In the Laboratory
Birge–Sponer Estimation of the C–H Bond Dissociation Energy in Chloroform Using Infrared, Near-Infrared, and Visible Absorption Spectroscopy An Experiment in Physical Chemistry M. L. Myrick,* A. E. Greer, A. A. Nieuwland, R. J. Priore, J. Scaffidi, Danielle Andreatta, and Paula Colavita Department of Chemistry and Biochemistry, University of South Carolina, Columbia, SC 29208; *
[email protected] Physical chemistry students are initially exposed to vibrational spectroscopy via the harmonic oscillator model. Although anharmonic oscillators are more realistic, little quantitative analysis is usually performed at the undergraduate level using anharmonic models. Anharmonic models are, however, required to explain bond breaking. The connection between spectroscopy and quantum mechanics as taught in undergraduate physical chemistry and the concept of a bond dissociation energy as learned in general and organic chemistry is often left unexplored. The physical chemistry laboratory is an excellent setting in which to make this connection. Birge–Sponer plots (1) are simple treatments of spectroscopic data that are normally limited in application to diatomic molecules such as I2 (2). However, Hyodo, Tamagake, and Fujiyama (3) indicate this treatment can be applied to pseudo-diatomic molecules such as HCCl3, in which the C−H bond is nearly pure owing to the large masses and low vibrational frequencies of the remaining portions of the molecule. For higher vibrational levels, the normal mode approximation breaks down and the C−H bond can be treated even more properly as an isolated unit. Experimental Overview The experiment reported here uses HCCl3 as the subject of infrared, near-infrared, and UV–vis absorption spectroscopy. This experiment connects physical chemistry with general and organic chemistry concepts of bond strengths and dissociation energies. It also offers an opportunity to discuss the approximations in use in harmonic oscillator and Morse oscillator models of vibrating molecules. Further, this experiment helps students realize that hydrogen-containing compounds have measurable absorption bands in the visible spectral window due to vibrational motions even if the eye cannot readily detect them. It is something of a revelation to many students that “transparent” solvents have absorption bands that continue upwards in energy well into the visible spectral region. This experiment fits into the physical chemistry laboratory sequence as an experiment in pure vibrational spectroscopy. Because HCCl3 is studied in condensed phase, no obvious rotational fine structure complicates the appearance of the vibrational bands. It requires between one and two hours to collect data for this experiment. Spectrometers To perform the experiment fully, a collection of spectrometers is needed that span the spectral region between 3000 cm‒1 and 15,000 cm‒1 (between 3300 and 670 nm). In our laboratory, 1276
we use a HP 8452-A diode array spectrophotometer (Agilent Technologies, Palo Alto, CA) for measurements with energies between 50,000 cm‒1 and 9000 cm‒1 and a Mattson Infinity AR60 spectrometer for energies between 9000 cm‒1 and 400 cm‒1. The AR60 is a Fourier-transform instrument that changes light sources and beamsplitters when measurements are required in the mid-infrared and near-infrared regions. The near-infrared region is best obtained with a quartz beamsplitter and a tungsten filament light source, while the mid-infrared is obtained using a silicon beamsplitter and a globar light source. The AR60 is no longer commercially available, but other instruments with similar capability are available. One example is the Nicolet 6700 FTIR spectrometer, which can be configured to cover all the ranges of the Mattson AR60. Several other possibilities exist for instruments in this laboratory. First, some UV–vis instruments have responses that extend below 6000 cm‒1, while some common mid-infrared instruments have responses that extend above 6000 cm‒1. Alternatively, if the absorption band nearest 8676 cm‒1 in our measurements is omitted from the study, a common mid-infrared FTIR and a common diode-array-based UV–vis spectrophotometer can be used to perform the experiment. The mid-infrared and near-infrared spectrum of HCCl3 has been known at least qualitatively since 1924 (4–7). Because the overtones become progressively weaker as the number of quanta involved increase, it is necessary to provide the laboratory with at least three sample cells. A pair of salt plates (e.g., NaCl or KCl) with a drop of solvent between them serves satisfactorily for the conventional mid-infrared spectrum including the complete fundamental region. A 1 mm path length cell with quartz windows permits the first and second overtones to be recorded adequately, although a 1 cm path length cell with a quartz window would provide a better spectrum of the second overtone. A 10 cm path length cell with quartz windows can be used satisfactorily for the third and fourth overtones. The fourth overtone near 13850 cm‒1 is sufficiently weak that a longer path length would be better, but most UV–vis spectrometers cannot accommodate a substantially larger path length without a special accessory for multiple passes. Hazards Chloroform causes moderate eye and skin irritation on contact. Prolonged contact may cause poisoning, even through intact skin. Ingestion causes nausea, vomiting, and diarrhea, and can damage the liver and heart. Ingestion can lead to hallucinations or distorted perceptions. Liquid breathed into the lungs can be fatal. Chloroform is reasonably anticipated to be
