Reaction rate constant intrinsic

Figure 10 shows that Tj is a unique function of the Thiele modulus. When the modulus ( ) is small (- SdSl), the effectiveness factor is unity, which means that there is no effect of mass transport on the rate of the catalytic reaction. When ( ) is greater than about 1, the effectiveness factor is less than unity and the reaction rate is influenced by mass transport in the pores. When the modulus is large (- 10), the effectiveness factor is inversely proportional to the modulus, and the reaction rate (eq. 19) is proportional to k ( ), which, from the definition of ( ), implies that the rate and the observed reaction rate constant are proportional to (1 /R)(f9This result shows that both the rate constant, ie, a measure of the intrinsic activity of the catalyst, and the effective diffusion coefficient, ie, a measure of the resistance to transport of the reactant offered by the pore stmcture, influence the rate. It is not appropriate to say that the reaction is diffusion controlled it depends on both the diffusion and the chemical kinetics. In contrast, as shown by equation 3, a reaction in solution can be diffusion controlled, depending on D but not on k. 

When the effectiveness factors for both reactions approach unity, the selectivity for two independent simultaneous reactions is the ratio of the two intrinsic reaction-rate constants. However, at low values of both effectiveness factors, the selectivity of a porous catalyst may be greater than or less than that for a plane-catalyst surface. For a porous spherical catalyst at large values of the Thiele modulus s, the effectiveness factor becomes inversely proportional to (j>S9 as indicated by equation 12.3.68. In this situation, equation 12.3.133 becomes... 

Here kgr is the surface reaction rate constant, Rr is the adsorption equilibrium constant for product R, Pr is the partial pressure of R and Kp is the reaction equilibrium constant. At low loading the reaction rate simply becomes proportional to the product of the intrinsic rate constant and the Henry coefficient. 

The pure compound rate constants were measured with 20-28 mesh catalyst particles and reflect intrinsic rates (—i.e., rates free from diffusion effects). Estimated pore diffusion thresholds are shown for 1/8-inch and 1/16-inch catalyst sizes. These curves show the approximate reaction rate constants above which pore diffusion effects may be observed for these two catalyst sizes. These thresholds were calculated using pore diffusion theory for first-order reactions (18). Effective diffusivities were estimated using the Wilke-Chang correlation (19) and applying a tortuosity of 4.0. The pure compound data were obtained by G. E. Langlois and co-workers in our laboratories. Product yields and suggested reaction mechanisms for hydrocracking many of these compounds have been published elsewhere (20-25). 

For Ha > 0.02, there is a considerable scope for process intensification. If a reaction is intrinsically fast (a large reaction rate constant) the design aim is to provide sufficiently intense mixing to move it into the slow reaction regime (Ha < 0.02) such that the reaction is limited by the intrinsic reaction rate rather than the mass transfer rate. 

Intrinsic reaction rate constant, s overall apparent rate constant, s solubility coefficient, cur liquid-atm/mol stirrer speed, RPM partial pressure, atm... 

C = oxygen concentration at the reaction surface, kg = convective mass transfer coefficient, ks = intrinsic reaction rate constant,... 

A, cross sectional area, m2 k. intrinsic reaction rate constant, 1/s... 

Fig. 15. Changes in effective diffusivity of methanol in SAPO-34 and intrinsic reaction rate constants for methanol conversion on SAPO-34 as a function of the coke content in crystals with average sizes of 0.25 and 2.5 m (89).

Another approach to determine diffusion coefficients under catalytic conditions can be achieved most effectively by studying the effectiveness fector in catalytic experiments on samples of different crystal size (the intrinsic reaction rate constant and the equilibrium constant must be known) as done by Haag et al. (55) for the cracking of n-hydrocarbons over HZSM-5. 

Ky and ky are the equilibrium constant and cross reaction rate constant for Eq. 2, kii and kjj are the self-exchange ET rate constants, and Z is a preexponential factor usually set at 10 (results are quite insensitive to its value). Because Ky can be calculated from the difference in formal oxidation potentials for the components, Eq. 2 states that ky only depends upon the formal oxidation potential and intrinsic (AG° = 0, or self-ET) rate constant for each couple involved. 

The rate at which ligand molecules are bound by a receptor is equal to the intrinsic reaction rate constant kon times the ligand concentration at the receptor surface, L evaluated at r = s 5 is often termed the encounter radius. At steady state, this must be equal to the ligand diffusion rate (moles/time) to the receptor surface (the diffusive flux multiplied by the surface area, again evaluated at r = s). This provides the second boundary condition needed for Eq. (29) ... 

Turning to receptor processes on cell membranes (case c of Fig. 9), we could infer the degree of diffusion limitation from a ratio analogous to that in Eq. (52), where k+ is given by Eq. (50b). Unfortunately, values for an intrinsic reaction rate constant, koa, are extremely difficult to deter-... 

To relate knowledge of elementary reaction rate constants with the intrinsic overall kinetics of a heterogeneous catalyst one has to explicitly deal with non-ideal mixing effects of adsorbed reactants. 

The reaction kinetics dictate the intrinsic selectivity of the system We opted for a simple model system in which both reactions are first order in the reactant concentration and both elementary reaction rate constants are equal. Physically this implies that the catalyst is always in quasi steady state. 

The reaction of (NPCI ) with phenol using a liquid-liquid phase-transfer catalyzed reaction in a batch reactor was reported in our previous work 64, and the intrinsic reaction-rate constants were also obtained. Since the intrinsic reaction-rate constant in a triphase reaction was ditlicult to obtain, we assumed that the intrinsic reaction-rate constants in a liquid-liquid phase-transfer catalyzed reaction w cre the same as those in a triphase reaction in order to discuss the ctTectivcness factor of the catalyst, although they might be differem. The elTectivencss factors calculated are listed in Table 2. The etTcctivcncss factors of SR and FBR are much smaller than 1. It is demonstrated that the triphase reaction was inHuenced by particle dilTusion of the reactant. 

Wang and Wu [70] analyzed the extraction equilibrium of the effects of catalyst, solvent, NaOH/organic substrate ratio, and temperature on the consecutive reaction between 2,2,2-trifluoroethanol with hexachlorocyclotriphosphazene in the presence of aqueous NaOH. Wu and Meng [69] reported the reaction between phenol with hexachlorocyclotriphosphazene. They first obtained the intrinsic reaction-rate constant and overall mass transfer coefficient simultaneously, and reported that the mass transfer resistance of QX from the organic to aqueous phase is larger than that of QY from the aqueous to organic phase. The intrinsic reaction-rate constant and overall mass transfer coefficients were obtained in three ways. 

Viscosity of dilute solutions. A capillary viscometer (Cannon-Manning semimicro, No. 100) was used for determination of the intrinsic viscosity and for study of enzymatic degradation. Measurements were carried at 37 C. For the latter study specific fluidities, the reciprocal of specific viscosity, were plotted against reaction time. With random degradation of a chain polymer a straight line is obtained by this plotting, and the slope of the line is proportional to the reaction rate constant (4). 

And is called kinetic equation or reaction rate law. Here r. is rate of reactions normalized over volume, C.,. is molar concentrations of reac-tants, k. is constant value characterizing the rate reactions at reactants concentration equal to 1, which is called reaction rate constant or intrinsic reaction rate, v.. is stoichiometric coefficient of the component i usually called partial order of reaction. Sum of one reaction partial order determines order of the reaction overall or order of its rate law. Elementary reactions (acts) dominate, which are subject to the rate law of zero, first and second order. For instance, for an elementary direct reaction... 

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