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 Chemicals calorimeter (double Styrofoam cups), thermometer, thermometer Iron metal clamp, stirring rod, utility clamp, burner Unknown metal 600 mL beaker, crucible tongs, iron ring, wire gauze
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Procedure Obtain a piece of iron and an unknown metal sample either from the stockroom or from your instructor. At the same time, pick up the calorimeter (2 Styrofoam cups), a 600-mL beaker and a thermometer clamp. Record the code number of the unknown. 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. 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. While the beaker is warming up, pour about 70 mL of deionized water into the calorimeter. Weigh it with the water. Using the hook, gently 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. When the water in the 600-mL beaker is boiling, record the temperature to the nearest 0.1°C. Set the thermometer aside and allow it to cool. Measure the water temperature in the Styrofoam calorimeter to the nearest 0.1 °C. Using the hook, 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. Measure the temperature of the water in the Styrofoam calorimeter without letting the thermometer touch the metal, while gently moving the Styrofoam cup in small circular movements, 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 the metal object, (Tf). 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 or the instructor.
2. Calculations Calculate the specific heat of the metal for each run of the experiment, using the equation m cwater ∆Τ = − m cm ∆Τ 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.
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Specific Heat Values of Elements ( Joules / g-K ) (for elements at 300K)
Li Be B C 3.58 1.825 1.03 0.709
Na Mg Al Si P S 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 Ge As 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 Y Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I 0.363 0.3 0.3 0.278 0.265 0.25 0.24 0.238 0.242 0.244 0.232 0.233 0.233 0.228 0.207 0.202 0.145
Cs Ba La Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi 0.24 0.204 0.19 0.14 0.14 0.13 0.137 0.13 0.13 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.
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CHEMISTRY 60 EXPERIMENT 14: CALORIMETRY Name: ______REPORT SHEET Section______
1. Data and Calculations Table for Iron: Run Number 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 temp of metal & water (calorimeter)
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 ∆Τw Specific Heat of iron (cm) Qm = mm x cm x ∆Τm *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 Fe: ______Specific heat of Fe from a table: ______***Provide a sample calculation below for Run 1 for the three starred items – show a complete setup for each calculation. Indicate formulas and all units clearly.
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2. Data Table for Unknown Metal: Code # of metal: ______Run Number: 1 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!
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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 ?
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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).
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