In the Laboratory
Introduction of Differential Scanning Calorimetry in a General Chemistry Laboratory Course: Determination of Molar Mass by Freezing Point Depression
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Ronald D’Amelia,* Thomas Franks, and William F. Nirode Department of Chemistry, Hofstra University, Hempstead, NY 11549; *Ronald.P.D'
[email protected] In first-year general chemistry undergraduate courses, colligative properties such as vapor pressure lowering, boiling point elevation, osmotic pressure, and freezing point depression of solutions are commonly discussed. However, these properties are infrequently reinforced in the general chemistry laboratory with actual examples and experiments. There have been experiments done in general chemistry laboratories for the determination of molar mass by freezing point depression using the classical methodology as described elsewhere (1–4). Differential scanning calorimetry (DSC) is commonly used to determine many thermodynamic properties (5) and used in a wide variety of applications ranging from food analysis to polymer analysis (6–8). DSC has been used in some physical chemistry laboratories to study physical properties of polymers (9) and bilayer membrane phase transitions (10). In the general chemistry laboratory setting, DSC has been used as a viable alternative to traditional calorimetry experiments to determine heats of fusion (11). The development of these aforementioned 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 work described herein uses DSC to determine the molar mass of unknown nonvolatile hydrocarbons using freezing point depression. To our knowledge the DSC has not previously been reported for a freezing point depression experiment in the undergraduate general chemistry laboratory class. The experiment has been developed to introduce general chemistry students to DSC. The goals of this experiment are to: • Enhance the lecture discussion of colligative properties and calorimetry with a hands-on activity using modern instrumentation, • Facilitate student understanding of the use and role of DSC in upper-level chemistry classes, and • Promote student understanding of the various disciplines of chemistry.
Learning Outcomes With this experiment students should learn: (i) the fundamental concept of colligative properties, (ii) the determination of molal freezing point depression constant, (iii) effects of the addition of a solute to a solvent on the freezing point of the solvent, (iv) determination of the molar mass of an unknown solute, and (v) how DSC can be used and applied to scientific problems.
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Materials All chemicals were purchased from Aldrich with 99.9% purity and were used without further purification. Purity of cyclohexane was confirmed by gas chromatography analysis with a Hewlett Packard 5890 Series II gas chromatograph. Experimental Procedures A Perkin-Elmer power-compensated DSC model Pyris I was used. All DSC experiments were run with samples ranging from 5 to 15 mg under dry nitrogen flowing at 20 mLmin to prevent any moisture pickup or oxidative degradation. All samples were prepared at a room temperature of 21 ⬚C, weighed on an analytical balance as described below, and placed in reusable stainless steel capsules with an internal volume of 30 µL. In one laboratory period students determine the freezing point of pure cyclohexane, determine the molal freezing point depression constant of cyclohexane by adding varying amounts of para-dichlorobenzene, and observe the depression in freezing point relative to that of cyclohexane for a nonvolatile organic hydrocarbon unknown to determine its molar mass. All freezing point data were obtained by taking the onset temperature of the exothermic change from the thermal baseline.
Freezing Point of Cyclohexane The pure cyclohexane samples were subjected to two thermal cycles: one heating and one cooling. First, the cyclohexane was heated from ᎑20.0 ⬚C to 30.0 ⬚C at 5.0 ⬚Cmin, equilibrated at 30.0 ⬚C for 30 s, and then cooled from 30 ⬚C to ᎑20.0 ⬚C at 1.0 ⬚Cmin. Molal Freezing Point Depression Constant Samples of para-dichlorobenzene ranging from 0.1 m to 0.2 m were prepared in an appropriate quantity of cyclohexane. The solutions were prepared by first weighing the appropriate quantity of para-dichlorobenzene in a tared 4-dram screw-top vial on an analytical balance to the nearest 0.0001 g. Next, 10.00 mL of cyclohexane was added using a transfer pipet. The entire contents of the vial were reweighed so that accurate masses of both the para-dichlorobenzene and the cyclohexane were known. The solutions were subjected to only a cooling cycle from 10.0 ⬚C to ᎑15.0 ⬚C at a rate of 1.0 ⬚Cmin with a 10 s instrument equilibration time at 10 ⬚C. Molar Mass by Freezing Point Depression Samples of three nonvolatile organic hydrocarbons (dodecane, tetradecane, and pentadecane) ranging from approximately 0.1 m to 0.2 m were prepared by the same procedure as the para-dichlorobenzenecyclohexane solutions.
