In the Laboratory
An Investigation into the Absorption of Infrared Light by Small Molecules1 A General Chemistry Experiment William B. Heuer and Edward Koubek Chemistry Department, United States Naval Academy, Annapolis, MD 21402
The past few decades have witnessed spectacular advances in both the development of new spectroscopic techniques and refinement of existing ones. Given the central role that spectroscopy now plays in the chemical sciences, it would seem that this topic deserves greater exposure in the introductory college chemistry course. Too often, however, discussion of spectroscopy at this level is limited to a description of atomic emission spectra offered in conjunction with discussion of the Bohr model of the hydrogen atom. This brief, historical treatment of atomic emission serves to establish the experimental evidence for the quantization of electronic energy levels in atoms; however, it does not convey to students any appreciation for either the versatility of modern spectroscopic methods or their use as a structural tool in the contemporary laboratory. This paper describes a two-part classroom/laboratory activity that introduces a broader perspective on spectroscopy into the general chemistry curriculum. In Part I, qualitative models for molecular vibration and the mechanism by which such vibrations may be excited by infrared light are developed through class discussion. By stressing the direct analogy between harmonic motion on the macroscopic scale and on the molecular scale, this discussion presents complex concepts in an intuitive manner accessible to students having a range of science backgrounds. Part II involves a series of quantitative experiments in which students first explore the physics of harmonic motion on the laboratory scale and then use their results to predict the vibrational behavior of a molecular system as probed by a simple IR experiment. By demonstrating the successful application of a macroscopic physical model to a molecular system, and by experimentally confirming that infrared absorption frequencies do in fact correlate with the frequencies of molecular vibration, the laboratory investigation validates two key concepts from the pre-lab discussion.
ized to include the other cases.2 The mechanism of resonant energy transfer from the electromagnetic wave to molecular motions is introduced in an intuitive manner by considering the analogy of a person pushing a child on a swing. Students can readily identify from personal experience the importance of the timing of the pushes (i.e., their “frequency” and “phase”) in achieving efficient energy transfer, and the periodicity of the swing motion establishes this as an example of “resonant” energy transfer. The analogy may then be translated to the microscopic scale by first considering the vibrational motions of an individual molecule. Like the motion of the swing, these vibrations are periodic functions, but the time scale of the motion is much faster (ca. 10 14 s {1). The vibrational motions of a three-dimensional molecule are also considerably more complex than the motion of a swing. Fortunately, these complex molecular vibrations can be resolved into a limited number of simpler vibrational motions or “normal modes”, each with a characteristic frequency and symmetry. If a molecule contains polar bonds, stretching and/or bending vibrations involving these bonds will change the magnitude of the molecular dipole moment (or some component of it) in a periodic manner,3 and this vibrationally induced modulation of the molecular dipole moment may in turn couple with the oscillating electric field of an infrared wave. However, this coupling between the radiation field (the “pusher”) and the vibrating molecule (the “swing”) will only give rise to resonant absorption of energy if the frequency of the electromagnetic wave coincides with the frequency of a vibrational normal mode (or some combination of normal modes) of the molecule. Once this model of molecular vibration and infrared absorption is established, the pre-lab discussion is concluded by soliciting suggestions from the class about how the model might be experimentally tested. Part II: Laboratory Investigation
Part I: Pre-Lab Discussion Prior to the experimental portion of the lab, foundational concepts are introduced in a class discussion format. Discussion is initiated by recalling familiar examples of absorption of electromagnetic energy by matter, such as the absorption of visible light by colored fabrics or solutions, the use of infrared lamps for warming french fries, and microwave cooking. Students are encouraged to express their own ideas of how the energy is transferred from the radiation source to the matter and where the energy “goes” in each of these cases. Most will recognize that the energy source in each case is a form of electromagnetic radiation, which is described classically in terms of its wavelike character. However, many students will not appreciate the fact that the nature of the excitation differs depending upon the frequency of the radiation. To understand why this is so, discussion is directed toward developing a postulated mechanism for infrared absorption which may then be general-
The laboratory portion begins with an exploration of factors governing the vibrational frequency of a simple spring oscillator. The quantitative results are then applied to a molecular system by drawing an analogy between the spring and a chemical bond. While the content of these initial experiments is certainly not original, the context in which they are presented (i.e., with direct analogy to the molecular scale) is novel and, we believe, highly instructive. Hooke’s Law Students are initially presented with a simple apparatus4 consisting of a variable mass suspended from a spring, one end of which is fixed to a stationary support. This system is assumed to constitute a physical model for a chemical bond, and if chemical bonds may be regarded as springs, then the strength of a chemical bond should be analogous to the force constant, k, of the spring. A measure of the “stiff-
Vol. 74 No. 3 March 1997 • Journal of Chemical Education
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In the Laboratory
Figure 1. Applied force vs. extension for three springs (actual student data). Least-squares fits to the data using eq 1 yielded the following parameters: m, k = 8.59 kg?s{ 2; j, k = 9.19 kg?s{2; d, k = 13.4 kg?s–2 .
