In the Laboratory
Introduction of Differential Scanning Calorimetry in a General Chemistry Laboratory Course: Determination of Heat Capacity of Metals and Demonstration of Law of Dulong and Petit Ronald D’Amelia,* Vincent Stracuzzi, and William F. Nirode Department of Chemistry, Hofstra University, Hempstead, NY 11549; *Ronald.P.D’
[email protected] General chemistry experiments illustrating the principles of calorimetry and thermodynamic properties such as molar and specific heat capacity have been reported in this Journal (1–6) and thermodynamic properties such as heat capacity are commonly introduced in many general chemistry textbooks (7–9). In the general chemistry laboratory specific heat capacities of metals are typically determined using the classical calorimetry method. Heat capacity is defined as the quantity of heat necessary to raise the temperature of a system or substance at constant pressure by one degree without a phase change occurring. On the other hand, specific heat capacity is defined as heat capacity when using 1 g of material. Therefore, specific heat capacity is an intensive property of matter because it depends on 1 g of material used. For a more detailed description of heat capacity see the online supplement. Most modern day general chemistry textbooks make no mention of the relationship between specific heat capacity and the molar mass of a metal (7–9). The empirical law of Dulong and Petit was introduced in 1819 relating the specific heat capacity through a constant to the molar mass of a metal (10). Therefore, from the determination of the specific heat capacity of an unknown metal, the molar mass of the unknown metal can be calculated. Differential scanning calorimetry (DSC) is commonly used to determine many different thermodynamic properties (11) and used in a wide variety of applications that range from polymer analysis to food analysis (12–14). DSC has been used in some physical chemistry experiments and even some general chemistry experiments (15–18). The development of these DSC experiments suggests that there is a need for more laboratory experiments to be developed at the general chemistry level involving the hands-on use of DSC. The purpose of this experiment is to demonstrate the use of DSC in determining the specific heat capacity of metals and introduce the empirical law of Dulong and Petit. The goals of this experiment are as follows:
• supplement the classroom lecture of thermodynamic properties with a hands-on experiment
• determine the specific heat capacity of metals using DSC
• introduce the empirical Law of Dulong and Petit
• have the students compare their experimental data to accepted data provided by the National Institute of Standards and Technology (NIST)
Learning Outcomes In using the DSC and doing this experiment students should learn how to: (i) use the DSC instrument, (ii) determine the specific heat capacity from a DSC thermogram, (iii) determine the specific heat capacity as a function of temperature using the Shomate equation as obtained from NIST, (iv) evaluate their experimental data by comparing the data to the accepted values obtained from NIST, and (v) apply the empirical relationship between specific heat capacity and molar mass as outlined by the empirical law of Dulong and Petit. We found that almost all of the students who performed the experiment had a very favorable response to performing an instrumental experiment versus a classical calorimetry experiment. Experimental Procedure The experiment was completed by a student or group of students in one laboratory period (typically 2.0–2.5 hours in length). They analyzed a sapphire standard, three known metals, and an unknown metal. The specific heat capacities of the three known metals were determined and used to demonstrate the empirical law of Dulong and Petit. The Dulong and Petit constant was then used to determine the molar mass of the unknown metal. Aluminum, copper, iron, lead, nickel, titanium, and zinc were examined. All metals were purchased from Alfa Aesar with 99.99% purity or greater and were used without further purification. A Perkin-Elmer power-compensated DSC model Pyris I was used. All DSC experiments were run with samples ranging from 5 to 25 mg under dry nitrogen flowing at 20 mL∙min to prevent any moisture pickup or oxidative degradation. Samples were weighed on an analytical balance and placed in a DSC aluminum pan designed to contain volatile liquids and crystalline solids. A thermal baseline was established by running empty sample pans for both the sample and reference cells. The method for the specific heat capacity analysis consisted of scanning a sapphire standard, a blank (no sample baseline), and a metal over the temperature interval 0–90 °C at 10 °C∙min. The experimental data used for this project were taken over a temperature interval of 25–75 °C. All experimentally obtained specific heat capacity data were determined from the DSC thermograms using the Pyris for Windows software. The NIST (accepted) specific heat capacity data were calculated using the Shomate equation so that a comparison could be made with the experimentally
© Division of Chemical Education • www.JCE.DivCHED.org • Vol. 85 No. 1 January 2008 • Journal of Chemical Education
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In the Laboratory 10
heat flows:
4
8
sapphire
3
6
aluminum
2 1
4 2
baseline specific heat capacity Al
0 0
10
20
30
40
50
60
Temperature / pC
70
80
0
specific heat capacity of 0.914 J g‒1 K‒1 (± 0.007). Three heating curves (pan baseline, standard sapphire, and aluminum metal) were used to determine the specific heat capacity curve of the metal. The students’ experimentally determined specific heat capacity values were then compared to the NIST values. This comparison was done by calculating a specific heat capacity at a certain temperature from the Shomate equation obtained from the NIST Web site,
J Specific Heat Capacity g °C
Heat Flow (Endo Up) mW
5
90
Figure 1. A DSC thermogram of aluminum metal is shown. The specific heat capacity of aluminum was determined to be 0.914 J g‒1 K‒1 from Pyris for Windows software by using the sample baseline, sapphire, and aluminum heating curves to generate the specific heat curve.
determined specific heat capacity values (19). A more detailed description of the experimental procedure can be found in the online supplement. Hazards Lead powder is toxic and can be harmful if inhaled or ingested. Care should be taken to avoid contact with the skin and mouth. Care should be taken when operating the DSC because high temperatures can cause skin burns. See the online supplement for additional DSC instrument safety precautions.
