THE FUNDAMENTALS OF CALORIMETRY

CHEMISTRY

The Fundamentals of
Calorimetry

Investigation
Manual

THE FUNDAMENTALS OF CALORIMETRY

Overview
This investigation uses calorimetry to measure the heat of solu-
tion for two salt compounds commonly used in hot packs and
cold packs. You will perform a graphical analysis of the calorim-
etry data for an endothermic and exothermic salt and predict
how many grams of each salt are required to achieve a specific
temperature when activated. After determining the heats of
solution for both compounds, you will design a proposal for
constructing a hot pack and a cold pack containing 100 g of
water.

Objectives
• Construct and use a simple calorimeter
• Calculate the heat capacity of the calorimeter.
• Calculate the enthalpy of solution for ammonium chloride and

calcium chloride from graphical analysis.
• Design a chemical hot pack and cold pack that meets given

volume and temperature specifications for first aid treatment.

Time Requirements
Preparation …………………………………………………………… 15 minutes
Activity 1: Heat Capacity of the Calorimeter …………….. 30 minutes
Activity 2: Enthalpy of Solution for Calcium Chloride …. 30 minutes
Activity 3: Enthalpy of Solution for
Ammonium Chloride ………………………………………….. 30 minutes
Activity 4: Design Proposal for a Hot Pack and a
Cold Pack ………………………………………………………… 15 minutes

2 Overview
2 Objectives
2 Time Requirements
3 Background
6 Materials
7 Safety
7 Preparation
8 Activity 1
9 Activity 2
9 Activity 3
9 Activity 4
11 Disposal and Cleanup

Key
Personal protective
equipment
(PPE)

goggles gloves apron

warning corrosion flammable toxic environment health hazard

link to results and required
video submit

47

Background
When people sprain their ankle they are often
given an instant cold pack to prevent swelling at
the injury site. After 48–72 hours, a hot pack can
be applied to relieve pain and stimulate blood
flow for faster healing. These packs are activated
by breaking an internal water pouch, which
mixes with a salt contained in the outer bag. The
amount of heat absorbed or released depends
on the salt used and can be determined by the
science of chemical thermodynamics.

Chemical thermodynamics is the study of energy
changes that accompany physical and chem-
ical transformations. These changes occur
through the generation or absorption of a quan-
tifiable amount of heat (q). If heat is generated
during the reaction or physical change, it is an
exothermic reaction. If the heat is absorbed or
needs to be added to the reaction or physical
change, then it is called an endothermic
reaction.

Scientists use the term enthalpy (H) to measure
the total energy of a system at constant pres-
sure. Enthalpy also accounts for any change in
volume during a reaction, which is important
when dealing with gas reactions. The equation
for the enthalpy change of a reaction is:

ΔH = Δq + PΔV

Where ΔH is the change in enthalpy, Δq is the
heat change, P is pressure (which remains
constant), and ΔV is the change in volume. In
most calorimeters, pressure and volume are
constant. Therefore, the equation becomes:

ΔH = Δq

Enthalpy is dependent on the amount of
substance present. The enthalpy change for a

reaction is generally written as a molar quantity.
To calculate the molar enthalpy of a reaction,
divide the reaction heat by the number of moles
of reactant or product:

ΔHrxn = qrxn/mol

Heat energy is always conserved within a
system and all the parts of that system will
adjust so that everything is the same tempera-
ture. For example, if a hot piece of copper metal
is added to room temperature water, the heat
energy transfers from the copper to the water.
The energy transferred from the copper to the
water because of the temperature difference is
the heat (q). If the system is left undisturbed, the
energy will continue to flow from the copper to
the water until both are the same temperature,
indicating that the system is at equilibrium.

Calorimetry is the act of measuring heat energy.
The magnitude and the direction of heat transfer
can be determined by using a calorimeter. A
calorimeter is an insulated apparatus designed
to create a closed system by preventing heat
from flowing in or out. In this lab the calorimeter
is two foam coffee cups stacked together and
placed in a 250-mL beaker. The double foam
walls and the air surrounding the cups in the
beaker insulate the system.

