In the Laboratory edited by
filtrates & residues
James O. Schreck University of Northern Colorado Greeley, CO 80639
Guided Discovery: Law of Specific Heats Thomas H. Bindel* and John C. Fochi Pomona High School, 8101 West Pomona Drive, Arvada, CO 80005 The following is a presentation of a laboratory investigation that guides students into discovering the concepts of calorimetry, specific heat capacity, and the law of Dulong and Petit (1). We are in the process of moving away from traditional experiments in which a concept is presented in class and then verified in laboratory (2). We believe some experiments should be illustrative of the scientific method. That is, the main purpose of these experiments is to give students a feeling for “how science is done”. This viewpoint is shared by others: discovery chemistry (3–6), guided inquiry laboratory (7), laboratory-driven instruction (8), experimental design (9, 10), and thinking scientifically (11). This laboratory investigation has enough structure that students will be successful in discovery, but not so much that the element of discovery has been lost or greatly diminished. The guided discovery approach allows the student to pose a scientific question, prepare and execute an experiment to attempt to answer the question, analyze experimental data, and then use the analysis to pose a follow-up scientific question, which leads directly to another connected experiment. This approach allows the student to make discoveries using scientific methodology in a format that sets parameters and keeps the student focused on the central theme. The Investigation Before the investigation, students have knowledge of the scientific method, graphical analysis (can recognize linear, reciprocal, and power functions from shapes of curves), and the calorie, and they are able to calculate the amount of heat energy transferred to a given quantity of water. Students do not start with a knowledge of specific heat capacity; instead, it is developed during the investigation. Students calculate the amount of heat energy transferred (in calories) from the mathematical product of the mass and the temperature change of water. We realize that this is pedagogically incorrect—the specific heat capacity of water (1 cal g {1 °C{1) should not be ignored in the calculation. However, we feel it is all right to give students this “half truth” at this point. It gives them the opportunity to discover for themselves the concept of specific heat capacity and to use it correctly in energy-transfer calculations. (See Analysis 2 and Treatment of Data.) We use a model of the scientific method1 that is a cyclic process2 consisting of several steps: making observations, gathering data, analysis of data (searching for patterns), making a proposal or hypothesis as to some cause and effect relationship that would explain the data (a possible pattern between two or more variables), and lastly, designing another experiment to test the hypothesis. This process can be entered at any step and the cycle can be repeated as often as needed to formulate or to validate a hy*Author is known by his students as “Captain Carbon”.
pothesis. Once a hypothesis is established and generally accepted, it becomes a scientific law.
Problem The following broad fundamental problem is proposed to the students for investigation. Problem: A hot object in contact with a cooler object will transfer energy until the two objects are at the same temperature. Is the amount of energy transferred 3 dependent upon the nature or composition of the material?
Students are guided into realizing that the scope of the problem is too broad for an initial investigation. The problem is refocused to include only metallic elements. The scientific-method process is entered at the “design experiment” step. Students are guided through the experimental design by the following discussion-leading questions.
Questions 1. How will the energy transfer situation be constructed? a. What material will be used to accept the heat energy from the hot metal? How should the contact be made between the material accepting the heat energy and the hot metal, in order to insure total and complete energy transfer? [A liquid contact between water and metal is desirable.] What other factors should be considered in selecting the material? [Students are guided into considering factors such as safety, availability, cost, … .] b. Is the rate of transfer important? [No, but the rate cannot be so slow that an appreciable amount of heat energy has been lost to the environment.] c. How will we know when energy transfer is complete? [The water temperature will no longer rise.]
2. What are the variables in the experiment? [The variables in the experiment are: the nature of the material, the quantity of metal, the quantity of water, the starting temperature of hot metal, and the starting temperature of the water. A discussion follows as to the importance of holding all variables constant except the one to be studied (nature of material). 3. What metals should be used in the investigation? a. What factors should be considered in selecting the metallic elements? [Students are guided into considering familiarity, cost availability, safety, and water reactivity. Copper and aluminum are good choices.] b. What form should the metal be in, a powder, a rod, a wire, etc.? [Students are guided into selecting the rod form.]