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Figure 1. A cooling DSC thermogram of pure cyclohexane is shown. The freezing point was determined to be 3.47 ⬚C by taking the onset temperature of the cooling curve.
Figure 2. Cooling DSC thermograms of 0.0863, 0.137, 0.181, and 0.222 m solutions of para-dichlorobenzene in cyclohexane solutions are shown. Experimental conditions were the same as those in Figure 1. The freezing points were determined by using the onset temperature of the cooling curves to be 1.73 ⬚C, 0.613 ⬚C, 0.263 ⬚C, and ᎑0.891 ⬚C, respectively, for 0.0863, 0.137, 0.181, and 0.222 m solutions.
These unknown cyclohexane solutions were analyzed under the same conditions as the para-dichlorobenzenecyclohexane solutions (see previous description).
individual student’s average value of 3.6 ⬚C for the freezing point of cyclohexane was used in all subsequent calculations by the individual student.
Results and Discussion
Molal Freezing Point Depression Constant To determine the molal freezing point depression constant, kfp, of cyclohexane, para-dichlorobenzene was used as the known solute. Thermograms for the paradichlorobenzenecyclohexane solutions are shown in Figure 2. The average value of kfp was determined from a linear leastsquares plot of ∆T versus molality using Microsoft Excel (Figure 3) where ∆T is given by ∆T = Tsolvent − Tsolution. The linear least-squares plot produced is good with a R 2 value of 0.98 or better. A kfp of 20.5 (±0.45) ⬚C kg mol᎑1 is determined from the slope of the linear least-squares plot that is in excellent agreement with that reported in the literature (20.0– 20.8) for cyclohexane (12–14). (An alternative method of determining kfp from enthalpy of fusion data can be found in the Supplemental Material.W) Once the kfp is determined, an unknown nonvolatile organic hydrocarbon is obtained and analyzed for the molar mass determination.
Freezing Point of Cyclohexane Cyclohexane was chosen as the pure solvent and has been used in other freezing point depression experiments using the conventional or traditional methods of analysis (1, 2). A typical student thermogram of pure cyclohexane is shown in Figure 1 with a freezing point of 3.5 ⬚C. The freezing point of cyclohexane was measured several times and the average freezing point of pure cyclohexane was determined to be 3.6 ⬚C (±0.5 ⬚C) by the individual student. The reported literature value for the melting point of cyclohexane is 6.5 ⬚C (12). We were able to obtain a melting point of 6.5 ⬚C (±0.1 ⬚C) for pure cyclohexane (thermogram not shown). The discrepancy in the values of the freezing point and melting point can be attributed to supercooling or undercooling of the solvent. It is possible to minimize supercooling by using slower cooling rates; however, there is a practical limitation in analysis time. Experiments were done to minimize supercooling and provide reasonable analysis times. Furthermore, traditional methods of freezing point depression determination require constant stirring to promote effective nucleation and obtain a liquid–solid equilibrium. In this experiment, we were unable to provide constant stirring to the sample. Even though these phenomena lower our freezing point temperature from the literature value, it does not significantly affect the results of this experiment because we are using temperature changes that are relative to each other and not specific to the absolute temperatures. Furthermore, our subsequent calculations and data (see below) are excellent with low percent relative errors from the literature values. Therefore, the
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Molar Mass by Freezing Point Depression A typical DSC thermogram of an unknown nonvolatile organic hydrocarbon, tetradecane, is shown in Figure 4. Using the freezing point of the tetradecanecyclohexane solution to be ᎑0.647 ⬚C (T solution ), the freezing point of cyclohexane to be 3.6 ⬚C (Tsolvent), and kfp to be 20.5 ⬚C kg mol᎑1, one can calculate the molar mass from the following equation, ∆T = kfpm i
(1)
where ∆T = Tsolvent − Tsolution, kfp is the molal freezing point constant, m is the molality of the solution, and i is the Van’t
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Figure 3. Plot of temperature change versus molality of para-dichlorobenzene in cyclohexane is shown. The slope of the line yields a kfp (⬚C kg mol᎑1) (within the standard deviation) value that matches the reported literature value. The origin was included in the plot and the determination of the best fit line.
