E XPERIMEN T
2
Specific Heat of Substances
OBJECTIVES
Determine the specific heat of a solid and understand the relative heat
properties of substances having different specific heats.
INTRODUCTION
Substances respond differently upon being heated or cooled. For example,
one calorie (4.18 J) of heat raises the temperature of 1.00 gram of water by
1.00 8C. The same amount of heat raises the temperature of 1.00 gram of
lead by 32.4 8C. The physical quantity which relates the temperature
change and mass of a substance to the amount of heat absorbed is called
the specific heat. Specific heat is a physical property that is unique to a
given substance that can be measured and used to identify an unknown
material. In this experiment, the specific heat of an unknown solid will be
determined and used to identify the solid.
The specific heat (C) of a substance is the quantity of energy (J or cal)
required to change the temperature of 1.00 gram of that substance by 1.00 8C.
(A related quantity is the molar heat capacity of a substance which is the
quantity of energy required to change the temperature of 1.00 mole of a
substance by 1.00 8C.)
C¼
heat ðJ or calÞ
ðmassÞðchange in temperatureÞ
ðEq: 1Þ
Specific heat typically has units of cal/g8C or J/g8C. The molar heat
capacity has units of cal/mol8C or J/mol8C. The specific heat of an
unknown substance can be determined with a device called a calorimeter.
Calorimeters are used to measure the heat lost or absorbed by a substance in
physical or chemical changes. Calorimeters are insulated containers that
prevent heat exchange between the process occurring inside the calorimeter
and the outside surroundings. This experiment will employ two styrofoam
cups, one nested inside the other, to serve as an inexpensive but effective
calorimeter.
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Experiments in General Chemistry Featuring MeasureNet n Stanton et al.
The First Law of Thermodynamics, or Law of Conservation of Energy,
states that energy can neither be created nor destroyed during ordinary
physical or chemical changes, but it can be transferred from one system to
another. The Second Law of Thermodynamics implies that energy normally flows from substances at higher temperatures to substances at lower
temperatures. Both laws will be used in this experiment to determine the
specific heat of a substance.
The heat (energy) lost or gained by a substance as its temperature
changes can be calculated using the equation
q ¼ m & C & DT
ðEq: 2Þ
where q is the heat change (units of J or cal) of the substance, m is the mass
of the substance in grams, and DT is the change in temperature (in degrees
8C) of the substance (DT ¼ Tfinal % Tinitial).
One way to determine the specific heat of a substance is to measure the
heat lost by a given mass of a heated substance after it has been transferred
into a known mass of water that is initially at room temperature. The
aforementioned laws of thermodynamics indicate what will happen as the
water and substance contact each other. The total amount of heat energy
will be conserved and the cooler substance (water) will experience a
temperature rise as the warmer substance cools. After a period of heat
exchange, the equilibrium temperature, or final temperature, of the system
will be attained. Given the specific heat of water (4.18 J/g8C), the mass of
the water, and the changes in the temperature of the water and the substance; the heat absorbed by the water can be calculated. From the First
Law of Thermodynamics, it is known that the heat absorbed by the water
must be equal in magnitude to the heat lost by the substance. Mathematically this statement can be written as
%q lost by substance ¼ q gained by water
(The minus sign, preceding % q above, indicates that heat flows from the
substance to the water). From Eq. 2, this can be rewritten as
%ðmsubstance & Csubstance & DTsubstance Þ ¼ mwater & Cwater & DTwater
ðEq: 3Þ
Equation 3 can be rearranged to calculate the specific heat of the substance.
Csubstance ¼
mwater & Cwater & DTwater
%ðmsubstance & DTsubstance Þ
ðEq: 4Þ
If the heat exchanged in this experiment were solely limited to the
metal and the water, Eq. 4 would be sufficient. However, heat will be lost
to the surroundings (air, lab bench, etc.) near the mixture. Heat loss to the
surroundings can be minimized by performing the experiment in a calorimeter that inhibits heat exchange with the surroundings. However, the
calorimeter will also absorb some of the heat from the substance. The heat
lost to the calorimeter must also be accounted for in this experiment.