4. How is the metal to be heated to an elevated temperature that can be found accurately? [Completely submerge the metal in water and heat to the boiling point of the water.]
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In the Laboratory Experiment 1 The experiment is similar to one reported by one of us (2). Copper and aluminum are tested separately using water calorimeters. Aluminum is found to have a higher heat capacity than copper, if the same masses are used. Analysis 1 The class data are gathered, presented, and discussed. Cause and effect relationships are proposed to explain the differences in heat capacity between copper and aluminum. Students realize that there are many possible causes (color of the metal, density of the metal, and so on). The large number of possible causes comes from having only two pieces of data. In other words, anything that is different about the two metals could correlate with the observed heat differences. More data are needed.
Experiment 2 Fourteen other metallic elements are tested in a second experiment, similar to the first.4 At least four or five replicates of each element should be done. The metallic elements range on the periodic table from magnesium to lead (see Materials section). However, during the experiment, unbeknownst to the groups, the quantity of metal supplied to them is different for each metal. Analysis 2 Students are made aware of the mass differences that existed between metals. An instructor-guided class discussion reveals that the data may still have some meaning if they are treated in a way that removes the mass differences and temperature differences.
ume: {.15; atomic weight: {.83; electronegativity: {.58; and melting point: {.16. A representative graph from each group is posted. None of the graphs has a good linear correlation. However, two of them, atomic weight and atomic number, appear to have good curvilinear correlations, which appear to be reciprocal relationships. Density has some curvilinear correlation, but not as good as the two mentioned. Analysis 4 The apparent reciprocal nature is tested. Each student constructs a graph of specific heat capacity (SpH) versus the reciprocal of atomic weight (1/at. wt). Excellent linear correlation is seen (r = .987, slope = 5.5 cal mole{1 °C{1, and y-intercept = 0.006 cal g{1 °C{1).6 Further analysis reveals that the data point corresponding to silicon is out of line with respect to the rest. If this data point is deleted, the correlation is almost perfect (r = .999, slope = 5.9 cal mole{1 °C{1, and yintercept = 0.002 cal g{1 °C{1). A discussion follows about why silicon might deviate from the linear correlation. The correlation is with metallic elements and not with metalloids. Analysis 5 Students write the equation for the line, eq 1. The yintercept is close enough to zero to approximate it as zero, eq 2. Both sides of the equation are divided by the at. wt, eq 3. Equation 3 is one form of the law of Dulong and Petit in which the product of the SpH and at. wt is a constant. 7 Dimensional analysis gives eqs 4 and 5.
Treatment of Data All of the data are treated by dividing the energy the metal lost by the mass and the temperature change of the metal. This gives the amount of energy lost by the metal per gram of metal, per degree Celsius change in temperature. This quantity is the specific heat capacity (or just specific heat). At this point the concept of specific heat is discussed and the correct equation for calculating heat energy is developed (specific heat × mass × change in temperature). All students calculate the specific heat capacity for their metallic elements. The resulting class data contain a large amount of error. A discussion brings out the possible sources of error and the need for a better experimental design. The design and testing of a new or revised experimental method would be too lengthy and time consuming. It is pointed out that scientists have already done this for us. The published specific heat capacity values are then used. 5 Analysis 3 It is difficult to find correlations with so much data. The best way to find correlations is to make graphs of the specific heat capacity versus possible causes (variables). The class is broken down