Rate diffusion function

In order to determine wether the speed of reaction is limited by the diffusion of the condensate, the following rate diffusion function for sperical particles (6 14) was applied on the reaction data for several partical sizes... 

In figure 4 can be seen that none of the particle size ranges follow this diffusion function. The rates of reaction in the 3.3[Pg.144]

Diffusion. Often, the most important mode of mass transport is diffusion. The rate of diffusion can be defined in terms of Pick s laws. These two laws are framed in terms of flux, that is, the amount of material impinging on the electrode s surface per unit time. Pick s first law states that the flux of electroactive material is in direct proportion to the change in concentration c of species i as a function of the distance x away from the electrode surface. Pick s first law therefore equates the flux of electroanalyte with the steepness of the concentration gradient of electroanalyte around the electrode. Such a concentration gradient will always form in any electrochemical process having a non-zero current it forms because some of the electroactive species is consumed and product is formed at the same time as current flow. 

Contaminant volatilization from subsurface solid and aqueous phases may lead, on the one hand, to pollution of the atmosphere and, on the other hand, to contamination (by vapor transport) of the vadose zone and groundwater. Potential volatihty of a contaminant is related to its inherent vapor pressure, but actual vaporization rates depend on the environmental conditions and other factors that control behavior of chemicals at the solid-gas-water interface. For surface deposits, the actual rate of loss, or the pro-portionahty constant relating vapor pressure to volatilization rates, depends on external conditions (such as turbulence, surface roughness, and wind speed) that affect movement away from the evaporating surface. Close to the evaporating surface, there is relatively little movement of air and the vaporized substance is transported from the surface through the stagnant air layer only by molecular diffusion. The rate of contaminant volatilization from the subsurface is a function of the equilibrium distribution between the gas, water, and solid phases, as related to vapor pressure solubility and adsorption, as well as of the rate of contaminant movement to the soil surface. 

The functional dependence of other parameters on the reaction rate also becomes modified when diffusion controls the overall rate. Writing the reaction rate for an nth-order reaction in a porous pellet in which diffusion is rate determining (i = [Pg.159]

The activity of polymer-supported crown ethers is a function of % RS as shown in Fig. 11 149). Rates for Br-I exchange reactions with catalysts 34, 35, and 41 decreased as % RS increased from 14-17% to 26-34%. Increased % RS increases the hydro-philitity of the catalysts, and the more hydrated active sites are less reactive. Less contribution of intraparticle diffusion to rate limitation was indicated by less particle size dependence of kohMi with the higher % RS catalysts149). 

The electrostatic interaction between the charge clouds will be large only when there is a spatial overlap of the donor and the acceptor wave functions, i.e. when the two actually collide n kinetic sense. Therefore, it can only be a short range phenomenon. No transfer outside the boundaries of the molecule is expected by this mechanism. The transfer occurs at diffusion-controlled rate. 

A further important result which arises because of the functional form of is that the apparent order of reaction in the diffusion controlled region differs from that which is observed when chemical reaction is rate determining. Recalling that the reaction order is defined as the exponent n to which the concentration CAm is raised in the equation for the chemical reaction rate, we replace f(CA) in equation 3.8 by CJ . Hence the overall reaction rate per unit volume is (1 - e)rjkCA. When diffusion is rate determining, tj is (as already mentioned) equal to f1 from equation... 

Spry and Sawyer (1975) developed a model using the principles of configurational diffusion to describe the rates of demetallation of a Venezuelan heavy crude for a variety of CoMo/A1203 catalysts with pores up to 1000 A. This model assumes that intraparticle diffusion is rate limiting. Catalyst performance was related through an effectiveness factor to the intrinsic activity. Asphaltene metal compound diffusivity as a function of pore size was represented by... 

If HA is a stronger acid than the ammonium function of 2, the rate constant for proton transfer to 2, kuA, will be for diffusion and the observed rate constant will be independent of the acidity of HA. On the other hand, if HA is a weaker acid than the ammonium function of 2, the proton transfer from general acids, HA, to the nitrogen of 1 in Scheme 11.8 will be given by k K /K, where K A is the acid dissociation constant of HA and kA is the diffusion-controlled rate constant. The observed rate will nowbe dependent upon the acidity of the catalyst HA as described by a Bronsted correlation with slope equal to —1. 

The yield of the hydrolysis reaction depends on the competition between recombination and diffusion. The rate of diffusion (kD) depends sharply on the molar mass of the fragments, since the diffusivity of a given molecular species is a decreasing exponential function of its molar volume (Van Krevelen, 1990). Thus one can imagine a process in which all the groups A-B are equireactive (kH constant), but in which the yield of small molecules (high kD) is higher than predicted from the hypothesis of a random process. 

The reactivity of an organic compound toward eaq depends on its functional groups because the main hydrocarbon chain is non-reactive. Aliphatic alcohols, ethers, and amines are also nonreactive (k 106 M 1 s-1), although alkylammonium ions show a slight reactivity and can transfer a proton to the hydrated electron. Isolated double bonds are practically nonreactive, for ethylene k <2-5 X 106 M -1 s-1, but conjugated systems or double bonds with an electron withdrawing group attached to them are very reactive. For example, butadiene and acrylic acid react with practically diffusion controlled rates ( 10 0 M -1 s-1). 

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