9.10.4: Part II - FTIR spectrum of SO2

Reminder

The general approach to Part II of this experiment is adapted from D. P. Shoemaker, C. W. Garland, and J. W. Nibler, Experiments in Physical Chemistry, 6th edition, McGraw Hill Co. Inc, NY, 1996. In preparation for this experiment please read Experiment 35 in Shoemaker, Garland and Nibler beginning on page 383. You will want to read and understand the theory section including the subsections on the valence-force model and the vibrational partition function.

Prepare the sample of \(\ce{SO2}\)

A vacuum line will be used to evacuate the IR gas cell of HCl/DCl gas. Then transfer the toxic SO₂ gas from its high-pressure containers to the evacuated IR cell. The cell should be loaded with \(\ce{SO2}\) to a pressure of \(0.5-1.0\) cm Hg. Use assistance from your TA and use the protocols and precautions described earlier as a guide. 

Note

You will use a pressure of SO₂ less than or equal to 1 cm Hg. If the pressure of SO₂ in the gas cell is much higher, you will not be able to observe the fine structure on the most intense fundamental frequency. If the gas pressure is too low, you may not be able to observe the weak combination bands. Depending on your skill with transferring known pressures of gases on the vacuum line, you may find it easier to record the spectrum using two different gas pressures so that all the features of the spectrum are well resolved.

Collect the FTIR spectrum of \(\ce{SO2}\)

Use the protocols and precautions described earlier as a guide. 

1. Record an FTIR absorbance spectrum of \(\ce{SO2}\) at 0.125 cm^–1 resolution, and under the same conditions used for the HCl/DCl sample, and ratio against the background spectrum of the evacuated cell.
2. Plot the absorbance spectrum over the range \(4000-400 \; cm^{–1}\) (or a range suggested by your TA). Determine the frequency of each band seen in the spectrum. Inspect the data carefully and identify combination bands and overtone bands that are visible in the spectrum.
3. Use the Omnic Annotation Tool (look to the bottom of the spectrum window for the button) to label the center position of each fundamental band and of any overtone or combination bands you observe.
   • You use this tool by clicking on the button, position the cursor (now with an associated T) at the point you want to measure.
   • Then click and drag a line up (maybe up and over).
   • When you click again the wavelength at that position on the spectrum will be added as an annotation to the spectrum (see picture).
   • If you want to delete an annotation, drag a box around the annotation (the actual wavelength added to the screen) and select Delete Annotation from the Edit menu.

     Note

     Notice that in determining the frequency of vibration in you are estimating the center of the feature by eye and hand, rather than having the Omnic software determine the peak position. To get an estimate of the uncertainty of your determination, do between three and five repeated trials of estimating the frequency and find the mean and standard deviation.

     Notice also that because we are using both an instrument and a gas cell with KBr windows, we will not be able to see the bending mode clearly or completely as the KBr starts to absorb strongly in that region of the spectrum. You should, however, see enough of the bending mode to get a crude estimate of its frequency. Get help from your TA, and comment in your ELN why this frequency may show greater deviation from expected values than the others.

     

     Figure \(\PageIndex{1}\): The Symmetric Stretch of SO_2(g). (CC-NC-BY-DUKE CHEM)

Clean up/ Shut down

Please use the vacuum line to evacuate the gas cell and store the evacuated cell in the desiccator. Please work under supervision of your instructor to shut down the gas line using the protocols and precautions described earlier as a guide. 

Treatment and Analysis of Data 

1. Assign the fundamental bands of SO₂ as: symmetric stretch, \(\widetilde{\nu}_1\); bend, \(\widetilde{\nu}_2\); asymmetric stretch, \(\widetilde{\nu}_3\) ; and, report their frequencies. Compare your value with those reported in the literature.
2. Then assign any other bands, comparing the observed frequencies with those calculated from combinations of the fundamental values \(\widetilde{\nu}_1\), \(\widetilde{\nu}_2\), \(\widetilde{\nu}_3\).
3. Calculate k₁ and \(\large \frac{k_{\delta}}{\ell^2}\) from Equations (1) and (3) (on page 385 of Shoemaker, Garland and Nibler) using your values of \(\widetilde{\nu}_1\), \(\widetilde{\nu}_2\), and \(\widetilde{\nu}_3\). Check the valence-force model by calculating both sides of Eq. (2) (also on p. 385 of Shoemaker) and comparing them. Again, compare your results with literature values.

   Note

   When finding literature values for the force constants of SO₂, you will likely notice that different notations are used. It may be difficult to find the k₁ and \(\large \frac{k_{\delta}}{\ell^2}\) notation used in Shoemaker, Garland and Nibler (and as such in this manual). For example, Kivelson⁸ reports these same vales as \(f_d\); and, \(\large \frac{f_a}{d^2}\) and reports the values in units of \(\large \frac{dynes}{cm}\) rather than \(\large \frac{N}{m}\). Be prepared to convert.

4. Using your values of \(\widetilde{\nu}_1\), \(\widetilde{\nu}_2\), and \(\widetilde{\nu}_1\), calculate \(\tilde{C}_{v(vib)}\) at 298 K and at 500 K from Eq. (8) on page 386 of Shoemaker, Garland and Nibler.
5. At these same temperatures, calculate \(\tilde{C}_{v}\) from the expression \[ \tilde{C}_{v}=3R+\tilde{C}_{v(vib)} \] and compare your results with the following \(\tilde{C}_{v}\) values (obtained from directly measured values of \(\tilde{C}_{p}\) and the expression \[ \tilde{C}_{v} = \tilde{C}_{p} - R \] \(\tilde{C}_{v}\) = 30.5 J K^–1 mol^–1 at 298 K and 37.7 J K^–1 mol^–1 at 500 K.
6. Calculate the uncertainty of each result you report in this experiment.

References and further reading 

1. Herzberg, G. Molecular Spectra and Molecular Structure II. Infrared and Raman Spectra of Polyatomic Molecules, Van Nostrand, Princeton, New Jersey, 1945, pps. 168-172, 251-269, 285.
2. Herzberg, G. Molecular Spectra and Molecular Structure II. Infrared and Raman Spectra of Polyatomic Molecules, Van Nostrand, Princeton, New Jersey, 1966, p. 605.
3. Atkins, P.W. Physical Chemistry, 5th ed., Freeman, New York, 1994, Chapter 14; McQuarrie, D.A. Statistical Thermodynamics, Harper & Row, New York, 1976.
4. Lewis. G.N., Randall, M. (revised by Pitzer, K.S. and Brewer, L), Thermodynamics, 2nd ed., McGraw-Hill, New York, 1961, p. 419ff.
5. Silbey, R.J., Alberty, R.A., and Bawendi, M.G., Physical Chemistry, 4th ed., Wiley, NY, 2005, Chapter 13, Sections 13.6, 13.8, and 13.10.
6. Colthup, N.B., Daly, L.H., and Wiberley, S.E. Introduction to Infrared and Raman Spectroscopy, 3rd ed., Academic Press, Boston, 1990.
7. Shoemaker, D.P.; Garland, C.W.; Nibler, J.W. Experiments in Physical Chemistry, 6th ed., McGraw-Hill, New York, 1996, Chapter XIV, Experiments 35 and 37.
8.  Kivelson, D., The Determination of the Potential Constants of S0₂ from Centrifugal Distortion Effects, J. Chem. Phys., 22 (5), 904, 1954.