Kinetic molecular diameter

Fig. 8. Variation of activation energy with kinetic molecular diameter for diffusion in 4A 2eohte (A), 5A 2eohte (0)> carbon molecular sieve (MSC-5A) (A). Kinetic diameters are estimated from the van der Waals co-volumes. From ref. 7. To convert kj to kcal divide by 4.184.

Typical values of b and D for a range of membranes are given in Table 9.10 together with some other parameter values. The range in D values reflects differences in membrane quality, the smallest D values being formed in high quality membranes. The diffusion coefficients become smaller in the same order as the kinetic molecular diameter (see Table 9.6) increase. The large differences in the D values indicate that the pore diameter is of the order of the molecular diameters (0.4-0.5 nm). 

Table 7-2 compares the pore apertures of some zeolites with the kinetic molecular diameters of some starting materials. On the basis of these data, a preliminary choice of a suitable zeolite for a particular starting material can be made. However, it should not be forgotten that molecules are not rigid objects and that the kinetic diameter gives only a rough estimate of the molecular size. 

Kinetic molecular diameter This estimates the maximum diameter if the molecule were a spherical. 

Figure 2. Variation of permeance with kinetic molecular diameter for light gases in DDR type zeolites at 301 K (o) and 373K ( ). From Tomita et al. [8]...

The chance of a collision will obviously depend upon the number of gas molecules per unit volume or, alternatively, upon the pressure. The chance of a collision will also depend upon the size of the gas molecules. For example, the chance of two basketballs thrown toward one another undergoing a collision is much greater than the chance of having a similar collision between two golf balls. An expression for the mean free path in terms of pressure and molecular diameter may be derived from kinetic theory. We give only the result, which may be expressed as... 

One of the most signiflcant variables affecting zeolite adsorption properties is the framework structure. Each framework type (e.g., FAU, LTA, MOR) has its own unique topology, cage type (alpha, beta), channel system (one-, two-, three-dimensional), free apertures, preferred cation locations, preferred water adsorption sites and kinetic pore diameter. Some zeolite characteristics are shown in Table 6.4. More detailed information on zeolite framework structures can be found in Breck s book entitled Zeolite Molecular Sieves [21] and in Chapter 2. 

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). 

It has also been suggested that the molecular diameter of nitrogen pentoxide is effectively much greater for activating collisions, as well as for deactivating collisions, than that calculated in the ordinary way from the kinetic theory. The difficulty about this suggestion is that the... 

Observations on the dimensions of the constituent molecules were made by A. 0. Rankine,8 E. Dorn, W. Sutherland, W. Altberg, C. Ramsauer, and P. Lenard. The mean velocity of the molecules, at 0° and 760 mm. press., is given as 44,690 cm. per second the mean free path, 0-05608 cm. and the molecular diameter, 0-0731 cm. K. S. van Dyke, and E. Blankenstein discussed the coeff. of slip, and of momentum transfer in air and D. Brunt, the kinetic energy of the atmosphere. 

Thus the only way to make a complex is to transfer some of the internal energy to another system. In practice, this means three or more molecules have to all be close enough to interact at the same time. The mean distance between molecules is approximately (V/N)1 /3 (the quantity V/N is the amount of space available for each molecule, and the cube root gives us an average dimension of this space). At STP 6.02 x 1023 gas molecules occupy 22.4 L (.0224 m3) so (V/N)1/3 is 3.7 nm—on the order of 10 molecular diameters. This is expected because the density of a gas at STP is typically a factor of 103 less than the density of a liquid or solid. So three-body collisions are rare. In addition, if the well depth V (rmin) is not much greater than the average kinetic en-... 

We can use Eq. (4.23) to calculate the magnitude of the pre-exponential factor and compare it to experimental data. Molecular diameters d (or dB) may, e.g., be estimated from gas viscosity data based on the standard model of the kinetic theory of gases, or from an analysis of the elastic scattering of molecules (see Section 4.1.3). Some values are given in Table 4.1 and are typically around 2-3 A. Table... 

The primary requirement for an economic adsorption separation process is an adsorbent with sufficient selectivity, capacity, and life. Adsorption selectivity may depend either on a difference in adsorption equilibrium or, less commonly, on a difference in kinetics. Kinetic selectivity is generally possible only with microporous adsorbents such as zeolites or carbon molecular sieves. One can consider processes such as the separation of linear from branched hydrocarbons on a 5A zeolite sieve to be an extreme example of a kinetic separation. The critical molecular diameter of a branched or cyclic hydrocarbon is too large to allow penetration of the 5A zeolite crystal, whereas the linear species are just small enough to enter. The ratio of intracrystalline diffusivities is therefore effectively infinite, and a very clean separation is possible. 

An attempt to calculate the viscosity of a liquid on the basis of the classical kinetic theory led to the formula rj=Pal2c, where P=internal pressure, or=molecular diameter, and c=molecular velocity, and this was confirmed for liquid hydrogen (when molecular rotation is included), P being taken as afrom the van der Waals equation. 

Molecule Molecular weight Mean free path (nm) Kinetic sieving diameter (nm)... 

Numerical evaluation of the Kassel integral permitted a comparison between theoretical and experimental fall-off behaviour . With an average molecular diameter of 5.5 A the calculated rate coefficient-azoethane pressure curve showed the best agreement with experiment at an effective number of oscillators of 18, somewhat less than half of the maximum 2N— 6. Because of the complexity of the reaction the experimental curve is probably in error, rendering comparison unreliable. Similar calculations for azomethane using the earlier uninhibited kinetic data showed best agreement with experiments at a molecular diameter of 4.7 A and an effective number of oscillators of 12, one half of the total normal modes of vibrations. 

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