Relative Rate Of Diffusion

An example of this is the commercial process for preparing puru-xylene, the precursor to terephthalic acid, which is polymerised to give polyjethy-lene terephthalate) (PET). In this case, the mixture of xylenes obtained from crude oil is reacted in a zeolite (known as HZSM5). The relative rates of diffusion in and out of the pores are sufficiently different (by a factor of about ten thousand) to allow the extremely efficient and selective conversion of all the isomers to the desired paia isomer, which is the narrowest and can thus move through the structure most rapidly (Figure 4.3). 

Heterogeneous catalysts can thus have a major influence on selectivity. Changing the catalyst can change the relative influence on the primary and by product reactions. This might result directly from the reaction mechanisms at the active sites or the relative rates of diffusion in the support material or a combination of both. 

The relative rates of diffusion of Cl Disperse Orange 3 on nylon, acetate and polyester indicated in Table 3.14 are reasonably consistent with those measured independently in the early days of polyester dyeing [113], as shown in Table 3.15. These figures, for three disperse... 

The crystals form very slowly, as diffusion brings the reagents into contact. When a sufficient crop has been secured, carefully remove the paraffin, siphon off the solution as well as possible, and lift out the small beakers with their contents. Collect the crystals and dry them on paper. The place where they will form will depend on the relative rates of diffusion of the two ions concerned in the precipitation. 

PRANDTL NUMBER. A dimensionless number equal to the ratio of llie kinematic viscosity to the tlienuoiiielric conductivity (or thermal diffusivity), For gases, it is rather under one and is nearly independent of pressure and temperature, but for liquids the variation is rapid, Its significance is as a measure of the relative rates of diffusion of momentum and heat m a flow and it is important m the study of compressible flow and heat convection. See also Heat Transfer. 

Assume that you have a sample of hydrogen gas containing H2, HD, and D2 that you want to separate into pure components (H = JH and D = 2H). What are the relative rates of diffusion of the three molecules according to Graham s law ... 

PROBLEM 9.20 Which gas in each of the following pairs diffuses more rapidly, and what are the relative rates of diffusion ... 

A less widely used approach (8,9) has been to expose a surface of pesticide to an air flow under conditions of a rapid rate of air change such that the concentration of the pesticide in the air surrounding the stagnant boundary layer is far below saturation. Under these conditions the relative rates of diffusion of two pesticides will be inversely related to the square root of their respective molecular weights (Graham s law of Diffusion) and directly related to their saturated vapour concentrations in the boundary layer. 

Uranium isotopes have been separated by taking advantage of the different rates of diffusion of the two isotopic forms of UF6. One form contains uranium of atomic mass 238 and the other of atomic mass 235. What are the relative rates of diffusion of these two molecules if Graham s law applies ... 

The relative rates of diffusion and polymer relaxation can conveniently be examined using the diffusion Deborah number (9) defined as ... 

Qfis may ask the reason for the functional form of Eq. (6-4). Physical reasoning, based on the experience gained with the analyses of Chap. 5, would certainly indicate a dependence of the heat-transfer process on the flow field, and hence on the Reynolds number. The relative rates of diffusion of heat and momentum are related by the Prandtl number, so that the Prandtl nunfber is expected to be a significant parameter in the final solution. We can be rather confident of the dependence of the heat transfer on the Reynolds and Prandtl numbers. But the question arises as to the correct functional form of the relation i.e., would one necessarily expect a product of two exponential functions of the Reynolds and Prandtl numbers The answer is that one might expect this functional form since it appears in the flat-plate analytical solutions of Chap. 5, as well as the Reynolds analogy for turbulent flow. In addition, this type of functional relation is convenient to use in correlating experimental data, as described below. 