ness” of the spring, k is defined by the proportionality between the elongation of the spring from its equilibrium position, x, and the magnitude of the restoring force, F: F = {kx
(1)
This relationship, known as Hooke’s Law, is readily verified and the numerical value of k (along with appropriate units) for a specific spring evaluated by measuring the elongation produced by different masses. The applied force in newtons, calculated as the product of the mass times the acceleration due to gravity (9.80 m/s 2), is equal in magnitude but directionally opposed to the restoring force; thus, a plot of applied force vs. extension for a series of masses yields a straight line with positive slope = k (Fig. 1). Simple Harmonic Motion Once the force constant of the spring has been determined, students are introduced to Galileo’s relationship between the period of vibration (T) of a spring and the mass (m) suspended from it:5
T = 2π m / k
(2)
or, in terms of the frequency of vibration, ν,
ν= 1 = 1 k/ m T 2π
(3)
Taking into account the mass contribution of the spring itself, this becomes:
ν= 1 2π
k mm + ms
2
2 2 2 = 2π ⋅ m m + m s = 2π ⋅ m m + 2π ⋅ m s k k k
(5)
Consequently, a plot of (1/ν)2 vs. the mass on the spring should yield a straight line with slope = (2π)2/k (Fig. 2). Students are instructed to verify this relationship using their experimental setup and to calculate the percent deviation between the values of k obtained using eqs 1 and 5.
314
IR Absorption Spectrum of CHCl3 and CDCl3 Having developed a quantitative relationship between the mass, force constant, and vibrational frequency of a onedimensional spring oscillator, students now investigate what this model can tell us about vibrational harmonic motion at the molecular level by observing the effects of deuterium substitution on the infrared absorptions of chloroform. The infrared spectrum of CHCl3 is first recorded either as a demonstration or, if time permits, by groups of students.6 Force constants for the presumed stretching and bending7 vibrations of the C–H bond are then calculated by substituting the observed absorption frequencies (Table I) into eq 3:
ν= c = 1 λ 2π
k mH
where c is the velocity of light (2.9979 × 1010 cm/s) and mH = 1.6735 × 10{27 kg. Now, if the model is valid on a molecular scale, it should be possible for the student to use these calculated force constants to accurately predict the frequencies for the corresponding C–D absorptions of CDCl3 by substituting mD = 3.3443 × 10{27 kg into the above equation. 8 The spectrum of CDCl3 is then recorded, and students are instructed to compute the percent deviation between the predicted and observed values. Finally, the existence in both spectra of several additional low-frequency bands (the C–Cl symmetric and asymmetric stretches) is noted, and students are asked to propose an assignment for these absorptions that is consistent with the model just developed.
(4)
where ms and mm represent the effective mass of the spring and the mass suspended from it, respectively. Inverting both sides and squaring yields:
1 ν
Figure 2. Inverse frequency squared vs. mass on the spring (actual student data) for the same three springs shown in Figure 1. Least-squares fits to the data using eq 5 yielded the following parameters: m, k = 8.37 kg?s{2 , ms = 0.069 kg; j, k = 10.1 kg?s{2, m s = 0.081 kg; d, k = 12.7 kg?s{2, m s = 0.040 kg.
