Molecular diffusion rate

External diffusion of reactants. This step depends on the fluid dynamic characteristics of the system. Reactants must first diffuse from the bulk gaseous phase to the outer surface of the carrier through a stagnant thin film of gas. Molecular diffusion rates in the bulk have the activation energy E1 = 2 to 4 kcal/mol and they vary with Tm. 

If there is no mass transfer resistance within the catalyst particle, then Ef is unity. However, it will then decrease from unity with increasing mass transfer resistance within the particles. The degree of decrease in f is correlated with a dimensionless parameter known as the Thiele modulus [2], which involves the relative magnitudes ofthe reaction rate and the molecular diffusion rate within catalyst particles. The Thiele moduli for several reaction mechanisms and shapes of catalyst particles have been derived theoretically. 

In reality, of course, mixing cannot be perfectly instantaneous. In practice, CSTR reactors are designed to create high-intensity turbulence that enhances mixing. Also very low-pressure systems can often be considered as stirred reactors. At low pressure (e.g., below 1 Torr), the molecular-diffusion rate is very high owing to long mean-free paths. 

Steady-state modeling calculations were performed to examine how congener-specific properties (such as sediment-water partition coefficients, Henry s law constants, and molecular diffusion rates) affect the transport and fate of PCBs. A basic description of the model, along with modeling results, is presented here to further explain the importance of physiochemical weathering processes in controlling the fate and distribution of PCB congeners in Twelve Mile Creek and the upper portion of Lake Hartwell. 

Another way of evaluating enzymatic activity is by comparing k2 values. This first-order rate constant reflects the capacity of the enzyme-substrate complex ES to form the product P. Confusingly, k2 is also known as the catalytic constant and is sometimes written as kcal. It is in fact the equivalent of the enzyme s TOF, since it defines the number of catalytic cycles the enzyme can undergo in one time unit. The k2 (or kcat) value is obtained from the initial reaction rate, and thus pertains to the rate at high substrate concentrations. Some enzymes are so fast and so selective that their k2/Km ratio approaches molecular diffusion rates (108—109 m s-1). This means that every substrate/enzyme collision is fruitful, and the reaction rate is limited only by how fast the substrate molecules diffuse to the enzyme. Such enzymes are called kinetically perfect enzymes [26],... 

Some enzymes are so fast and so selective that their k2/Km ratio approaches the molecular diffusion rates (108-109m s-1). Such enzymes are called kinetically perfect [21]. With these enzymes, the reaction rate is diffusion controlled, and every collision is an effective one. However, since the active site is very small compared to the entire enzyme, there must be some extra forces which draw the substrate to the active sites (otherwise, there would be many fruitless collisions). The work of these forces was dubbed by William Jencks in 1975 as the Circe effect [22], after the mythological sorceress of the island of Aeaea, who lured Odysseus men to a feast and then turned them into pigs [23,24]. 

As a matter of interest, we might calculate the molecular diffusion rate of water vapor from Eq. (11-35), taking z, as the 5-ft dimension above the standard pan. Since... 

Unless the pressure is so low that the molecular mean free path (Appendix E) is comparable to the dimensions of the chamber enclosing the gas, the rates of the first and last steps, 1 and 5, are governed by molecular diffusion rates (or by rates of mass transfer through a boundary layer, if the gas is in motion). Although these macroscopic transfer processes, which lie within the realm of fluid mechanics (Appendixes C-E), often are the ratedetermining steps [62] (see also Chapter 12), we shall assume here that they are so fast that they can be neglected. 

The acdvitities of silica-supported phosphonium are support pore size dependent with ca. 100 A typically giving the most active catalysts. This is very similar to more simple physisorbed silica-based supported reagents and seems to support the view that for liquid-phase reactions catalysed by porous solids, a reasonably large pore is required to give a good molecular diffusion rate. 

Walton M (1960) Molecular diffusion rates in supercritical water vapor estimated from viscosity data. Am JSci 258 385-401... 

Although it has been stated as a rule by Ruzicka and Hansen that dispersion diminishes with a decrease in Aow-rate in a narrow tube [1,6], this statement holds true only at extremely low flow-rates where molecular diffusion rates approach the rate of convection cieated by the flow. Karlberg and Pacey have shown experimentally that with a fixed manifold, the flow-rate have very little influence on the dispersion within a broad range of flow-rates (1.6-4.0 ml min ), used most frequently in FIA [2]. 

The most straightforward cause of shape selectivity is the discrimination between molecules on the basis of their diffusion rates through the channels or cage windows. Microporous solids act as true molecular sieves, because the well-defined pores are able to select molecules on the basis of differences in dimensions of 0.1 A or less. Examples of strong molecular sieving effects include the selection of normal alkanes over branched ones by small-pore solids and the selection of para-substituted over ortho- and meta-substituted aromatics over medium-pore zeolites. This type of selectivity according to molecular diffusion rate may act on both reactant and product molecules. The much faster dehydration of n-butanol compared to isobutanol over Ca-A demonstrated by Frilette and Weisz is the classic example of reactant diffusion... 

Concentration of gaseous species near atmosphere-water boundary is governed by molecular diffusion rate. Time to reach steady state concentration of gaseous species is expressed as (Table 6.6)... 

Hi) Use of pulse field gradients to measure molecular diffusion rates, particle and pore size distribution, and homogeneity of mixing (at low fields 1-10 MHz mainly for QC) and (iv) Peak ratio in low-field solution-state NMR spectra. 

In atmospheric distillations, the gas film many times offers a resistance to mass transfer similar to that of the liquid film. The vapor density is low, providing a high molecular diffusion rate in that phase. The diffusion coefficient in the vapor phase at atmospheric pressure may be several orders of magnitude times that in the liquid phase. However, the liquid-phase resistance becomes increasingly important as the liquid viscosity increases, which reduces the diffusion rate in that phase. Also, there is a tendency for the liquid-film resistance to increase as the liquid molecular weight increases. 

When the adhering materials are partially or fully miscible with one another, there will be formed between them an interphase consisting of interdiffiised molecules from each material. The thickness of this interlayer depends on the thermodynamic compatibility of the materials as well as molecular diffusion rates. Molecular interdiffusion is quite different from mechanical interlocking. The former involves interpenetration at the molecular level, whereas in the latter case, the bulk adhesive flows into and... 

The assumed thickness of the actively mixed upper layer of sediment was an important difference between agency (30 cm) and PRP (10 cm) models (Redder et al., 2005). Sediment porewater diffusion at rates exceeding molecular diffusion rates was also extended to 30 cm in the agency model, and limited to the top 10 cm in the PRP model. The model developed by the PRPs also included contaminant exchange between the water column and the top layer of porewater to help account for water-column PCBs under low-flow conditions, a process that was not included in the agency model (LimnoTech, 2002c). 

Evaporation-limiting molecular diffusion rates will be determined in a complex manner by the double diffusion of each molecular species within the regions of the surface sub-layer. 

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