The deposition on about 1 mm porous Si02 granules via urea hydrolysis has been studied for Mn(2+l As expected, the rate determining step is the urea hydrolysis step itself. In these conditions, the metal profile over the granules is determined by the relative rates of diffusion of hydrolysed Mn species in the pores and of reaction of these species with the Si02 surface. This is relatively well described with the Thiele concept, as is evident from Fig. 9.15. The rate of the surface reaction is lower for Rh(3+) and Ni(2+) than for Mn(2+), which should lead... 

As stated above, shape selectivity due to molecular sieving depends on the relative rates of diffusion and reaction, hence on the respective sizes and shapes of molecules and pores and on the characteristics of active sites (e.g. concentration, nature and strength of acid sites). Obviously the diffusion rate, hence the selectivity depend also on the length of the diffusion path (i.e., on the size of the zeolite crystallites). The selectivity of a zeolite catalyst can be optimized by an adequate... 

Contrary to molecular sieving, spatioselectivity does not depend on the relative rates of diffusion and reaction, hence both can be easily distinguished changing the crystallite size has no effect on spatioselectivity whereas it increases selectivity by molecular sieving. However, the two types of selectivity may act simultaneously as was shown by Song et al. (42) for naphthalene isopropylation over H-mordenite. 

Depending on the relative rates of diffusion of these species, the reaction can take place at either the AO/AB2O4 or the B2O3/AB2O4 interface. When diffusion is slower than the rate of reaction, the thickness of the product layer follows a parabolic growth law like that observed in Figure 5.20 for NLA1204. 

Depending on the relative rates of diffusion and reaction, the following diffusion-reaction regimes occur ... 

Graham s Law states that under equal conditions of temperature and pressure, gases diffuse at a rate that is inversely proportional to the square roots of their molecular masses. If your teacher asks you which of a group of gases will diffuse most quickly under equal conditions, the answer will be the least massive gas. If the question involves the relative rate of diffusion, you would solve the problem as shown in the comparison just presented. Let s try a typical example. 

Calculate the relative rate of diffusion of propane (C3H8) molecules to methane (CH4) molecules. 

Calculate the relative rate of diffusion for argon and neon gas under identical conditions of temperature and pressure. 

Use To form a protecting layer of the tiny spheres over liquid surfaces, such as oils in big tanks, to reduce evaporation to separate helium from natural gas because of the wide difference in relative rates of diffusion through the spheres as an extender in plastics to achieve low density. 

The relative rates of diffusion and reaction are important in the regulation of biochemical pathways. Transcription factors are proteins that bind to specialized regions of DNA and thereby facilitate transcription by RNA polymerase. The binding of one class of transcription factors, the basic leucine zipper (bZIP) proteins, is illustrated in Figure 4.30. The bZIP factors have a C-term-inal leucine zipper domain, a basic region that binds to DNA, and a domain that is important for transcriptional regulation. The bZIP factors must dimerize for transcriptional activity and, therefore, it is usually assumed that dimerization occurs before DNA binding (dimer pathway). A recent study shows... 

Bulk diffusion into adhesive Joints has been studied considerably [9], however little work has focused on diffusion at adhesive interfaces, largely because of the limitations of experimental techniques. Mass uptake experiments are a convenient method to study fluid absorption in adhesives. This method has been used to study interfacial diffusion by comparing the relative rates of diffusion from non-bonded or free-standing films with diffusion into the actual adhesive joint [10,11]. A disadvantage of mass uptake experiments is that the method does not provide any direct evidence of the concentration of fluid at the interface. 

To determine whether the mechanism can underlie the propagation of the two types of wave, it is useful to consider the model based on CICR, governed by eqns (9.1), and to incorporate the diffusion of intracellular Ca into these equations. In view of the data obtained on the relative rate of diffusion of Ca and IP3 within the cytosol (Allbritton et al, 1992), it will be necessary to incorporate the diffusion of IP3 as well. It is reasonable, however, to consider the effect of cytosoUc diffusion as being predominant in a model based on CICR. When assuming that the Ca -sensitive Ca pool is homogeneously distributed within the cell, in the case of two-dimensional diffusion, eqns (9.1) become ... 

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