EXPERIMENT 14:
CALORIMETRY
Introduction: You will calculate the ”specific heat” constant of a metal, “c,” by measuring
the heat exchanged in a calorimeter. Once “c” is determined, use the Law of Dulong and Petit to
calculate the approximate atomic mass of an unknown metal.
Background: Heat energy can be gained or lost by an object when it warms or cools. One
unit of heat energy is the joule, J, a derived unit representing kg-m2/s2. 4.184 joules = 1 calorie
(the amount of heat required to change the temperature of 1 g of water by 1oC (or K) say from
4oC to 5oC). Although calories are much more familiar to most of you, the SI uses joules. In the
US, and especially in health science, calories are more commonly used. The nutritional calorie is
actually a kilocalorie (kcal) or 1000 cal.
Heat flow, Q, measured in joules or calories, is proportional to the mass of the object, its change
in temperature, and the specific heat constant “c”.
Q = m x c x T
c is “specific heat” in joules per gram per degree, or J/g-C, and T = Tfinal – Tinitial.
Specific heat is a property of a pure substance. The specific heat of water is 4.184 J/g-C When
two objects at different temperatures come into contact, heat flows from the hotter to the colder
object until the two objects reach the same temperature (Tf). The double Styrofoam cups in this
experiment serve as a calorimeter, an insulated device where there is no loss of heat to the
outside.
In this experiment, you will measure the specific heat of two metals, one known, Fe, and the
other unknown. Iron has a specific heat of 0.449 J/g-Co. Your value may differ and you will
calculate the % error. The same method will be used to find the specific heat of the unknown
metal. The hot metal is placed into the calorimeter, with water and the final temperature reached
by both the metal and water is recorded Thus the heat lost by the metal (Qm) is equal to the heat
gained by the water (Qw)
Qw = –Qm
thus, mw x cw x Tw = - (mm x cm x Tm)
All the values are known except cm. Note the negative sign on the right side of the equation.
This cancels out since Tm is a negative quantity (Tf – Ti is negative).
The specific heat of the unknown metal will be used to estimate its atomic mass. The identity of
the metal can be guessed from the Law of Dulong and Petit, stating that the atomic mass of a
solid element equals 26 divided by the specific heat, ± 10%.
Atomic mass = 26 / (specific heat)
Safety
No hazardous chemicals are used but you will be working with fairly large quantities of boiling
water, pouring from one container to another, and dropping pieces of metal into boiling water. If
you have long hair, be sure to tie it back.
Materials Needed
Equipment
calorimeter (double Styrofoam cups), thermometer, thermometer
clamp, stirring rod, utility clamp, burner
600 mL beaker, crucible tongs, iron ring, wire gauze
Chemicals
Iron metal
Unknown metal
Procedure Work in pairs for this experiment.
1. Obtain a piece of iron and an unknown metal sample from the stockroom.
At the same time, you will check out the calorimeter (2 Styrofoam cups), a 600-mL beaker and a
thermometer clamp. Record the code number of the unknown on your data sheet. Weigh the iron
and unknown metal and the calorimeter to the nearest 0.01 g
If you’re not sure which metal is the Fe and which is the unknown, ask the instructor.
2. Fill a 600-mL beaker with 400 mL deionized water and place on a wire gauze on a ring stand
over a burner and start heating it
3. While the beaker is warming up, pour about 70 mL of deionized water into the calorimeter.
Weigh it with the water.
4. Using crucible tongs, immerse the iron object in the beaker of hot water. Don’t drop it in.
(The beaker may break.) Bring the water to a slow boil for 5 minutes.
5. Measure the water temperature in the Styrofoam calorimeter to the nearest 0.1oC.
6. When the water in the 600-mL beaker is boiling, clamp the thermometer above the beaker
and immerse it in the boiling water. Record the temperature to the nearest 0.1C. Set the
thermometer aside and allow it to cool.
7. Using crucible tongs, lift the metal from the boiling water and hold it above the water level
but below the top of the beaker for about 2 seconds to allow the boiling water to drain. Then, as
quickly as possible, place it into the calorimeter water. Keep the water in the beaker boiling, as
you’ll need it soon for another run on the Fe and two runs on the unknown. Add water as
needed.
8. Measure the temperature of the water in the Styrofoam calorimeter without letting the
thermometer touch the metal, while gently stirring the water with a glass stirring rod, being
careful not to break the bulb of the thermometer. Read and record to the nearest 0.1 C the
highest temperature that is reached before it begins to drop again. This may take several
minutes. This is the final temperature of water and iron, (Tf).
9. Take out the metal, pour out the water from the calorimeter and refill with a new portion of
water. Weigh the calorimeter and water. Place the metal back into the boiling water and heat for
a second run. Make at least two, preferably three, runs each with your iron sample and your
unknown. At the end of the lab period, dry the metal pieces and return them to the stockroom.
2. Calculations
Calculate the specific heat of the metal for each run of the experiment, using the equation
m cwater  m cm in which cm is the only unknown. Find the percent error for each run
with the iron, using the equation:
% error = experimental value – accepted value x 100
accepted value
Find the average specific heat for the runs with the unknown metal. Estimate the atomic
mass of the metal using the Law of Dulong & Petit (see introduction) and try to identify the
unknown metal. For example, using an atomic mass range of 34 – 42 (±10% from an
experimental value of 38 g/mol), your element could be chlorine, argon, potassium, or calcium.