E Cp, m M cp A Bt Ct 2 D t 3 2 t
(1)
where Cp, m is the molar heat capacity at constant pressure; M is the molar mass; A, B, C, D, and E are constants given for a set temperature range for a given metal as provided by NIST (19); and t =T∙(1000 K). The experimental data from three trials, accepted data from NIST, and relative percent errors for aluminum are summarized in Table 1. The experimentally determined specific heat capacity for aluminum (and the other six metals studied) were in good agreement with the accepted values reported by NIST (19). By taking the molar mass of the metal multiplied by the average specific heat capacity of the metal one can obtain a constant as defined by the empirical law of Dulong and Petit:
M cp 25.5
J mol K
(2)
Results and Discussion
The Dulong and Petit constant (DP) for aluminum is shown in the last column of Table 1. (A summary of the data for the other six metals is in Appendix 1 of the online supplement.)
Determination of Specific Heat Capacity Using DSC The specific heat capacities (cp) of seven high-purity metals were analyzed in triplicate from 25–75 °C. A specific heat capacity analysis of aluminum is shown in Figure 1 showing a
Determination of Molar Mass of an Unknown Metal Using DSC An unknown metal (chosen from the seven metals studied) was analyzed using the DSC. Analogous to the aluminum analy-
Table 1. Summary of Specific Heat Capacity Data for Aluminum T/oC
Shomate Value/ (J g‒1 K‒1)
Trial 1/ (J g‒1 K‒1)
Trial 2/ (J g‒1 K‒1)
Trial 3/ (J g‒1 K‒1)
Avg/ (J g‒1 K‒1)
Error (%)
SD
DP/ (J mol‒1 K‒1)
25.0
0.897
0.903
0.892
0.888
0.894
-0.319
0.008
24.1
30.0
0.901
0.906
0.896
0.891
0.898
-0.381
0.008
24.2
35.0
0.905
0.910
0.900
0.894
0.901
-0.388
0.008
24.3
40.0
0.908
0.914
0.903
0.897
0.905
-0.415
0.009
24.4
45.0
0.912
0.918
0.906
0.902
0.909
-0.354
0.008
24.5
50.0
0.915
0.923
0.910
0.908
0.914
-0.170
0.008
24.7
55.0
0.918
0.927
0.914
0.913
0.918
-0.047
0.008
24.8
60.0
0.922
0.931
0.918
0.918
0.922
0.087
0.008
24.9
65.0
0.925
0.935
0.924
0.924
0.928
0.339
0.006
25.0
70.0
0.927
0.938
0.927
0.929
0.931
0.421
0.006
25.1
75.0
0.930
0.942
0.932
0.935
0.936
0.655
0.005
25.3
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Journal of Chemical Education • Vol. 85 No. 1 January 2008 • www.JCE.DivCHED.org • © Division of Chemical Education
In the Laboratory Table 2. Summary of Specific Heat Capacity Data for Metals cp/ (J g‒1 K‒1)
Shomate Values/ (J g‒1 K‒1)
Relative Error (%)
DP/ (J mol‒1 K‒1)
26.98
0.914 ± 0.007
0.915
0.109
24.7
63.55
0.388 ± 0.006
0.388
0.000
24.7
55.85
0.460 ± 0.004
0.460
0.000
25.7
58.69
0.451 ± 0.002
0.454
0.661
26.5
0.129 ± 0.001
0.131
1.53
26.8
Metals
M/ (g/mol)
Aluminum Copper Iron Nickel Lead
207.2
Titanium
47.87
0.530 ± 0.003
0.537
1.30
25.4
Zinc
65.39
0.393 ± 0.004
0.392
0.512
25.6
sis described above, a specific heat capacity curve was generated and specific heat capacity value was calculated over a 25–75 °C temperature range. The molar mass of the unknown metal was calculated from the experimentally determined specific heat capacity and the empirical law of Dulong and Petit (eq 2). The molar mass of the unknown metal was determined by taking the average of the Dulong and Petit constants of the three known metals and dividing by the average experimentally determined specific heat capacity of the unknown metal. From the molar mass, the students determined the identity of the unknown metal. A summary of the experimentally determined specific heat capacities, the NIST accepted specific heat capacities, and the Dulong and Petit constants for the seven metals are shown in Table 2. Conclusion With this experiment the specific heat capacities of metals can be determined by DSC. This experiment demonstrates that the specific heat capacity of a metal is characteristic of that metal. A specific heat capacity can be calculated from the thermograms of a baseline (no sample), reference material (sapphire), and the metal sample. The accepted specific heat capacities of the metals can be calculated by using the Shomate equation as provided by NIST. Comparing experimental values to the accepted values allows students to calculate percent relative errors in their experiments. Furthermore, students are given an unknown sample to analyze and can experimentally identify the unknown metal using the empirical law of Dulong and Petit. Overall, this experiment reinforces the teaching of thermodynamic properties in general chemistry. Using the DSC in the general chemistry laboratory allows for hands-on experience with more sophisticated instrumentation providing students with the foundation for more complex experiments and the use of instrumentation in advanced chemistry classes that they may take later. Acknowledgment This work was supported by the Chemistry Department of Hofstra University through various private donations and Hofstra University itself.
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Supporting JCE Online Material
http://www.jce.divched.org/Journal/Issues/2008/Jan/abs109.html Abstract and keywords Full text (PDF) Links to cited URLs and JCE articles Supplement Instructor notes and student handouts Fact sheet on thermal analysis Summary of all experimentally determined data in both a low temperature and high temperature mode Safety precautions using the DSC
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