In this investigation, the temperature change
that occurs when a salt is dissolved in water will
be measured. The heat released or absorbed
during the reaction will be calculated by
measuring the temperature change. However,
heat is not the same as temperature. Tempera-
ture measures how hot or cold the sample is
and is independent of mass. Heat or heat energy

continued on next page

measures the energy a sample contains. It is an
extensive property and depends on the material
quantity (mass). For example, a drop of boiling
water and a gallon of boiling water both have a
temperature of 100 °C, but the gallon of water
has significantly higher heat energy because
there is more of it.

The amount of heat that is given off or absorbed
by a substance depends on both the mass and
the substance composition. Every substance
has its own specific heat (Cp), which is defined
as the amount of heat energy necessary to raise
the temperature of 1 gram by 1 °C. The specific
heat of water is 4.18 J/g °C, which means it takes
4.18 joules of energy to raise the temperature of
1 g of water by 1 °C. More examples of specific
heat include aluminum, which has a specific
heat of 0.22 cal/g °C or 0.91 J/g °C, and copper
whose specific heat is 0.09 cal/g °C or 0.385
J/g °C. Water requires more energy to heat than
aluminum and copper metal.

In the calorimeter, a measured mass of water at
a given temperature will be placed in the inner
cup and a chemical will be added. When the
chemical dissolves in the water the heat can
either be transferred to the water or absorbed
from the water by the act of chemical solvation.
Since this reaction is carried out at constant
(atmospheric) pressure, the heat of the reaction
can be calculated using the change in tempera-
ture of the water.

The heat transfer or change in enthalpy for
a reaction (qrxn) is related to the mass of the
solution (m), the specific heat capacity of the
solution at constant atmospheric pressure (Cp),
and the temperature change (ΔT = Tfinal– Tinitial)

as shown in Equation 1. The minus sign on the
right side of the equation means that if a solute
releases heat, the water will absorb it, and if a
solute absorbs heat, the water will release it.

Equation 1.
qrxn = –(m × Cp × ΔT)

No calorimeter is a perfect insulator. There will
be a small amount of energy transferred to and
from the calorimeter. If the temperature of the
reaction solution inside the calorimeter is higher
than the calorimeter, some heat will be lost from
the solution to heat up the calorimeter. There-
fore, a calculation for the calorimeter itself must
be added to the solution calculation on the right
side of Equation 1, as shown in Equation 2.

Equation 2.
qrxn = –[(msolution × Cp solution × ΔTsolution) +

(mcalorimeter × Cp calorimeter × ΔTcalorimeter)]

Since the mass and specific heat of the calo-
rimeter remain constant, they can be multiplied
together to form another constant (m × Cp = C).
C represents the heat capacity of the calorimeter
with the unit J/ ºC in Equation 3.

Equation 3.
qrxn = –[(mwater × Cp water × ΔTwater)

+ (Ccalorimeter × ΔTcalorimeter)]

The change in temperature for the calorimeter
is assumed to be the same as the change in
temperature for water since they are in contact
with each other.

Sample Calculations
In Activity 1, the heat capacity of the calorimeter
will be determined by analyzing the tempera-

Background continued

THE FUNDAMENTALS OF CALORIMETRY

continued on next page

ture change of the cold water in the calorim-
eter when hot water is added. The difference
between the heat lost by the hot water and the

heat gained by the cold water will be due to the
heat absorbed by the calorimeter.

A calibration curve is used to determine the heat

capacity of the calorimeter. The calibration curve
is a plot of the water temperature in the calorim-
eter as a function of time. Plotting the tempera-
ture as a function of time will determine the
cooling rate of the mixture. You can accurately
measure the initial mixing temperature by fitting
the data with a linear trend line using Excel.
Figure 1 shows a calibration curve generated
by adding 50 g of 96 °C water to 50 g of
24 °C water. The initial temperature of the
mixture should have been 60 °C [(96 + 24)/2 =
60]. The y-intercept from the linear trend curve is
57.4 °C and will represent Tfinal.

ΔT(hot water) = 57.4 °C – 96 °C = –38.6 °C

ΔT(cold water) = 57.4 °C – 24 °C = –33.4 °C

The energy lost by this reaction (Δq (hot water) +
Δq (cold water)) will be gained by the calorimeter
(Δq (cal)), so the value of Δq(cal) should be set to
be positive in Figure 2.

Since the mass and specific heat of the calorimeter remain constant, they can be
multiplied together to form another constant (m x Cp = C). C represents the heat
capacity of the calorimeter with the unit J/ºC in Equation 3.