into seven groups. Each group selects one variable from a list of seven possibilities and constructs a graph of the specific heat capacity versus the selected variable. The choice of variables is based on student familiarity—or, in the case of thermal conductivity, some apparent connection to heat. The variables are thermal conductivity (W cm{1 K{1), density (g cm {3), atomic number, atomic volume (cm3 mole{1), atomic weight (g mole{1), electronegativity (Pauling), and melting point (K).5 Graphical analyses, linear regression analysis, and calculation of Pearson’s linear correlation coefficient (r) are conducted. The values of linear correlation are thermal conductivity: .089; density {.79; atomic number: {.83; atomic vol-
956
SpH = 5.9 × at. wt{1 + 0.002
(1)
SpH = 5.9 × at. wt{1
(2)
SpH * at. wt = 5.9
(3)
(cal g{1 °C{1)/(g mol {1) = 5.9
(4)
cal mol{1 °C{1 = 5.9
(5)
Equation 5 represents the molar heat capacity. This shows that it is the molar heat capacities that are constant. That is, the amount of thermal energy metallic elements absorb or release in energy transfer is independent of the nature of the material. The amount of thermal energy is dependent only upon the number of atoms present in the material. If one delves further into heat capacities (which is beyond the scope of this paper), one finds that the law of Dulong and Petit is not a general law for all temperatures. Heat capacities are constant only for moderately high temperatures (13, 14). As the temperature approaches absolute zero, heat capacities approach zero. A couple of theories have been proposed to explain this behavior. The first was the Einstein theory; later came the Debye theory, which works the best. It is interesting that minerals have molar heat capacities, at or near room temperature, that are representative of the number of atoms within the material (10). Materials Team Labs PSLTM can be used in the investigation, but is not required.8 One can use the traditional calorimetry materials and methods. PSL offers the capability of collecting two sets of data simultaneously. Besides being more efficient, this gives the student an immediate visual comparison of two metals. Thermos brand “Snak Jars” (15) were used as calorimeters. A 3/16′′ hole was drilled in the lid 3/ 4′′ from the edge for the PSL temperature probe. Other materials required are balances, metals, thermometers or temperature probes, forceps, and beakers (for heating the metals).
Journal of Chemical Education • Vol. 74 No. 8 August 1997
In the Laboratory It is desirable to have a piece of metal about 25 g in mass and in either rod (stick) or lump form. Wire, strip, foil, sheet, shot, piece, granular, ribbon, chip, flake, mossy, or powder forms are undesirable. The following are commercial suppliers of various metals:9 Flinn: Cd, Cr, Fe, Si Aldrich: Al, Cd, Cr, Co (pieces), Fe, Pb, Mg, Mn (chips), Ni, Si, Ag, Sn, Zn, W, Ti Sargent-Welch: Cr, Si, Zn Some inexpensive sources are, for Al, cut aluminum ring-stand rods (2); for Cu, coinage: U.S. pennies dated before 1982; for Mg, camping-supply stores; for Fe, washers, sinkers for fishing; for Ag, a coin dealer: one troy ounce bullion; for Sn, split-shot for fishing—attach to nylon fishing line; for Pb, sinkers for fishing. We are in the process of incorporating the metallic elements Nb, Bi, and Ta. Experimental Procedure S AFETY NOTE: Cadmium, chromium, and nickel are listed as carcinogens by the EPA (16). Cadmium is highly toxic and lead has acute human toxicity (16). These materials should never be handled with bare hands. It is recommended that the handling of these metals should be done with a pair of forceps. The PSL setup is as follows. Select Experiment: Two Temp vs. Time Reset Parameters: Duration: 600 s Ranges of Axes: Lower: y-min: 20; y-max: 35 Upper: y-min: 20; y-max: 35.
The metallic elements are heated in boiling water for at least a couple of minutes (the temperature is recorded) and then transferred to a water calorimeter (80 g of water, or just enough to cover the metal, at or near room temperature). In the transfer the metals are not dried. The calorimeter is then gently agitated to increase the rate of heat transfer. After the transfer is complete, the temperature is recorded.