Table 1. Observed and Calculated Values for Infrared Spectra of CHCl3 and CDCl3 Mode
CHCl3 obs. k (calc) CDCl3 obs. Predicted Deviation (cm{1) (N·m{1) (cm{1) (eq 4) (%)
C–H/D stretch
3020a
542.3
2254
2136
5.2
C–H/D bend
1222
88.8
912
864
5.2
C–Cl stretch
770 756(shldr) 669
—
744 730(shldr) 651
—
—
Journal of Chemical Education • Vol. 74 No. 3 March 1997
In the Laboratory Results and Discussion This experiment has been used successfully with general chemistry students having a considerable range of abilities and backgrounds. Examples of student data for the Hooke’s Law and Simple Harmonic Motion experiments are shown in Figures 1 and 2, respectively. The values of k obtained by the two independent methods typically agree to within ±5%. A greater variety of force constants can be achieved by physically shortening some of the springs; as the students’ data show, this increases the force constant while at the same time reducing the mass contribution of the shortened spring. The application of eq 3 to the infrared absorptions of the CHCl3 molecule is based on the assumption that the C– H vibrations are local modes. This is equivalent to treating the CCl3 group as a rigid body. For simplification it is also assumed9 that the massive CCl3 group remains motionless during vibration of the C–H bond, a condition similar to that imposed by the spring oscillator used in the preceding measurements. The values of the C–H stretching and bending force constants calculated using eq 3 are within 10–20% of the “typical” values given in the literature (1). The predicted C– D bending and stretching frequencies are typically 3–5% lower than the observed values (Table 1), an error that is apparently introduced by the local mode approximation used in the calculations. The fact that the IR absorptions of chloroform actually arise from excitation of normal modes involving contributions from both C–H and C–Cl bonds is reflected nicely by the small but significant shift of the C– Cl stretching absorptions upon deuteration (Table 1). Conclusion This laboratory investigation into the absorption of infrared radiation by small molecules offers a number of benefits to students of general chemistry. Through its liberal use of qualitative, intuitive analogies, the pre-lab discussion provides a level-appropriate description of molecular vibration and the mechanism of resonant absorption of infrared light. By emphasizing the importance of the dipolar character associated with both individual bonds and molecules as a whole in mediating this interaction, the discussion provides a practical application for elementary theories of bonding and molecular structure covered in most general chemistry courses. The laboratory investigation then translates the qualitative development of the pre-lab discussion into the quantitative realm. By showing that a quantitative physical relationship developed through experiments with a macroscopic model system can be used to successfully predict vibrational behavior of molecules, the experi-
ments reinforce the analogy drawn earlier in the pre-lab discussion and enhance student’s abilities to visualize dynamic processes occurring on a molecular level. The observed correlation between the frequencies of molecular vibration and infrared absorption established by the experiments also validates the postulated resonant absorption mechanism, which provides a convenient entry into discussions of such interest-generating topics as the greenhouse effect and microwave cooking. Notes 1. Presented at the 13th Biennial Conference on Chemical Education, Bucknell University, Lewisburg, PA, 31 July–4 August 1994. 2. For example, the absorption of microwave energy by rotational excitation of dipolar molecules may be accounted for in an analogous manner. A laboratory investigation of the microwave heating effect on liquids has been previously described: Watkins, K. W. J. Chem. Educ. 1983, 60, 1043. 3. It should be noted that some normal modes will not alter the molecular dipole owing to their symmetry. For example, the strong infrared absorptions of the greenhouse gases CO2 and CH4 are associated exclusively with the antisymmetric vibrational modes, whereas the symmetric modes are infrared-inactive. 4. Central Scientific Company Model #75490. 5. According to legend, Galileo made his initial observations regarding simple harmonic motion as a very young man while attending mass. Noticing a swinging chandelier, he used his pulse as a time reference and discovered that although the amplitude of the swings gradually decreased, the period remained the same. 6. If an IR spectrometer is not available, spectra can be looked up in a compendium of standard spectra such as the Aldrich or Sadtler collections. This approach has the advantage of making students aware of the tremendous diversity of known chemical structures, and it emphasizes the utility of the spectrum as a “fingerprint” that can be used to identify molecules. 7. The effect of the C–H bending mode on the molecular dipole moment of chloroform is completely analogous to that of the C–H stretch. This can be readily seen by resolving the bending motion into its components; in the limit of small-amplitude motion, the bend causes an oscillating component of the dipole moment oriented perpendicular to the C–H bond direction. 8. It should be pointed out that since 1H and 2H are isotopes of the same element, their bonding characteristics will be essentially the same. 9. This allows the use of the hydrogen mass, mH, in the calculations rather than the true reduced mass, µ, of the vibrating system. Since mCCl 3 >> mH, µ = [m HmCCl 3/(mH+ mCCl 3)] . m H; the error incurred by this approximation is negligibly small (