Other things you know about those elements should help you in selecting the most likely one as
your unknown. (i.e., we are dealing with metallic solids in this experiment, not gases so you
would eliminate chlorine. Use the table of specific heat values on the next page for reference.
Specific Heat Values of Elements
( Joules / g-K )
(for elements at 300K)
Li
Be
B
3.58 1.825
C
1 .03 0.709
Na Mg
Al
1.23 1.02
0.900 0.70 0.769 0.71
K
Ca
Sc Ti
V
Cr Mn
Fe Co
Ni
Cu Zn Ga
Si
P
Ge As
S
Se
0.757 0.647 0.568 0.523 0.489 0.449 0477 0.449 0.421 0.444 0.385 0.388 0.371 0.230 0.330 0.32
Rb
Sr
0.363 0.3
Cs
Y
Zr Nb Mo Tc
0.3 0.278 0.265 0.25
Ba
La
0.24 0.204
0.19
Hf Ta W
0.14
0.14
Ru
Rh
Pd
Ag Cd In
Sn
Sb
Te I
0.24 0.238 0.242 0.244 0.232 0.233 0.233 0.228 0.207 0.202 0.145
Re
0.13 0.137
Os
Ir
0.13 0.13
Pt
Au
Hg Tl
Pb
Bi
0.13 0.128 0.140 0.129 0.129 0.122
Note: if you have a very large metal object, you may want to use up to (but not more
than) 100 mL of water. Immersing the entire object is not critical, since heat flow between metal
and water is much more efficient than between metal and air.
EXPERIMENT 14: REPORT
CALORIMETRY
1. Data Table for Iron:
Run Number:
Name: _________________________
Section __________
1
2
3
1
2
3
Mass of iron
T of boiling water ( Ti(m) )
(initial T of metal)
Mass of Calorimeter
Mass of calorimeter &
water
Initial T (Ti(w)) of
calorimeter water
Final temperature of metal
and water (calorimeter)
Calculations and results:
Run Number:
Mass of water
in calorimeter
T of water (Tf – Ti(w))
T of metal ( Tf – Ti(m))


Heat (J) gained by the water
*
Qw = m x cw x w
Specific Heat of iron (cm)
* (calculate from equation)
Qm = mm x cm x metal
Note: Q lost by water = − Q gained by
metal
Percent error
*
(Compare your value of c
with value from a table)
Average specific heat of iron: _____________
Specific heat of iron from a table: _____________
***Note – on the three starred items – show a complete setup for each calculation, neat and
organized on an attached piece of paper!! – Show similar calculations for the unknown metal
on the same sheet of paper. Indicate formulas and all units clearly.
2. Data Table for Unknown Metal:
1
Run Number:
Code # of metal: _______
2
3
Mass of metal
Temperature of boiling water
Mass of calorimeter
Mass of calorimeter with water
Initial temperature of
calorimeter water
Final temperature of
calorimeter, water & metal
Calculations and results:
Run Number:
1
2
3
Mass of water
T of water
T of metal
*
Heat (J) *
Qw = mw x cw x Tw
Cw = 4.184 J/mol-K
Specific Heat ( cm) *
Qm = mm x cm x Tm
Average specific heat of unknown metal:
Average Atomic mass _________ ± _______
(Calculate the range from the high & low values allowed by the uncertainty in the Law of Dulong & Petit)
Unknown element _______ (based on the value calculated from the Law of Dulong & Petit)
Unknown element _______ based on comparison with a table of actual c values. Note: some tables are
given in calories/g-oC; other tables are in joules/g-oC. Use the factor 4.184 J = 1 cal to convert.
* As with the iron, show your calculations on a separate sheet of paper attached after this page,
along with the calculations on the iron. Also show a reference value of cm from a table (see pg
71) or other source such as the CRC Handbook. Cite your reference!
Questions
Some of these should be done before coming to lab, as preparation, to save time, and increase
your understanding of the complex calculations involved in this experiment.
1) A student places 138 g of an unknown metal at 99.6 C into 60.50 g of water at
22.1 C. The entire system reaches a uniform temperature of 31.6 C. Calculate the
specific heat of the metal.
2)
If the correct specific heat of the metal in Problem 1 is 0.25 J/g-C, calculate the percentage
error.
3) While transferring the piece of unknown metal to the calorimeter, the student drops the
metal into the calorimeter roughly, and some water splashes out of the calorimeter. Why
must this be avoided? Be specific – how would the loss of water from the calorimeter affect
the calculated value of specific heat for the metal ?
4) The calorimeter used in this experiment has no lid. Is this a potential source of error in this
experiment? Explain how this could affect your determination of the specific heat. Be
specific. Would the value of cm be high or low? Why?
5) This experiment has several potential sources of error. Discuss two more possible
systematic errors, (besides the errors covered in the previous questions), which may cause
the calculations to be in error. Again – be specific as to how the calculated value of specific
heat would be affected. (Note – student errors such as weighing the samples wrongly are
not systematic errors. Assume the student follows directions as well as possible).