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Vibrational Spectrum of SO2 and CO2

Teaching Assistant: TA Name

Chem 375-003

Group #5


Lab Partner: Name 1

Introduction & Theory

The infrared spectrum extends from 10 000 cm-1 down to 10 cm-1 (1 m to 1000 m). The range from 4000 to 400 cm-1 is of the most interest, as vibrational frequencies of most molecules lie within this region.

When a photon strikes a molecule, the photon may be absorbed if the energy of the photon (hv) corresponds to the energy difference from the molecules current state to a more excited state. This excited state may be manifested by moving electrons to higher shells or changes in vibration, rotation, or translational energy. This experiment investigates changes in vibrational energy, however the other effects may be seen at different wavelengths (energies).

Vibrational energy may be stored in a number of ways. A nonlinear molecule containing N atoms has 3N-6 degrees of freedom, so a molecule like SO2 has three different forms of vibration. These forms of vibration are called normal modes. Linear molecules, such as CO2, have one additional normal mode, the linear stretch.

Each vibrational mode has numerous rotation modes within it, giving rise to the fine structure found in vibrational spectra. The resolution of the apparatus used will determine whether the fine structure will be visible.

In CO2 molecules, the linear stretch is not infrared-active, so there will be no peak corresponding to it. In addition, the ranges of two peaks within the spectrum of CO2 overlap, so only one peak is seen. As a result, only two peaks are expected. On the other hand, all of the modes of SO2 are optically active and non-degenerate, so three peaks are expected. The bending frequency v2 is given by the lowest frequency band, the antisymmetric stretch frequency v3 is given by the highest frequency band, and the symmetric stretch frequency is given by the frequency of the band between the previous two.

At high pressure, much weaker bands may be observed due to overtones (2vi, 3vi, . . .) or combination bands (vi vj, 2vi vj, . . .).

Using SO2 as an example, the normal vibrational modes may be expressed using the atomic masses (mS and mO), the O-S-O bond angle (2), changes in the O-S-O bond angle (), changes in S-O distances (r1 and r2), and force constants ki. The potential energy of SO2 is then given by

From this, using classical mechanics for harmonic oscillators, one can obtain

By expressing v in wavenumber units (cm-1), mO=15.995 amu
, and mS=31.972 amu, one can replace 42 with 42c2/103N0=5.8918x10-5 to obtain k1 and k/l2 in units of N m-1. Sulfur dioxide has a bond angle 2 of 119.5, and l=0.1432 nm.

The heat capacity at constant volume for ideal gases is the sum of contributions from translational, rotational, and vibrational modes. For nonlinear polyatomic molecules, the molar heat capacity due to translation is equal to 3/2 R, and that due to rotation is 3/2 R as well. As the energy levels of a harmonic oscillator are represented by (v + )hv, the harmonic oscillator partition function for the ith normal mode qiHO is given by

The vibrational partition function qvib is well approximated by

This can then be used to calculate the vibrational contribution to the molar heat capacity at constant volume by

Where ui=hvi/kT=1.4388(wavenumberi)/T and the summation is made over all modes.


The goal of this experiment is to collect FTIR vibrational spectra for SO2 and CO2. From these spectra, the fundamental vibrational frequencies of the gases, the heat capacity at constant volume, and other constants are to be determined.


FTIR instrument; gas cell with KBr windows; cylinder of SO2 with needle valve; cylinder of CO2 with needle valve; and a vacuum apparatus (with cold trap before vacuum pump) for filling the cell with pure gas at various known pressures (via a manometer).

Experimental Observables

The absorbance of the sample over the IR region will be measured directly, and the pressure of the sample will be measured with a manometer. All other determinations are derived from these observations.

Experimental Procedure

Ensure the needle valve on the SO2 cylinder is closed, then assemble and evacuate the entire system for a few minutes. Close off the vacuum source and slowly open the needle valve to pressurize the system to about 900 mm Hg, then close off the SO2 source. Seal the cell and remove to take a spectrum.

Return the cell, and evacuate the manifold. Close off the vacuum and allow SO2 to pressurize the apparatus to about 300 mm Hg. Seal the cell and remove to take a spectrum. Repeat this part at 100, 20, and 5 mm Hg additionally.

Repeat the entire procedure with CO2.


Mercury and mercury vapor are highly poisonous. Inhalation of vapor may lead to fever, nausea, vomiting, diarrhea, headache, chest pain, and possibly death. Skin contact may lead to a rash or allergic reaction, and if extensive may also cause the same effects as inhalation of vapor. Affected persons should be removed to fresh air and contaminated clothing removed. Necessary first aid techniques should be performed. Seek medical attention immediately.

Inhalation of carbon dioxide gas in low to medium concentrations can cause nausea, dizziness, headache, affect blood circulation, and acidify bodily fluids. High concentrations can lead to death, especially if oxygen is displaced. Persons affected should be removed to fresh air and necessary first aid techniques performed. Seek medical attention immediately.

Sulfur dioxide is extremely corrosive and can cause severe irritation to exposed areas. Inhalation of vapor may lead to fever, nausea, vomiting, diarrhea, headache, chest pain, and possibly death. Sulfur dioxide is heavier than air, and will tend to accumulate in low lying areas, possibly causing asphyxiation. While not flammable or explosive, cylinders of SO2 increase in pressure rapidly with temperature increases. If possible, cool cylinders with water in the event of fire. Affected persons should be removed to fresh air. Necessary first aid techniques should be performed, including administration of pure oxygen. Seek medical attention immediately.


1. Safety data taken from the internet at "",



2. D.P. Shoemaker, C.W. Garland, J.W. Nibler, Experiments in Physical Chemistry, 6th ed., The McGraw-Hill Companies (1996).