Gases kinetic diameter

Harpoon reactions of alkaline metal atoms with halogen molecules in the gas phase seem to be the first instance of the observation of chemical electron transfer reactions at distances somewhat exceeding gas-kinetic diameters. Actually, as far back as 1932, Polanyi, while studying diffusion flames found for these reactions cross-sections of nR2, somewhat exceeding the gas-kinetic cross-sections [69]. Subsequently, more precise measurements which were carried out in the 1950s and 1960s with the help of the molecular beam method, confirmed the validity of this conclusion [70],... 

Figure 2.37 Permeability coefficients as a function of the gas kinetic diameter in micro-porous silica hollow fine fibers [58]. Reprinted from J. Membr. Sci. 75, A.B. Shelekhin, A.G. Dixon and Y.H. Ma, Adsorption, Permeation, and Diffusion of Gases in Microporous Membranes, 233, Copyright 1992, with permission from Elsevier...

From these relations it can be seen that for an opaque gas inlet system the parameters which define the beam depend on the gas kinetic diameter a (for this quantity see equ. (10.94)). Therefore, as was said above, the properties of a certain gas inlet system determined for one kind of gas cannot be transferred to a different gas without great caution. 

The existence of a surface relief poses, naturally, the problem of the geometrical relations between the localization region and the adspecies size. The latter may be somewhat arbitrarily selected in the range between a gas-kinetic diameter and a first incomplete electronic shell, the bond lengths of the surface molecule in some cases differing from those in the gaseous phase. One uses, as a unit of measure, a lattice site area ([Pg.355]

With R > 3.5 A (gas-kinetic diameter of the Hg atom) we obtain 0.86 V for the dissociation energy if the repulsive forces have a sudden effect. 

The values of n and k for the gas pairs comprising O2, N2, He, H2, CO2, and CH4 are listed in Table 2. The kinetic diameters determined by a least-squares fit of the data yielded the values noted in Table 3, which are compared with the zeolite-determined gas kinetic diameters (Breck data ), the Lennard-Jones diameters, and the Dal-Cin diameters determined from upper bound data. The values of the kinetic diameter from the noted least-squares fit should be the most realistic values for gas diffusion behavior in polymers. 

The more permeable component is called the. st ga.s, so it is the one enriched in the permeate stream. Permeability through polymers is the product of solubihty and diffusivity. The diffusivity of a gas in a membrane is inversely proportional to its kinetic diameter, a value determined from zeolite cage exclusion data (see Table 22-23 after Breck, Zeolite Molecular Sieves, Wiley, NY, 1974, p. 636). 

Advanced Materials Experimental membranes have shown remarkable separations between gas pairs such as O2/N2 whose kinetic diameters (see Table 20-26) are quite close. Most prominent is the carbon molecular sieve membrane, which operates by ultramicro-porous molecular sieving. Preparation of large-scale permeators based on ultramicroporous membranes has proven to be a major challenge. 

The acidic and adsorptive properties of the samples in gas phase were evaluated in a microcalorimeter of Tian-Calvet type (C80, Setaram) linked to a volumetric line. For the estimation of the acidic properties, NH3 (pKa = 9.24, proton affinity in gas phase = 857.7 kJ.mol-1, kinetic diameter = 0.375 nm) and pyridine (pKa = 5.19, proton affinity in gas phase = 922.2 kJ.mol-1, kinetic diameter = 0.533 nm) were chosen as basic probe molecules. Different VOC s such as propionaldehyde, 2-butanone and acetonitrile were used in gas phase in order to check the adsorption capacities of the samples. 

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). 

Gas molecule Kinetic diameter (A) Lennard-Jones diameter (A)... 

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. 

In order to achieve high selectivities with thermostable zeolite-based membranes, zeolites can be choosen with pore apertures matching the kinetic diameters of the molecules to be separated. Moreover, the hydrophobicity of all-silica zeolites provides continuous separation, independently of traces of water in the gas streams applied. In the total spectrum of tectosilica(te)s there is only one all-silica 8-ring system Deca-dodecasil 3R (DD3R) but several all-silica 6-ring systems Table 6). 

In another study by Nishiyama et al. [53], the Vapour-phase Transport method was applied on alumina supports. No permeation of 1,3,5-triisopropylbenzene (kinetic diameter 0.85 nm) could be observed through the 10 pm thick membrane. Mordenite has parallel channels with an elliptical pore dimension of 0.65 x 0.7 nm. Pervaporation of benzene-p-xylene (molar ratio 0.86) at 22°C resulted in a separation factor of 164 (total flux 1.19 10" mol.m s ). The theoretical value based on the gas-liquid equilibrium amounts to 11.3. Apparently, the mordenite-based membrane shows high selectivity for aromatic hydrocarbons. 

In general, when carrying out a new separation, the kinetic diameter and the heat of adsorption of the gases, which compose the mixture, are the main variables used to select the most adequate zeolite. MFI, FAU, LTA, SOD, ANA, DDR, MOR, BEA, CHA, FER, KFI are zeolite structures widely used as membranes for different separations. In gas separation, MFI zeolite membranes (silicalite-1, ZSM-5, and with Al, Fe, B, and Ge isomorphously substituted into their stmctures) are the most commonly used membranes because their pores (-0.55 nm diameter) are in the size range of many industrial mixtures furthermore, their synthetic chemistry is well established in the literature. 

Distinctions in properties of ultrasiles modified from a gas phase and from a solution can be seen on the base of absorption results of hydrocarbons with the normal and branched chains, i.e. having a various kinetic diameter. 

Specific surface areas and pore size distributions of mesoporous materials are best probed by nitrogen/argon adsorption and capillary condensation which will be outlined in detail below. It should be emphasized that the concept of specific surface area is not applicable when the size of the sorbed molecules approaches the diameter of the pore. Thus, for microporous substances values for specific surface areas have no physical meaning, but are rather characteristic of the volume of gas adsorbed. Nevertheless, these values are frequently used as practical numbers to compare the quality and porosity of microporous materials. The average pore size of microporous materials has to be probed by size exclusion measurements. For this purpose the uptake of a series of sorbates with increasing minimal kinetic diameter on a solid are explored. The drop in the adsorbed amount with increasing size of the sorbate defines the minimum pore diameter of the tested solid. The method will be described in detail below. 

Fig. 7.—Gas-kinetic effective cross-section in a collision the centres of mass of the two equal molecules cannot come nearer than the distance G (G = diameter of a molecule).

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