Therefore, it will be necessary to calibrate the calorimeter. The calorimeter
constant (Ccal) is defined as the heat energy required to raise the
Experiment 2 n Specific Heat of Substances
15
temperature of the calorimeter by 1.00 8C. The heat absorbed by the calorimeter, qcal, can be determined according to the equation
qcalorimeter ¼ Ccalorimeter & DTwater
or
Ccalorimeter
q
¼ calorimeter
DTwater
ðEq: 5Þ
where Ccalorimeter is the calorimeter constant in J/8C, and DTwater is the
change in the temperature of the water.
If the heat absorbed by the calorimeter is included in Eq. 4, we can
derive an accurate expression for the specific heat of a substance.
heat lost by substance ¼ heat absorbed by water þ calorimeter
%qsubstance ¼ qwater þ qcalorimeter
%ðmsubstance & Csubstance & DTsubstance Þ ¼ ðmwater & Cwater & DTwater Þ þ ðCcalorimeter & DTwater Þ
ðEq: 6Þ
Equation 6 can be rearranged to yield the specific heat of the substance.
Csubstance ¼
%½ðmwater & Cwater & DTwater Þ þ ðCcalorimeter & DTwater Þ*
ðEq: 7Þ
msubstance & DTsubstance
The mass of the water and the substance are determined by difference
(weigh an empty container; add water or substance to the container and
reweigh, the difference in the two weights is the weight of water or substance). The specific heat of water is a well-established constant, 4.18 J/g8C.
The challenging aspect of this experiment is to accurately determine temperature changes for the water, DTwater, and the substance, DTsubstance.
Temperature changes will be monitored by recording temperature versus
time scans (thermograms) using the MeasureNet temperature probe. Figure 1 depicts a thermogram used to determine the calorimeter constant of a
styrofoam cup calorimeter.
NOTE: When determining DTwater or DTsubstance, subtract the initial temperature of the
water or substance, Ti, from the final temperature of the solution, Tf.
34.8 °C
38
o
Temperature, C
! 2010 Brooks/Cole, Cengage Learning
Calibration of Styrofoam Cup Calorimeter
Figure 1
Thermogram for the addition
of 31.152 grams of water at
51.0 8C to 31.284 grams of
water at 20.2 8C. The
equilibrium temperature of the
system is 34.8 8C.
33
28
∆T
20.2 °C
23
18
0
5
10
15
20
Time, s
25
30
35
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Experiments in General Chemistry Featuring MeasureNet n Stanton et al.
SAMPLE CALCULATIONS
Determination of the
Calorimeter Constant
In this example, a known amount of warm water is mixed with a known
amount of cool water. The hot water loses heat to the cool water until an
intermediate, equilibrium temperature is attained. The heat absorbed by
the calorimeter is the difference in the heat lost by the warm water and the
heat absorbed by the cool water. If 31.152 mL of water (31.152 g assuming
the density of water is 1.00 g/mL at ambient temperatures) at 51.0 8C are
mixed with 31.284 mL (31.284 g) of water in a calorimeter at 20.2 8C,
the equilibrium temperature attained by the system is 34.8 8C (Figure 1).
The specific heat of water is 4.18 J/g8C. Calculate the calorimeter constant
for this system in J/8C.
%qwarm water ¼ qcool water þ qcalorimeter
qcalorimeter ¼ %qwarm water % qcool water
qcalorimeter ¼ %ðmwarm water & Cwarm water & DTwarm water Þ % ðmcool water & Ccool water & DTcool water Þ
!
"
!
"
4:18 J
4:18 J
& ð34:8 % 51:0 8CÞ % 31:284 g &
& ð34:8 % 20:2 8CÞ
qcalorimeter ¼ % 31:152 g &
g8C
g8C
qcalorimeter ¼ 2110 J % 1910 J
qcalorimeter ¼ 200: J
Ccalorimeter ¼
qcalorimeter
DTcool water
Ccalorimeter ¼
200: J
¼ 13:7 J=8C
ð34:8 8C % 20:2 8CÞ
The calorimeter constant for the styrofoam calorimeter indicates that
the calorimeter absorbs 13.7 J of heat for every 1.00 8C change in the
temperature of the system. The value of the calorimeter constant will be
used in the following sample calculation to determine the specific heat of
an unknown substance.
When calculating Ccalorimeter, always use DTcool water because the calorimeter is initially at the same temperature as the cool water and both
absorb energy from the warm substance.
