Vibrational modes of carbon dioxide

When high-temperature products are in an equilibrium state, many of the constituent molecules dissociate thermally. For example, the rotational and vibrational modes of carbon dioxide are excited and their mohons become very intense. As the temperature is increased, the chemical bonds between the carbon and oxygen atoms are broken. This kind of bond breakage is called thermal dissociation. The dissociahon of H2O becomes evident at about 2000 K and produces H2, OH, O2, H, and O at 0.1 MPa. About 50% of H2O is dissociated at 3200 K, rising to 90% at 3700 K. The products H2, O2, and OH dissociate to H and O as the temperature is increased further. The fraction of thermally dissociated molecules is suppressed as the pressure is increased at constant temperature. 

The remaining two vibrational modes of carbon dioxide involve scissoring, as shown here. 

Fig. 1.6 Normal vibration modes of carbon dioxide molecule in its ground state...

A molecule can only absorb infrared radiation if the vibration changes the dipole moment. Homonuclear diatomic molecules (such as N2) have no dipole moment no matter how much the atoms are separated, so they have no infrared spectra, just as they had no microwave spectra. They still have rotational and vibrational energy levels it is just that absorption of one infrared or microwave photon will not excite transitions between those levels. Heteronuclear diatomics (such as CO or HC1) absorb infrared radiation. All polyatomic molecules (three or more atoms) also absorb infrared radiation, because there are always some vibrations which create a dipole moment. For example, the bending modes of carbon dioxide make the molecule nonlinear and create a dipole moment, hence CO2 can absorb infrared radiation. 

The linear three particle system A—H—X confined to one dimension has in general two fundamental vibrations, both stretching modes, analogous to the two stretching modes of carbon dioxide ... 

To compensate for the above, the number of theoretical normal vibrations may be reduced by two inherent factors of the molecule. Some vibrations may be degenerate. For example, a Unear triatomic molecule should, by theory, have four vibrational modes. However, the deformational mode of carbon dioxide (see Fig. 2, A, iii) is not uniquely defined, since the motions could take place either in the plane of the paper or in a plane perpendicular to it. If a molecule is highly symmetrical, it is probable that certain vibrations will not be accompanied by a change in the dipole moment, thus the frequency will be forbidden in the infrared. ... 

The four vibrational modes for carbon dioxide are shown in Fig. 25.3. The first vibration is the totally symmetric stretching vibration, = 1388.3 cm This vibration does not produce a band in the infrared since it does not produce an oscillation in the dipole moment of the molecule. The second and third vibrations in Fig. 25.3 differ only in that the bending occurs in mutually perpendicular planes. Thus the vibration is doubly degenerate the frequency is the same for both modes V2 = 667.3 cm The fourth mode is the asymmetric stretching vibration and has a third distinct frequency ... 

Figure 11.73 shows the vibrations in the sulfur dioxide molecule. Sulfur dioxide and carbon dioxide molecules have different shapes, and hence the vibrations causing changes in the dipole moment differ. The vibrational modes of sulfur dioxide are similar to those of water. ... 

Michaels C A, Mullin A S, Park J, Chou J Z and Flynn G W 1998 The collisional deactivation of highly vibrationally excited pyrazine by a bath of carbon dioxide excitation of the infrared inactive (10°0), (02°0), and (02 0) bath vibrational modes J. Chem. Phys. 108 2744-55... 

In tlie above discussion we have considered all the possible modes of vibration of carbon dioxide according to the formula 3 - 5, these should be (3 X 3) — 5=4 in number. The four oscillations will be the symmetrical, the non-symmetrical and two deformation vibrations. The deformation oscillation may occur in any plane passing through the axis of the molecule, but all such vibrations may be described by the projections on to two mutually perpendicular planes passing through the molecular... 

Ideal- s heat capacities increase smoothly with increasing temperature toward an upper limit, which is reached when all translational, rotational, and vibrational modes of molecular motion are fully excited [see Eq. (16.18)]. The influence of temperadireon C p for argon, nitrogen, water, and carbon dioxide is illnstrated m Fig. 4.1. Temperahire dependence is expressed... 

We saw earlier (p. 66) that the symmetric vibration of carbon dioxide does not give rise to an infrared spectrum because there is no change in dipole moment, although the antisymmetric mode does give an infrared spectrum as a result of the oscillating dipole moment. The situation with Raman spectra is the converse. The symmetric vibration stretches and compresses both bonds, and the polarizability therefore varies. As a result, this vibration gives rise to Raman lines. The antisymmetric vibration, on the other hand, does not lead to a net polarizability variation because as one bond lengthens the other bond shortens, and the two effects cancel. Thus there are no Raman lines associated with the antisymmetric vibration. To summarize the situation for CO2 ... 

It is of interest to compare the spectrum of carbon dioxide with iliai of a nonlinear Irialomic molecule such as water sulfur dioxide, or nitrogen dioxide. These molecules have (3x3)- 6 3 vibrational modes that lake the followine forms ... 

In contrast, the dipole moment of carbon dioxide fluctuates in phase with the asymmetric vibrational mode. Thus, an IR absorption band arises from this mode. On the other hand, as the polarizability of one of the bonds increases as it lengthens, the polarizability of the other decreases, resulting in no net change in the molecular polarizability. Thas, the asymmetric stretching vibration is Raman inactive, f-or molecules with a center of symmetry, such as CO, no IR active iraasi-lions arc in common with Raman aclive transitions. This is often called the mutual exclusion principle. 

Fig. 39. Schematic representation of the fundamental vibrations of carbon dioxide, COji mode Vj is twofold degenerated (Vja.Vjb)...

Figure 13. Infrared active vibration-rotation fundamental bands of carbon dioxide (a) antisymmetric stretching mode (V3) for which the selection rule is Avj = 1 and Ad = 1 ( ) bending mode (v,) for which the selection rules is Av2 = 1 and AJ — 0, 1.

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