Gases collision diameter

Gas Collision Diameter o(m) Mean Free Path k(m) Collision Frequency Z3 (s-i) Collision Frequency Zn (ari s-i)... 

An excellent review of the various theoretical expressions of this physical fact has been offered by Kumins and Kwei At a fixed temperature, many investigators have found that gas diffusion coefficients in rubbers can be correlated with the Lennard-Jones gas collision diameter. Michaels and Bixler have shown, however, that even in the rubbery state, some orientation of anisotropic molecules such as CO2 may occur during a diffusion step. 

Fig. 5-6 Diffusivity divided by the square of gas collision diameter versus gas collision diameter for polyethylene (8, 9).

The diffusivity values can be obtained from Figs. S-6-5-9. In order to determine these values, gas collision diameters (see Table 5-4) are needed. These are ... 

Using gas kinetic molecular theory, show that under typical atmospheric conditions of pressure and temperature corresponding to an altitude of 5 km (see Appendix V) collisional deactivation of a C02 molecule will be much faster than reemission of the absorbed radiation. Take the collision diameter to be 0.456 nm and the radiative lifetime of the 15-/rm band of C02 to be 0.74 s (Goody and Yung, 1989). 

In liquids the interactions between neighboring molecules are considerably more complicated than in gases. The resultant broadening obliterates the fine line structure seen in gas spectra, leaving only broad band profiles. There are many possible contributors to this broadening. In some cases, adequate approximation is obtained by assuming that the band contour is established by collisions. Ramsay (1952) has noted that substitution of appropriate molecular density and collision diameter numbers in the collision broadening formula results in realistic band widths for certain liquid-phase systems. In such systems, the bands typically show an approximately Lorentzian profile. Approximate deconvolution of inherently broadened liquid-phase spectra may therefore be obtained on the basis of the assumption of Lorentzian shape (Kauppinen et al., 1981). 

In SI units, T>jk is measured in m2/s. Consistent units in the first expression are ks = 1.38066 x 10-23 J/K is the Boltzmann constant, mjk is the reduced molecular mass (kg), p is the pressure (N/m2), T is temperature (K), and ajk is a reduced collision diameter (m). The second expression in Eq. 3.95 replaces the Boltzmann constant and the molecular mass with the gas constant R = 8.31451 J/g-mol K and the reduced molecular weight Wjk (g/mol), which requires Avogadro s number A. Assuming that Wjk is given in g/mol, the divide by 1000 is required to maintain SI units. The reduced mass and collision diameter are given as... 

The available data show a somewhat scattered correlation between the energy of activation and the diameter of the gas molecule, varying between the first and the second power of the molecular diameter of the penetrant molecule. In our experience the best correlation is obtained if En is assumed to be proportional to second power of the collision diameter (see Fig. 18.2, where the data of Table 18.3 for the collision diameters are used). If nitrogen is taken as the standard gas for comparison, we can use the product... 

Our final conclusion is, that the three determining parameters of the diffusion process of simple gases can be estimated from three hall-marks of the polymer-gas combination the (collision) diameter of the gas (glass transition temperature (Tg) and the degree of crystallinity (xc) of the polymer. 

As a standard gas nitrogen is used by preference, but in principle any other simple gas may be used, since the permeabilities of the different gases have a constant ratio determined by the collision diameter of the gas molecules (Table 18.3). 

For many energy transfer processes, the interaction takes place when the partners are separated by more than the sum of the gas-kinetic collision radii. For example, energy transfer between excited singlet states of hydrocarbons occurs as fast as spontaneous decay at concentrations in benzene corresponding to a distance, r, between exchanging molecules of about 5 nm, or about 10 times the collision diameter. The measured rate constants for transfer of excitation in the hydrocarbons also seem greatly to exceed the diffusion-limited rate, and do not depend on solvent viscosity. 

Thus, knowing the viscosity of a gas, the collision diameter a can be easily calculated. 

Example. At 27 C and 1 atm pressure, the coefficient of viscosity of nitrogen gas is 178 pP (i.e., micropoise). Calculate, (a) the mean free path X, and (b) the collision diameter o of nitrogen molecule using the Chapman equation. 

The diffusion constant is predicted by Eqs. (32) to (35) to be inversely proportional to the total pressure. Experimentally, this is the case to roughly the degree to which the perfect-gas law applies. The equations appear to predict that the diffusion constant will be proportional to the three-halves power of the temperature however, as in the case of viscosity, significant deviations from this behavior occur, as actual molecules are not truly hard spheres and have collision diameters that depend on the relative speeds with which molecules collide with one another. 

Reliable data on gas-phase bimolecular exchange reactions between molecules are rather rare. Most of these data are presented in Table XII.4, where k is given in terms of the simple collision equation, log k = —E/2,SRT + 0.6 log T + A. The temperature-independent term A, which is equal to the preexponential factor divided by is shown in column 3, and a collisional steric factor P is calculated in the last column on the arbitrary basis of a uniform collision diameter for all reactions of 3.5 A. ... 

At 0°C the coefficient of viscosity of N2 = 1.66 X 10 poise. From this compute the collision diameter of N2 and compare it with the diameter of N2 computed from (a) the volume of solid N2 assuming hexagonal close packing (i.e., 12 nearest neighbors), (h) Van der Waals constant b, computed from the critical volume of N2 gas. (c) Compute the coefficient of self-diffusion of N2 gas at STP. 

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