Equation 3. qrxn = -[(mwater x Cp water x ∆Twater) + (Ccalorimeter x ∆Tcalorimeter)]

The change in temperature for the calorimeter is assumed to be the same as the
change in temperature for water since they are in contact with each other.

Sample Calculations

In Activity 1, the heat capacity of the calorimeter will be determined by analyzing the
temperature change of the cold water in the calorimeter when hot water is added. The
difference between the heat lost by the hot water and the heat gained by the cold
water will be the due to the heat absorbed by the calorimeter.

Figure 1

A calibration curve is used to determine the heat capacity of the calorimeter. The
calibration curve is a plot of the water temperature in the calorimeter as a function of
time. Plotting the temperature as a function of time will determine the cooling rate of
the mixture. You can accurately measure the initial mixing temperature by fitting the
data with a linear trend line using Excel. Figure 1 shows a calibration curve generated
from adding 50 g of 96°C water to 50 g of 24°C water. The initial temperature of the
mixture should have been 60°C [(96 + 24)/2 = 60]. The y-intercept from the linear trend
curve is 57.4°C and will represent Tfinal.

y = -5x + 57.4
30
35
40
45
50
55
60
65
70

0 1 2 3 4 5 6

Calibration Curve

Figure 1.

Δq = C × ΔT × m
Δq(hot water) = 4.18 J/g °C × –38.6 °C × 50 g = –8,067 J

Δq (cold water) = 4.18 J/g °C × 33.4 °C × 50 g = 6,981 J

|Δq (hot water) + Δq (cold water)| = Δq (cal)
Energy gained by calorimeter = 1,086 J

Δq (cal) = 1,086 J = C (cal) × 33.4 °C

Ccal = 32.5 J/°C

Figure 2.

Materials
Included in the materials kit:

3 Foam cups, 8 oz Ammonium
chloride, 50 g

Calcium chloride,
anhydrous, 50 g

Needed, but not supplied:
• Water, bottled or purified
• Source of hot water (70–80 °C)
• Timing device
• Paper towels

Needed from the chemical kit:

THE FUNDAMENTALS OF CALORIMETRY

Needed from the equipment kit:

There are many solids found in tap water that
will affect your calculations. Bottled, purified,
or filtered water from a home water purifier
(e.g., Brita® or PUR®) should be used.

Reorder Information: Replacement supplies
for The Fundamentals of Calorimetry
investigation can be ordered from Carolina
Biological Supply Company, kit 580320.

Call 800-334-5551 to order.

2 Weigh boats Thermometer

2 Plastic
spoons

Electronic
balance

cylinder, 50 mL

Beaker, 250 mL

Safety
Goggles, gloves,
and a lab apron are
required at all times while conducting this
investigation.

Read all the instructions for this laboratory
activity before beginning. Follow the instructions
closely, and observe established laboratory
safety practices, including the use of appro-
priate personal protective equipment (PPE) as
described in the Safety and Procedure sections.

Use caution when heating water to 75–80 °C in
a microwave. Heat in short intervals, and check
the temperature with a thermometer. Do not
exceed 80 °C. Higher temperatures may melt
the plastic graduated cylinder when measuring
the water.

Calcium chloride and ammonium
chloride are harmful if swallowed and

can cause serious eye irritation.

Do not eat, drink, or chew gum while performing
this activity. Wash your hands with soap and
water before and after performing the activity.
Clean up the work area with soap and water
after completing the investigation. Keep pets
and children away from lab materials and
equipment.

Preparation
1. Read through the procedure.
2. Collect all the materials.
3. Select a clean work area.
4. Construct a calorimeter by placing one foam

cup inside another and placing these two
cups inside a 250-mL beaker. Placing the two
foam cups inside the beaker prevents the
calorimeter from tipping over.

!

ACTIVITY 1

A Heat Capacity of the Calorimeter
1. Measure 50.0 mL of water with a graduated

cylinder and pour into the inner foam cup of
the calorimeter. This will be the cold water.

2. Place the foam cup
with the cold water
inside the beaker.

3. Stir the water with
the thermometer until temperature is constant
and record it as the initial temperature of the
cold water (Tc) in Data Table 1.