Figure 4. A cooling DSC thermogram of a 0.208 m solution of tetradecane in cyclohexane is shown. The freezing point was determined to be ᎑0.647 ⬚C by taking the onset temperature of the cooling curve. The molar mass of tetradecane was calculated experimentally to be 194.6 g/mol.
Hoff factor, which is one for para-dichlorobenzene because it is molecular and therefore, nondissociative. Student results for the three unknowns used are shown in Table 1. Excellent percent errors were determined ranging from approximately 2% to 10% error from the accepted values.
volatile organic hydrocarbon provides students with an experiment using colligative properties. This enables the reinforcement of colligative properties from the lecture discussion. Using the DSC in the general chemistry laboratory setting allows for a hands-on experience with instrumentation. An early introduction of DSC in the general chemistry laboratory provides the foundation for more complex experiments and use of instrumentation in advanced chemistry classes that they will take later. The relevance and importance of using an instrumental technique was applied to a meaningful scientific problem.
Hazards Cyclohexane, dodecane, pentadecane, and tetradecane can be harmful if inhaled or ingested. Care should be taken to avoid contact with the skin and eyes as mild irritation may occur upon contact. Cyclohexane is extremely flammable and should be kept away from open flames and sparks. Paradichlorobenzene can cause health problems if inhaled or ingested and should be disposed of separate from the above reagents in an appropriate halogen hazardous waste material container. Small quantities of samples used help to reduce these risks.
Acknowledgments This work was supported by the Chemistry Department of Hofstra University through various private donations and Hofstra University itself. W
Conclusion
Supplemental Material
Instructor notes, student handouts, fact sheet on thermal analysis, and safety precautions using the DSC are available in this issue of JCE Online.
Determining the freezing point of cyclohexane, the kfp for cyclohexane, and the molar mass of an unknown non-
Table 1. Typical Student Results from DSC Thermograms Solvent
a
b
Molality/ (mol/kg)
Tf p
s o lu tio n
/o C
∆T/o C
Molar Mass/(g/mol) Exp
Actual
Error (%)
Cyclohexane
Dodecane
0.228
᎑0.825
4.425
175.6
170.3
᎑3.1
Cyclohexane
Tetradecane
0.208
᎑0.647
4.247
194.6
198.4
᎑1.9
0.212
᎑0.362
3.962
227.6
212.4
᎑7.1
Cyclohexane a
Unknown Solute
Pentadecane o
o
᎑1
Tfp of cyclohexane was taken as 3.6 C and the kfp was 20.5 C kg mol .
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b
Three trials were performed for each unknown solute.
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Literature Cited 1. Postma, J. M.; Roberts, J. L.; Hollenberg, J. L. Chemistry in the Laboratory, 6th ed.; W. H. Freeman: New York, 2004; pp 22-1–22-11. 2. Green River Community College Chemistry Department Home Page. http://www.instruction.greenriver.edu/knutsen/ chem150/freezpt.html (accessed Jul 2006). 3. Bare, W. D. J. Chem. Educ. 1991, 68, 1036–1038. 4. Wagner, R. S.; Strothkamp, R.; Ryan, D. Ideas, Investigation, and Thought, 3rd ed.; Whittier: New York, 2000; pp 199– 210. 5. Vyazovkin, S. Anal. Chem. 2004, 76, 3290R–3312R. 6. Folmer, J. C. W.; Franzen, S. J. Chem. Educ. 2003, 80, 813.
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7. Vebrel, J.; Grohens, Y.; Kadmiri, A.; Gowling, E. W. J. Chem. Educ. 1993, 70, 501. 8. Chowdrhy, B.; Leharne, S. J. Chem. Educ. 1997, 74, 236. 9. Kim, A.; Musfeldt, J. L. J. Chem. Educ. 1998, 75, 893. 10. Ohline, S. M.; Campbell, M. L.; Turnbull, M. T.; Kohler, S. J. J. Chem. Educ. 2001, 78, 1251. 11. Temme, S. E. J. Chem. Educ. 1995, 72, 916. 12. CRC Handbook of Chemistry and Physics, 76th ed.; Lide, D. R., Ed.; CRC Press Inc.: Boca Raton, FL,1995. 13. Lange’s Handbook of Chemistry; Dean, J. A., Ed.; McGraw– Hill Inc.: New York, 1979. 14. Internation Critical Tables of Numerical Data, Physics, Chemistry, and Technology; West, C. J., Ed.; McGraw–Hill Inc.: New York, 1933.
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