Journal of Chemical Education • Vol. 85 No. 9 September 2008 • www.JCE.DivCHED.org • © Division of Chemical Education
In the Laboratory
carcinogenic. To minimize exposure to chloroform, sample cells should be filled and emptied in a hood. Also, although chloroform is not flammable, it can produce toxic fumes when exposed to flame. Care should be taken to eliminate open flames near areas where chloroform is being used. Results Experimental measurements of the various C−H transitions are provided in Figure 1. The data were obtained under a combination of three different experimental conditions and are presented with five different vertical scalings as described in the caption for the figure. The noise observed in traces C and E results from shorter than optimal path lengths and resulting low absorbances. The spectral width of each trace in Figure 1 is the same in energy units, thus it is clear that the line width of the C−H transitions increases significantly with the number of vibrational quanta involved. A smaller band observed between 300 cm‒1 and 600 cm‒1 lower in energy relative to each C−H absorption band is attributed to the 1st overtone of the 1215 cm‒1 H−C−Cl bending mode in combination with 0–4 quanta of the C−H stretching mode. A Lorentzian fit to the central region of each peak shown in Figure 1 was used to estimate the band centers. These were found to be at 3019.9 cm‒1, 5909.9 cm‒1, 8674.4 cm‒1, 11324.5 cm‒1, and 13,848.5 cm‒1. Discussion The spectral curves shown in Figure 1 are usually simple to acquire and make the point that the C−H vibration of chloroform is not an example of simple harmonic motion. If harmonic, the fundamental absorption band at 3019.9 cm‒1 would cause us to predict overtone absorption bands at ~6040, 9060, 12,080, and 15,100 cm‒1, predictions that are in error by 2.2%, 4.3%, 6.3%, and 8.3%, respectively. The full spectra of HCCl3 (not shown) also provide a discussion point for fundamental versus combination and overtone transitions. In addition, when the spectral region is changed from mid-infrared to nearinfrared, students should note that the sample cell windows are changed from salt to quartz, a more commonly used optical material. This offers an opportunity to describe near-infrared spectroscopy, which became a significant tool in industry due to the ability of near-infrared light to pass through quartz and glass optical fibers. A related point to note is that the overtones of the ubiquitous O−H group in early glass and quartz optical fibers defined the spectral windows used for fiber-optic communications today. Students may assume that longer path lengths would enable them to observe even weaker C−H overtones further into the visible spectral region. This is true as at least one additional overtone has been reported near 16300 cm‒1 (7). However, in addition to the decreasing strength of the higher energy overtones, the line widths of these absorption bands and overlap with neighboring absorption bands increase as the transition energy increases. Both of these factors contribute to making direct observation of higher overtones in HCCl3 more difficult. Significant effort has been expended by others to explain quantitatively the origins of the line width of the C−H fundamental and overtone vibrational absorption bands in HCCl3 (8). Details of such a discussion are probably more appropriate
B
C
D
E
Absorbance
A
2.4 2.8 3.2 5.2 5.6 6.0 8.0 8.4 8.8
11.0 11.5
13.5 14.0
Transition Energy / (103 cmź1) Figure 1. C−H spectral regions for liquid HCCl3 at room temperature versus air reference. All curves cover 1100 cm‒1 on the energy axis. Curves A–E represent transitions from the lowest vibrational level to the v = 1 through v = 5 vibrational levels, respectively. Curve A was recorded from a thin film between salt plates as described in the text. Curves B and C were recorded in a 1 mm path length liquid cell. Curves D and E were recorded in a 10 cm path length cell. Curves A–C were recorded with 1 cm‒1 resolution on a Fourier-transform instrument, while curves D–E were recorded with 2 nm resolution on a dispersive instrument. The scale bar represents a 0.0723, 0.0963, 0.00429, 0.0244, and 0.00166 range in absorbance for curves A–E, respectively.