4. Fill a third foam cup ¾ full with the hottest tap
water possible.

5. Take the temperature of the hot water. If the
temperature is less than 80 °C, heat in a

ACTIVITY

Time
(min)

Trial 1
Temp. °C

Trial 2
Temp. °C

1

2

3

4

5

6

7

8

9
10

Trial 1 Trial 2

Initial temperature of cold water, Tc
Initial temperature of warm water, Th
Average temperature, Ta (Th + Tc )/2

Temperature at time 0 from graph, T0
Heat lost by hot water

Heat gained by cold water

Heat gained by calorimeter in J

Temperature change of the calorimeter

Heat capacity (C) of the calorimeter in J/°C

Average heat capacity (C) of calorimeter in J/°C

microwave with short bursts until it reaches
80 °C.

6. Measure 50.0 mL of the hot water with a
graduated cylinder. Place a thermometer
in the cylinder and gently stir to get a
constant reading. The temperature should be
75–80 °C. Record this as the temperature of
the hot water (Th) in Data Table 1.

7.
47

Quickly pour the 50.0 mL of hot water
into the cold water and start a timer.

8. Gently stir the mixed water with the
thermometer, and record the temperature at
1 minute and then at 1-minute intervals for 10
minutes in Data Table 1.

9. Discard the water, dry the cup with a paper
towel, and place it back in the calorimeter.

10. Repeat this activity, and collect a second set
of data.

Remember that 1 mL
of water = 1 g of water.

Data Table 1: The Heat Capacity of the Calorimeter

continued on next page

Create a spreadsheet and graph for the
temperature versus time data. Calculate the
linear trend line and use the y-intercept to
find the temperature at time 0 when the two
volumes of water are mixed.

ACTIVITY 2

B Enthalpy of Solution for Calcium
Chloride

1. Measure 100 mL of pure or bottled water
with a graduated cylinder, and pour it into the
calorimeter.

2. Stir the water with a thermometer until the
temperature is constant, and record it as the
initial temperature (Ti) in Data Table 2.

3. Weigh approximately 5 g of calcium chloride
(CaCl2). Record the exact mass in Data Table
2.

4. Add the calcium chloride to the calorimeter,
and stir the solution with the thermometer.

5. Keep stirring until the temperature stops
changing. Record this final temperature as Tf
in Data Table 2.

6. Discard the solution, and rinse the inner cup.
Dry the cup, and place back in the calorimeter.

7. Repeat steps 1–6 with 10.0 g and 15.0 g of
CaCl2.

ACTIVITY 3

C Enthalpy of Solution for Ammonium
Chloride

1. Measure 100 mL of pure or bottled water
with a graduated cylinder, and pour it into the
calorimeter.

2. Stir the water with a thermometer until the
temperature is constant, and record it as the
initial temperature (Ti) in Data Table 2.

3. Weigh approximately 5 g of ammonium
chloride (NH4Cl). Record the exact mass in
Data Table 2.

4. Add the ammonium chloride to the
calorimeter, and stir the solution with the
thermometer.

5. Keep stirring until the temperature stops
changing. Record this final temperature as Tf
in Data Table 2.

6. Discard the solution, and rinse the inner
cup. Dry the cup, and place back in the
calorimeter.

7. Repeat steps 1–6 with 10.0 g and 15.0 g of
NH4Cl.

ACTIVITY 4

D Design a Proposal for a Hot Pack
and a Cold Pack

Based on the data and graphs for calcium chlo-
ride and ammonium chloride, determine which
compound to use and what quantity of each
compound will be needed to make a chemical
hot pack and cold pack. Both packs should be
calculated based on using 100 g of water. The
hot pack should reach 60 °C, and the cold pack
should go down to 3.0 °C from a room tempera-
ture of 25 °C.

ACTIVITY

Calcium Chloride Ammonium Chloride
5 g

CaCl2
10 g

CaCl2
15 g

CaCl2
5 g

NH4Cl
10 g

NH4Cl
15 g

NH4Cl

Mass of water (g)

Mass of salt (g)

Moles of salt (g × mol/g)

Initial temperature (°C) Ti

Final temperature (°C) Tf

Change in temperature (°C)
ΔT = Tf – Ti

Heat absorbed by the
solution (J)
qw = –[cw × mw × ΔT]

Heat capacity of the
calorimeter
(J/°C)

Heat absorbed by the
calorimeter (J)
qc = –[C × ΔT]

Enthalpy of solution (J)

Enthalpy of solution (kJ)

Enthalpy/mole of solution
(kJ/mol)

Average enthalpy/mole of
solution (kJ/mol)

Data Table 2: The Heat of Solution for Calcium Chloride and Ammonium Chloride

Create a spreadsheet and graph for CaCl2
and NH4Cl. Plot the mass on the x-axis and
change in temperature on the y-axis for
both graphs. The slope will be the change in
temperature per gram of salt dissolved.

Hot Pack: Compound needed
to achieve 60 °C: ___________________________

Grams needed per 100 g of water: ________

Cold Pack: Compound needed
to achieve 3.0 °C: __________________________

Grams needed per 100 g of water: ________

Disposal and Cleanup
1. Solutions of CaCl2 and NH4Cl can be poured

down the drain with running water.
2. Discard all three foam cups and plastic

spoons.
3. Rinse the beaker and dry with a paper towel.
4. Clean and sanitize the work space.

www.carolina.com/distancelearning 11

CHEMISTRY
The Fundamentals of Calorimetry

Investigation Manual

CB780161511

• Overview
• Objectives
• Time Requirements
• Background
• Materials
• Safety
• Preparation
• ACTIVITY 1
• ACTIVITY 2
• ACTIVITY 3
• ACTIVITY 4
• Disposal and Cleanup

3

The Fundamentals of Calorimetry
Student Name
Date

## Data

### Activity 1

Data Table 1

 Time(min) Trial 1Temp. °C Trial 2Temp. °C 1 2 3 4 5 6 7 8 9 10
 Trial 1 Trial 2 Initial temperature of cold water, Tc Initial temperature of warm water, Th Average temperature, Ta Temperature at time 0 from graph, T0 Heat lost by water in J to calorimeter (Δq) Heat capacity (C) of calorimeter in J/°C Average Heat capacity (C) of calorimeter in J/°C

*Note that the Average Heat Capacity (C) calculated above is used in Activities 2 and 3.

1.

1. Create a spreadsheet and graph of the data from Data Table 1, plotting temperature vs. time, and use the Y intercept to find the temperature at time 0 when the two volumes of water are mixed.

a. Insert graph below.

### Activities 2 and 3

Data Table 2

 5g CaCl2 10gCaCl2 15gCaCl2 5gNH4Cl 10gNH4Cl 15gNH4Cl Mass of water (g) Mass of salt (g) Moles of salt(g x mol/g) Initial Temperature(°C)Ti Final Temperature(°C)Tf Change in Temperature (°C)∆T = Tf – Ti Heat absorbed by the solution (J)qw = -[cw x mw x ∆T] Heat Capacity of the Calorimeter (J/°C) Heat absorbed by the calorimeter (J)qc = -[C x ∆T] Enthalpy of solution (J)∆H = qw + qc Enthalpy of solution (kJ)*Note: 1 kJ = 1000 J Enthalpy/mole of solution (kJ/mol)∆H/moles of salt

2. Create a spreadsheet and graph for CaCl2 and NH4Cl, using the data from Data Table 2. Plot mass on the X axis and change in temperature on the Y axis for both graphs. The slope will be the change in temperature per gram of salt dissolved.

a. Insert graphs below.

3. What sort of relationship exists between the temperature change and the mass of the solid? Explain why that relationship exists.

4. How do the calculated molar heats of solution for calcium chloride compare to one another? How do the calculated molar heats of solution for ammonium chloride compare to one another?

5. The actual molar enthalpy of solution for calcium chloride is -81.3 kJ/mol, whereas the molar enthalpy of solution of ammonium chloride is 14.8 kJ/mol.

Calculate the average molar enthalpy of solution for each chemical based on your data, and then calculate the percentage error for each.

Percent error is (|Actual – Experimental|/Actual) * 100%

### Activity 4

6. Based on the data and graphs for calcium chloride and ammonium chloride, determine which compound to use and what quantity of each compound will be needed to make a chemical hot pack and cold pack. Both packs should be calculated based on using 100 g (100 mL) of water. The hot pack should reach 60 °C, and the cold pack should go down to 3.0 °C from a room temperature of 25 °C.

Hot Pack: Compound needed to achieve 60 °C above room temperature:

Cold Pack:Compound needed to achieve 3.0 °C:

7. What were some potential sources of error in this investigation?

8. Suggest some ways in which the calorimeter or lab protocol could be improved to have lower percentage of errors.