Controlling step intrinsic kinetics

Since the free energy of a molecule in the liquid phase is not markedly different from that of the same species volatilized, the variation in the intrinsic reactivity associated with the controlling step in a solid—liquid process is not expected to be very different from that of the solid—gas reaction. Interpretation of kinetic data for solid—liquid reactions must, however, always consider the possibility that mass transfer in the homogeneous phase of reactants to or products from, the reaction interface is rate-limiting [108,109], Kinetic aspects of solid—liquid reactions have been discussed by Taplin [110]. 

Examples (10.1) and (10.2) used the fact that Steps 4, 5, and 6 must all proceed at the same rate. This matching of rates must always be true, and, as illustrated in the foregoing examples, can be used to derive expressions for the intrinsic reaction kinetics. There is another concept with a time-honored tradition in chemical engineering that should be recognized. It is the concept of rate-determining step or rate-controlling step. 

If the overall reaction rate is controlled by step three (k3) (i.e. if that is the rate limiting step), then the observed isotope effect is close to the intrinsic value. On the other hand, if the rate of chemical conversion (step three) is about the same or faster than processes described by ks and k2, partitioning factors will be large, and the observed isotope effects will be smaller or much smaller than the intrinsic isotope effect. The usual goal of isotope studies on enzymatic reactions is to unravel the kinetic scheme and deduce the intrinsic kinetic isotope effect in order to elucidate the nature of the transition state corresponding to the chemical conversion at the active site of an enzyme. Methods of achieving this goal will be discussed later in this chapter. 

In summary, it can be seen for the three-step reaction scheme of this example that the net rate of the overall reaction is controlled by three kinetic parameters, KTSi, that depend only on the properties of the transition states for the elementary steps relative to the reactants (and possibly the products) of the overall reaction. The reaction scheme is represented by six individual rate constants /c, and /c the product of which must give the equilibrium constant for the overall reaction. However, it is not necessary to determine values for five linearly independent rate constants to determine the rate of the overall reaction. We conclude that the maximum number of kinetic parameters needed to determine the net rate of overall reaction is equal to the number of transition states in the reaction scheme (equal to three in the current case) since each kinetic parameter is related to a quasi-equilibrium constant for the formation of each transition state from the reactants and/or products of the overall reaction. To calculate rates of heterogeneous catalytic reactions, an addition kinetic parameter is required for each surface species that is abundant on the catalyst surface. Specifically, the net rate of the overall reaction is determined by the intrinsic kinetic parameters Kf s as well as by the fraction of the surface sites, 0, available for formation of the transition states furthermore, the value of o. is determined by the extent of site blocking by abundant surface species. 

Lawrence Stamper Darken (1909-1978) subsequently showed (Darken, 1948) how, in such a marker experiment, values for the intrinsic diffusion coefficients (e.g., Dqu and >zn) could be obtained from a measurement of the marker velocity and a single diffusion coefficient, called the interdiffusion coefficient (e.g., D = A ciiD/n + NznDca, where N are the molar fractions of species z), representative of the interdiffusion of the two species into one another. This quantity, sometimes called the mutual or chemical diffusion coefficient, is a more useful quantity than the more fundamental intrinsic diffusion coefficients from the standpoint of obtaining analytical solutions to real engineering diffusion problems. Interdiffusion, for example, is of obvious importance to the study of the chemical reaction kinetics. Indeed, studies have shown that interdiffusion is the rate-controlling step in the reaction between two solids. 

Adsorption of molecules proceeds by successive steps (1) penetration inside a particle (2) diffusion inside the particle (3) adsorption (4) desorption and (5) diffusion out of the particle. In general, the rates of adsorption and desorption in porous adsorbents are controlled by the rate of transport within the pore network rather than by the intrinsic kinetics of sorption at the surface of the adsorbent. Pore diffusion may take place through several different mechanisms that usually coexist. The rates of these mechanisms depend on the pore size, the pore tortuosity and constriction, the cormectivity of the pore network, the solute concentration, and other conditions. Four main, distinct mechanisms have been identified molecular diffusion, Knudsen diffusion, Poiseiulle flow, and surface diffusion. The effective pore diffusivity measured experimentally often includes contributions for more than one mechanism. It is often difficult to predict accurately the effective diffusivity since it depends so strongly on the details of the pore structure. 