Determination of the
Specific Heat of a Solid
7.050 grams of an unknown solid is heated to 100.0 8C. The warm solid is
added to a calorimeter containing 50.00 grams of water at 24.00 8C. The
system attains an equilibrium temperature of 24.90 8C. Use this information and Eq. 7 to determine the specific heat of the solid.
Csolid ¼
Csolid ¼
%½ðmwater & Cwater & DTwater Þ þ ðCcalorimeter & DTwater Þ*
msolid & DTsolid
%½ð50:00 gÞ ð4:18 J=g8CÞ ð24:90 % 24:00 8CÞ þ ð13:7 J=8CÞ & ð24:90 % 24:00 8CÞ*
7:050 g & ð24:90 % 100:08CÞ
Csolid ¼
%½190 J þ 12 J*
¼ 0:38 J=g8C
%529 g8C
Experiment 2 n Specific Heat of Substances
17
Table 1 Specific heat values for selected substances
Solids
Aluminum
0.897 J/g8C
Calcium Carbonate
0.837 J/g8C
Copper
0.385 J/g8C
Copper(II) Oxide
0.533 J/g8C
Graphite, C(s)
0.709 J/g8C
Iron
0.450 J/g8C
Lead
0.129 J/g8C
Zinc
0.389 J/g8C
Liquids
1,5-Pentanediol
3.08 J/g8C
1-Hexene
2.18 J/g8C
1-Propanol
2.40 J/g8C
Acetone
2.17 J/g8C
Ethanol
2.45 J/g8C
Glycerol
2.38 J/g8C
Water
4.18 J/g8C
Table 1 lists the specific heat values of several solids and liquids. From
the data presented in Table 1, the solid could be either copper or zinc
metal.
From Table 1, it is evident that solids generally have lower specific heat
values than liquids. In particular, water has a very high specific heat even
compared to the other liquids in the table. That is one reason why water is
commonly chosen as a coolant for automobile engines.
PROCEDURE
! 2010 Brooks/Cole, Cengage Learning
CAUTION
Students must wear departmentally approved eye protection while
performing this experiment. Wash your hands before touching your eyes and
after completing the experiment.
Part A - Determination of the
Calorimeter Constant
1. See Appendix A-1 – Instructions for Initializing the MeasureNet
Workstation to Record a Temperature versus Time Scan. Complete all
steps in Appendix A-1 before proceeding to Step 2 below.
2. See Appendix A-2 – Instructions for Recording a Temperature versus
Time Thermogram to Determine the Styrofoam Cup Calorimeter
Constant. Complete all steps in Appendix A-2 before proceeding to
Step 3.
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Experiments in General Chemistry Featuring MeasureNet n Stanton et al.
3. Steps 4–6 are to be completed after the laboratory period is concluded (outside
of lab). Proceed to Step 8, Determining the Specific Heat of a Solid
4. From the tab delimited files you saved, prepare plots of the temperature versus time data using Excel (or a comparable spreadsheet program). Instructions for plotting temperature versus time thermograms
using Excel are provided in Appendix B-1.
5. How do you determine the equilibrium temperature of the hot-cold
water mixture in the calorimeter? How do you determine the temperature changes for the warm water and the cold water? Should these
temperatures be recorded in the Lab Report and to how many significant figures?
6. What calculations are required to determine the calorimeter constant in
J/8C? From the results of Trials 1 and 2, determine the average calorimeter constant.
7. Use the same two styrofoam cups in Part B of the experiment that were used in
Part A. The calorimeter constant determined in Part A will be used in Part B
of this experiment to determine the specific heat of the unknown solid.
Part B - Determination of the
Specific Heat of a Solid
8. 45–50 grams of tap water should be added to the calorimeter to serve
as the cool water. Should the exact mass of the cool water be recorded
in the Lab Report? If so, to what number of significant figures should
the mass be recorded?
9. Place a stir bar in the bottom of the calorimeter and turn the power on
to a low to medium setting. Be sure the stir bar does not contact the
temperature probe or the walls of the container when spinning.
10. Obtain an unknown solid and record the Unknown Number in the Lab
Report.
Bobby Stanton/Wadsworth/Cengage Learning
11. 15 to 20 grams of the unknown solid must be added to a 25 & 200 mm
test tube (a large test tube), and nested inside of a 250 mL beaker. Must
the exact mass of the unknown solid be determined? Should the mass
be recorded in the Lab Report, and to how many significant figures?
