Determination of the Rate-Controlling Step

The kinetics and rate-controlling steps of a fluid-solid reaction are deduced by noting how the progressive conversion of particles is influenced by particle size and operating temperature. This information can be obtained in various ways, depending on the facilities available and the materials at hand. The following observations are a guide to experimentation and to the interpretation of experimental data. 

Temperature. The chemical step is usually much more temperature-sensitive than the physical steps hence, experiments at different temperatures should easily distinguish between ash or film diffusion on the one hand and chemical reaction on the other hand as the controlling step. 

Particles of constant size Gas film diffusion controls, Eq. 11 Chemical reaction controls, Eq. 23 Ash layer diffusion controls, Eq. 18 Shrinking particles Stokes regime, Eq. 30 Large, turbulent regime, Eq. 31 Reaction controls, Eq. 23 

Conversion-time curves analogous to those in Figs. 25.9 and 25.10 can be prepared for other solid shapes by using the equations of Table 25.1. 

Particle Size. Equations 16, 21, and 8 with Eq. 24 or 25 show that the time needed to achieve the same fractional conversion for particles of different but unchanging sizes is given by 

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A crucial aspect of process analysis is the determination of the rate-controlling step or steps. In soil bioremediation, three considerations for the rate-controlling step have been outlined (Li, