Rotation Spectra of Gases

The shape and width of individual lines in the vibration-rotation spectrum of a gas depend on the gas pressure, P. For gases at low pressure (typically, P 1 torr), the shape and width of each spectral line in the width are determined by the Doppler effect (i.e., by the variation of the speed of each molecule in the direction of the beam). The shape of a Doppler-broadened line centered at wavenumber vq is Gaussian that is, the absorbance at any wavenumber v is given by 

For a line in the H—CHH bending mode of water (Af= 18 g moP ) at 1500 cm , the Doppler width at room temperature (298 K) is about 0.0044 cm . Thus, an instrument with very high resolution is needed before Doppler-broadened spectra can be measured accurately. 

As the total pressure of the gas is raised above 1 torr, the mechanism of line broadening becomes more dominated by the effect of intermolecular collisions than by the Doppler effect. The shape of lines in collision-broadened spectra is Lorentzian  

Hence for mixtures of an analyte with helium, nitrogen, or air at atmospheric pressure, Yc of each of the rotational lines is usually between 0.1 and 0.2 cm .  

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It is important to realize that the relaxation times might depend on some factors that are properties of the atom or molecule itself and on others that are related to its environment. Thus rotational spectra of gases have linewidths (related to the rotational relaxation times) that depend on the mean times between coUisions for the molecules, which in turn depend on the gas pressure. In liquids, the collision lifetimes are much shorter, and so rotational energy is effectively non-quantized. On the other hand, if the probability of collisions is reduced, as in a molecular beam, we can increase the relaxation time, reduce linewidths, and so improve resolution. Of course, the relaxation time only defines a minimum width of spectral lines, which may be broadened by other experimental factors. 

Pure rotational spectra of gases have also been obtained in the far infrared. Hansler and Oetjen obtained the pure rotational spectra of HCl, DCl, HBr, and NHa from 40 to 140 n. Palik and Rao measured the rotational spectra of CO, NO, and N2O from 100 to 600 /i. Nitrogen dioxide [ ], ozone [ ], SO2 [ ], and HCN [ Ihave also been studied. From these studies, the centrifugal constant for distortion has been obtained for NO2, and the magnetic interaction for the oxides of nitrogen has been determined. 

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