Figure 2
Heating solid inside a test
tube immersed in boiling
water
12. Place the beaker containing the test tube with solid on a hot plate, and
add ' 125 mL of water to the beaker (Figure 2). Bring the water to a
gentle boil. Do not allow any water to splash into the test tube containing the solid. Secure the test tube to a ring stand with a utility
clamp.
13. Insert a thermometer into the solid (inside the test tube, see Figure 2).
The thermometer must not touch the bottom or the walls of the test
tube (tip of thermometer should be at least 1 cm from the bottom of the
test tube). The test tube containing the unknown metal should remain
in boiling water for 10 minutes.
14. Note the temperature on the MeasureNet workstation display. How
should the temperature of the cool water be determined? Should this
temperature be recorded in the Lab Report and to what number of
significant figures?
15. Leave the test tube containing unknown solid in the boiling water for
at least 10 minutes. How should the temperature of the solid be
determined? Should this temperature be recorded in the Lab Report,
and to what number of significant figures?
Experiment 2 n Specific Heat of Substances
19
16. Press Start on the MeasureNet workstation to start the scan. After
5–10 seconds have elapsed, raise the calorimeter lid. Remove the
thermometer from the test tube containing the hot solid. Using the
utility clamp to hold the hot test tube, quickly, but carefully, transfer all
of the hot solid from the test tube to the calorimeter. Do not splash
water from the calorimeter as the solid sample is added. Immediately
replace the lid on the calorimeter.
17. Be sure the stir bar is still turning. If a stir bar is not available, stir the
contents of the calorimeter with the wire stirrer. Be sure the probe stays
submerged in the water at all times. Do not slosh any water out of the
calorimeter.
18. Once the water temperature has risen and stabilized at a constant
temperature (reaching equilibrium), press Stop to end the scan.
19. Press File Options, then press F3 to save the scan. Enter a 3 digit code
when prompted, then press Enter. Save the file to a disk, flash drive, or
email the files to yourself via the internet.
20. Record the file name in your Lab Report. Note what type of information is contained in the file in the Lab Report.
21. Press Display to clear the previous scan. You are now ready to press
Start to record a subsequent scan for a new experimental trial.
22. Remove the stir bar from the calorimeter with a magnetic rod. Decant
the water in the calorimeter into a beaker. Remove any pieces of metal
from the beaker, and pour the water into the sink.
23. Thoroughly dry the unknown solid with a towel. Pour the solid into
the ‘‘Used Unknown Solid’’ container bearing the same number as your
unknown. Thoroughly dry the calorimeter.
24. Perform a second trial to determine the specific heat of the unknown
solid by repeating Steps 8–23.
25. When you are finished with the experiment, transfer the files to a flash
drive, or email the files to yourself via the internet.
26. Return the dry styrofoam cups and lid to your instructor.
! 2010 Brooks/Cole, Cengage Learning
27. From the tab delimited files you saved, prepare plots of the temperature versus time data using Excel (or a comparable spreadsheet program). Instructions for plotting temperature versus time thermograms
using Excel are provided in Appendix B-1.
28. How do you determine the equilibrium temperature of the hot solidcold water mixture in the calorimeter? How do you determine the
temperature changes for the hot solid and the cold water? Should these
temperatures be recorded in the Lab Report and to how many significant figures?
29. What calculations are required to determine the specific heat of the
unknown solid? From the results of Trials 1 and 2, determine the
average specific heat of the unknown solid.
30. Using the information provided in Table 1, identify the unknown solid.
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Section . . . . . . . . . . . . . . .
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2
E X P E R I M E N T 2
Lab Report
Submit all thermograms along with your lab report.
Part A – Determination of the Calorimeter Constant
Experimental data and calculations – Trial 1
! 2010 Brooks/Cole, Cengage Learning
Experimental data and calculations – Trial 2
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Experiments in General Chemistry Featuring MeasureNet n Stanton et al.
Average calorimeter constant __________ J/8C
Part B – Determination of the Specific Heat of a Solid
Unknown number __________
Experimental data and calculations – Trial 1
Experiment 2 n Specific Heat of Substances
Experimental data and calculations – Trial 2
Average specific heat of the solid __________ J/g8C
Using the specific heat values given in Table 1, identify the unknown solid.
! 2010 Brooks/Cole, Cengage Learning
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