fore not a general law. By the end of the investigation, students felt they had accomplished something they never had before: they had actually “done science”; and they came away with a better understanding of how science is conducted. This is not to say that they had not done science in their previous science classes; however, in most of the curricula, one or more aspects of the scientific method are explored, but rarely, all together. This method allows students to make discoveries using scientific methodology in a format that sets parameters for experimental exploration and focuses inquiry on the central theme. Notes 1. For pedagogical reasons, we present a scientific method for our students, even though it has been argued that a single method does not exist (12 ). 2. Perhaps a better term is a “spiral” process, for when the cycle is complete and comes back on itself, it will be at a higher level of understanding. 3. Many students confuse rate of transfer with the total amount transferred. This point must be made clear. 4. The cost of the metals could be an issue. One can purchase eleven of the metals (not including Mn, Ni, and W) for under $100. The other three can be purchased for less than $150. We feel that a chemistry program should have samples of most of the chemical elements for students to observe. This further justifies the expenditure required to purchase the metals. 5. The values were obtained from a Sargent–Welch notebooksized periodic table (1994). 6. If the student-generated specific heat capacity values are used, then r is .92, the slope is 5 cal mole{1 °C{1, and the y-intercept is {0.0005 cal{1 °C{1. If the data point for silicon is omitted, then r is .95, the slope is 5.6 cal mole {1 °C{1, and the y-intercept is -0.007 cal g {1 °C{1. 7. Dulong and Petit found a value of 0.37 for the product, when the atomic weight of oxygen is assigned a value of one. 8. Team Labs PSL (Team Labs, 6390B Gunpark Dr., Boulder, CO 80301). 9. ©Flinn Scientific, Inc. PO Box 219, Batavia, IL 60510-0219; Sargent-Welch, VWR Scientific, 911 Commerce Court, Buffalo Grove, IL 60089-2375; Aldrich®, 1001 West Saint Paul Avenue, Milwaukee, WI 53233.
Literature Cited Conclusion The guided-discovery activity takes a minimum of ten 50-minute class periods, including a period to introduce PSL. Nonetheless, we fell this was a very valuable use of the time. Students were guided, through the methodology of science, into discovering the concepts of calorimetry, specific heat capacity, and the law of Dulong and Petit. They came away with a deeper understanding of the nature of science from their many discoveries and interpretations. Through a guided discussion and their experiences in the activity, students understood how scientific laws are determined, how laws can be used to predict, the limitations of laws (extrapolation may not always yield a correct result), and that scientific theories are built around laws to explain why the laws exist. From the beginning of the investigation, students believed that the capacity for heat is dependent upon the kind of metal. This belief was perpetuated by analyses 2, 3, and 4. And finally, in analysis 5 students were confronted with the idea that it is only the total number of metal atoms that is important and not the kind of metal atoms. Again, this works only at moderately high temperatures and is there-
1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
11. 12. 13. 14. 15. 16.
Dulong, P.; Petit, A. Ann. Chim. Phys. 1819, 10, 395. Bindel, T. H. J. Chem. Educ. 1990, 67, 165. Ricci, R. W.; Ditzler, M. A. J. Chem. Educ. 1991, 68, 228. Ditzler, M. A.; Ricci, R. W. J. Chem. Educ. 1994, 71, 685. Ricci, R. W.; Ditzler, M. A.; Nestor, L. P. J. Chem. Educ. 1994, 71, 983. Ricci, R. W.; Ditzler, M. A.; Jarret, R.; McMaster, P.; Herrick, R. J. Chem. Educ. 1994, 71, 404. Allen, J. B.; Barker, L. N.; Ramsden, J. H. J. Chem. Educ. 1986, 63, 533. Lamba, R. S. J. Chem. Educ. 1994, 71, 1073. Mertitt, M. V.; Schneider, M. J.; Darlington, J. A. J. Chem. Educ. 1993, 70, 660. Ellis, A. B.; Cappellari, A.; Hunsberger, L.; Johnson, B. J. Experiment 1, Heat Capacities of Materials; in Teaching General Chemistry: A Materials Science Companion; Ellis, A. B.; Geselbracht, M.; Johnson, B. J.; Lisensky, G. C.; Robinson, W. R., Eds.; American Chemical Society, Washington, DC, 1993; p 353. Sardella, D. J. J. Chem. Educ. 1992, 69, 933. Bunge, M. A. Scientific Research; Springer: New York, 1967. Mahan, B. H. University Chemistry, 3rd ed.; Addison-Wesley: Menlo Park, CA, 1975; p 123. Laidler, K. J.; Meiser, J. H. Physical Chemistry, 2nd ed.; Houghton Mifflin: Boston, 1995. Ruekberg, B. J. Chem. Educ. 1994, 71, 333. Windholz, M.; Budavari, S. The Merck Index, 11th ed.; Merck and Co.: Rahway, NJ, 1989.
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