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This lab involves recording the fundamental vibration-rotation spectrum of acetylene and perdeuteroacetylene on a scanning spectrometer. The spectrum may be analyzed to yield accurate values of the mean CC and CH bond lengths, and the role of the Pauli Principle on rotational energy level populations will be seen and explained as well. For those students who would like to explore a more typical diatomic IR spectrum using an FTIR spectrometer, the HCl/DCl lab is suggested. In both experiments, sufficient experimental data are obtained to allow meaningful error analyses.
You can click here for a pdf version of the lab handout (about 60k in size). The pdf version has a diagram of the J = 0 through J = 3 spherical harmonic functions, used in a discussion of rotational wavefunction parity, that is in color. The photocopied handouts make it difficult to distinguish one color from the other, so this figure is also shown below. The images are taken from the "Hydrogen atom angular functions for chemists" Text Extra page and show the functions with m = 0 for, left to right, J = 0, 1, 2, and 3. The red color indicates an opposite algebraic sign from the blue color. Click on the Text Extra icon to the right of the figure to go to that page.
You can click here (or on the icon to the right) for an interactive
page that covers the fundamentals of vibration-rotation spectroscopy:
phenomenology, terminology, energy levels, appearance of the spectra,
etc. This page is a Text Extra as well.
You can click here (or on the icon to the right) for an interactive
page that covers the special aspects of the acetylene spectrum due
to the Pauli Principle. This page is a Text Extra as well.
Shown below is a "research-grade" spectrum of the C2H2 spectrum you will record. It was recorded in 1987 at Dartmouth by Dr. Brian C. Smith as part of his Ph.D. thesis research with Prof. Winn. Brian used a very high resolution FTIR in Prof. Winn's lab to study the acetylene spectrum throughout the IR and on into the visible where very weak overtone transitions can be seen. Such experiments give a great deal of information about the vibrational energy levels of acetylene, which has become an important test molecule for polyatomic molecular vibration. Since these transitions are so weak, Brian used a long-path gas cell that is 2 m long which, through a clever arrangement of mirrors, bounces the spectrometer light back and forth through the gas for total path lengths as large as 128 m. The spectrum below, however, required only a 10 cm path-length gas cell of the type you will use. Click on the spectrum to see a much larger version. The instrumental resolution for this spectrum was 0.004 cm-1, and individual lines are "at the Doppler limit" (see page 740 in Winn). You can use Eq. (19.51) in Winn to calculate that this linewidth is about 0.016 cm-1 for room temperature acetylene. Brian's results are published in the Journal of Chemical Physics in two papers: volume 89, page 4638 (1988) and volume 94, page 4120 (1991), in case you'd like to see them.
A high-resolution spectrum plotted this way looks like a stick spectrum - you can't see the individual lineshapes very well. Shown below is a close-up picture of just the R(9) line in this spectrum. This line is about 0.021 cm-1 wide, which is what you'd expect for a 0.016 cm-1 Doppler width line recorded at 0.004 cm-1 resolution. This spectrum covers only 0.35 cm-1, but it contains 175 data points. (A resolution of 0.004 cm-1 requires one point every 0.002 cm–1.) The full spectrum above had over 75,500 data points in its original form. Only the central 65,000 of them with the strongest signal are shown above!
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