Diatomic molecules, characteristic temperatures

If we sum the three contributions to calculate the value for the heat capacity at constant volume, as the characteristic temperatures of rotation are often lower than the Einstein temperature (see Table 7.3), the variation in the heat capacity, for example of a diatomic molecule, with temperature takes the form of the curve in Figure 7.12(c). At low temperatures, the only contribution is that of translation, given by 3R/2. Then if the temperature increases, the contribution of rotation, is added according to the curve in Figure 7.12(a) until the limiting value of this contribution is reached, then the vibrational contribution is involved until the molecule dissociates which makes the heat capacity become double that of the translational contribution of monoatomic molecules. The limiting value of the vibrational contribution is sometimes never reached. This explains why the values calculated in Table 7.2 are too low if we do not take into account the vibration and too high in the opposite case. 

Table IX-2.—Characteristic Temperature for Rotation, Diatomic Molecules...

Figure 15 shows the CI2 bond distance for two different trajectories for which the initial conditions of the Ari25Cl2 cluster are the same, i.e. the configuration and the center of mass velocity of the clusters at the beginning of each trajectory (before the collision with the surface) are identical. The only differences between the two trajectories are the velocities (randomly chosen from a one-dimensional thermal distribution at 30 K) of the hard cubes that mimic the surface. Despite the rather low temperature of the surface, one of the trajectories results in the dissociation of the diatomic molecule while the other one ends with a vibrationally excited reactant molecule. The effect of the hard cube velocity on the energy of the atom scattering from the surface is negligible but the history of a single trajectory is extremely sensitive to the details of the collisions with the surface, as shown in Fig. 15. This is a characteristic of so called chaotic systems. In...

Qualitatively sketch the heat capacity of an ideal gas of diatomic molecules as a function of temperature. Indicate the characteristic temperatures (in terms of vibrational frequency, moment of inertia, and so on) where various degrees of freedom begin to contribute. 

The molar mass M. of nitrogen is 28.02 gmole-i. The rotational characteristic temperature 0, is 2.87 deg and the vibrational characteristic temperature 0 is 3.35 x 10 deg (calculated from data in Herzberg, Molecular spectra of diatomic molecules , Prentice-Hall, 1939). 

Equation (28-71) indicates that the rotational motion of diatomic molecules yields rotation,classical = T/B, where B is a characteristic rotational temperature that is, at most, a few tens of Kelvin (see Table 28-2). The rotational contribution to the internal energy is... 

TABLE 28-2 Molecular Parameters and Characteristic Temperatures for Rotation and Vibration of Several Diatomic Molecules... 

In its most stable form, elemental oxygen exists as diatomic molecules (O2). Ozone is another form of oxygen that contains three oxygen atoms (O3) and is less stable than O2 (see Retouches section 10.R.1). At room temperature, ozone is a pale blue gas with a sharp odor, characteristic of the air after a thunderstorm or near an old Xerox machine (copying machine). Ozone is a very reactive gas, and, even at low concentrations, it is irritating and toxic. 

The characteristic rotational temperature, the rotational quantum Trot = h STt kl (1 is the moment of inertia) of some diatomic molecules [55] is, H2 85 K, O2 2.1 K, NO 2.4 K, CI2 0.4 K. As a consequence, the rotation of the diatomic molecules is classical at ambient conditions and each rotational degree of freedom has the energy 1/2 kT at equilibrium. That immediately yields an estimate of the rotational correlation time t,o, in the absence of an external field [58] ... 

TABLE 4.2. Typical Values of the Rotational and Vibrational Partition Functions of Diatomic Molecules at 500 K, along with Values of the Characteristic Temperatures of Rotation and Vibration, 0roi and 0vib ... 

Think About It (a) Iodine, like the other halogens, exists as diatomic molecules at room temperature. It makes sense, therefore, that atomic iodine would react quickly, and essentially completely, to form I2 at room temperature. The very low remaining concentration of I after 2.0 min makes sense, (b) As expected, the half-life of this second-order reaction is not constant. (A constant half-hfe is a characteristic of first-order reactions.)... 

For polyatomic molecules, there are several normal modes of vibration that must be considered, as well as the bond angle that determines whether triatomics are linear or bent. The information in Table 28-3 for seven triatomics and one polyatomic was obtained from the same sources as Table 28-2 for diatomics, as well as Reed and Gubbins (1973, p. 74). Degenerate vibrational energy levels are indicated in parentheses and, in some cases, the characteristic rotational temperature is included under the molecular formula. 

Mid-IR spectroscopy (400 000 cm ) has been shown by the group of Zecchina to be very informative when studying adsorption at different adsorption sites in zeolites.The spectroscopy is performed at low temperatures using small diatomics such as CO, N2 and H2 as probe molecules that have suitable IR characteristics and that can gain access to the entire pore space. As well as being unreactive, these probe molecules have IR characteristics that... 

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