heat absorbed by the gold as it warms and then melts?

**
4.**
An ice cube with a mass of 3.375 g sits in an empty glass of water on a hot day.
The ice cube is initially at −5.2°C. It melts and the liquid water warms to
27.3°C.

**
(a)
**Draw a
heating curve to represent what happens to the ice cube.

**
(b)
**What
is the total heat absorbed by the water as it warms from ice at −5.2°C to liquid
water at 27.3°C? The specific heat capacity of ice is 2.02 J/g°C.

**
5.**
1.55 kg of water vapour at 125.4°C cools to eventually form ice at −5.5°C. The
specific heat capacity of ice is 2.02 J/g°C. The specific heat capacity of water
vapour is 1.99 J/°C.

**
(a)
**Draw a
cooling curve to represent the process.

**
(b)
**How
much heat is released during this process?

**
6.**
During cold weather, fruit farmers spray their fruit with water to prevent frost
damage. Explain why this practice works.

**
7.**
Water vapour at 100°C causes more severe burns than liquid water at 100°C.
Explain why this is the case.

**
8.**
If you became lost in a forest in winter, why would it be better to drink water
from a stream rather than eat snow to quench your thirst?

**
9.**
Examine the heating curve for lead shown in Figure 16.21.

**
(a)
**What
is the boiling point of lead?

**
(b)
**What
is the melting point of lead?

**
(c)
**A 500
g sample of solid lead at −25.0°C is heated until it melts completely. How much
heat is absorbed? The specific heat capacity of solid lead is 0.127 J/g°C. The
enthalpy of melting of lead is 5.08 kJ/mol.

**
**