Albright, Hanson, et al (1,2,3 ) have reviewed the work of previous investigators and concluded that the criteria sometimes used to determine the rate-limiting step were not adequate. The reaction kinetics measured by some workers (4,5 ) exhibit considerable differences even though they claimed to be measuring intrinsic kinetics. Such differences may result from diffusion effects. Recently, Cox and Strachan (6 ) reported the nitration of chlorobenzene to be kinetically controlled at a nitric acid concentration of 0.032 mole/liter in 70 weight percent sulfuric acid for the nitration of toluene in the same acid, the rates of chemical reaction and diffusion were of comparable magnitude. 

The slow reaction regime is characterized by the fact that the amount of the aromatic reactant that reacts in the film at the interface between phases is negligible compared to the amount that diffuses into the acid phase. Either the intrinsic kinetics or the rate of bulk-diffusion of the aromatic reactant may be the rate controlling step. The second type of reaction system is designated as a fast reaction system, and benzene would react in... 

Intrinsic kinetics were probably the rate-controlling step in most if not all of the experimental runs made in this investigation. Reasonably high levels of agitation were provided, and... 

Any of these steps can be sufficiently slow, relative to others, to control the overall reaction rate. The net (overall) kinetics is called effective kinetics or macrokinetics, in contrast to the kinetics of chemical processes, which is termed intrinsic kinetics or microkinetics. 

The passage from one control to the other is pictured in Figure 2.5 for the cathodic peak potential and the peak width as a function of the scan rate and of the intrinsic parameters of the system. We note that increasing the scan rate tends to move the kinetic control from the follow-up reaction to the electron transfer step. It thus appears that the overall reaction may well be under the kinetic control of electron transfer, even if this is intrinsically fast, provided that the follow-up reaction is irreversible and fast. The reason is that the follow-up reaction prevents the reverse electron transfer from operating, thus making the forward electron transfer the rate-determining step. 

The motion of molecules in a liquid has a significant effect on the kinetics of chemical reactions in solution. Molecules must diffuse together before they can react, so their diffusion constants affect the rate of reaction. If the intrinsic reaction rate of two molecules that come into contact is fast enough (that is, if almost every encounter leads to reaction), then diffusion is the rate-limiting step. Such diffusion-controlled reactions have a maximum bimolecular rate constant on the order of 10 ° L mol s in aqueous solution for the reaction of two neutral species. If the two species have opposite charges, the reaction rate can be even higher. One of the fastest known reactions in aqueous solution is the neutralization of hydronium ion (H30 ) by hydroxide ion (OH ) ... 

Multiphase reactions can be significantly affected by how well mixed the system is and how intimately dispersed the phases are. The reason for this is easy to explain, but more difficult to quantify although the course of any reaction is determined exclusively by the local concentrations of the reactants and the intrinsic reaction kinetic rates, in any real reactive system, the local reactant concentrations depend not only on how fast the reactants are depleted by the reaction, but also on how fast they are locally replenished from the bulk of the phases in which they initially reside. The latter phenomenon is directly related to the existence of a mass transfer step (in series with the reaction step), which determines the rate at which the reactants in different phases are brought in contact with each other. In many cases, especially if the rate of reaction is fast with respect to the mass transfer rate, the latter mechanism can become controlling over the former, and the overall reaction process is dominated by mass transfer and, hence, multiphase mixing. 

For industrial reactors, the effectiveness factor (i]) is used to provide a measure of the actual reaction rate, as affected by operating conditions, in comparison to the intrinsic reaction kinetics. Assuming that the trickle bed reactor shown in Fig. 4 is operated so that interphase transport of one of the reactants, steps 2 or 8 above, is controlling. 

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