to a graduate-level spectroscopy class than to an undergraduate physical chemistry laboratory. However, the general result that the higher vibrational excitations are more sensitive to collisional broadening may be used to direct the discussion toward the Heisenberg uncertainty principle, diffusion, solvent cage complexes, and so forth. Based on the measured positions of fundamental and overtone transitions, the first five spacings between vibrational levels of the C−H stretching mode can be determined. These spacings can then be fit to a linear model,
%_ O a b vu
(1)
∼ ∼ where a is ν e and b is –2νe xe. In eq 1, Δν is the energy spacing between two adjacent vibrational energy levels expressed as wavenumbers, vu is the vibrational quantum number for the upper vibrational level of each pair for which a separation is ∼ measured, νe is the equilibrium vibrational frequency expressed as wavenumbers, and νe xe is the first anharmonicity constant, also expressed as wavenumbers. The bond dissociation energy is then estimated as
D0
a a b
2b
(2)
The experimentally obtained bond dissociation energy is 38400 ± 500 cm‒1 (458 ± 8 kJ mol‒1). The accepted value of the bond dissociation energy for the C−H bond in HCCl3 is 401 kJ mol‒1 (9). The bond dissociation energy of neutral molecules determined by the simple linear Birge–Sponer method is usually larger than the true dissociation energy by up to 50% of the true value (2). In the case of HCCl3, the Birge–Sponer
© Division of Chemical Education • www.JCE.DivCHED.org • Vol. 85 No. 9 September 2008 • Journal of Chemical Education
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In the Laboratory
approximation overestimates the bond dissociation energy by 58 kJ mol‒1, an error of 14.5%. This overestimation and error— which is found to be clearly outside the uncertainty limits for the calculation—is evidence that the higher anharmonicity terms that are omitted in eq 1 become significant for large values of v. Acknowledgments The authors gratefully thank R. Bruce Dunlap for the opportunity to work on new laboratory development in CHEM542L at University of South Carolina. PEC gratefully acknowledges support from the NSF graduate fellowship program. AEG, AAN, RJP, and DA thank the Department of Chemistry and Biochemistry for support of this work. Literature Cited 1. Steinfeld, J. I. Molecules and Radiation – An Introduction to Modern Molecular Spectroscopy, 2nd ed.; MIT Press: Cambridge, MA, 1993. 2. Herzberg, G. Molecular Spectra and Molecular Structure Volume I: Spectra of Diatomic Molecules, 2nd ed.; Krieger Publishing Co.: Malabar, FL, 1989; pp 438–441.
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3. Hyodo, S.; Tamagake, K.; Fujiyama, T. Bull. Chem. Soc. Japan 1982, 55, 1272–1276. 4. Ellis, J. W. Phys. Rev. 1924, 23, 48–62. 5. Ellis, J. W. Phys. Rev. 1928, 32, 906–912. 6. Rumpf, K.; Mecke, R. Zeitschrift für physikalische Chemie. Abteilung B 1939, 44, 299–312. 7. Herzberg, G. Molecular Spectra and Molecular Structure Volume II: Infrared and Raman Spectra of Polyatomic Molecules; Van Nostrand: New York, 1945. 8. Yamaguchi, T. J. Chem. Phys. 2000, 112, 8530–8533 and references therein. 9. CRC Handbook of Chemistry and Physics, 67th ed.; Weast, R. C., Ed.; CRC Press: Boca Raton, FL, 1986; pp F-186.
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Journal of Chemical Education • Vol. 85 No. 9 September 2008 • www.JCE.DivCHED.org • © Division of Chemical Education
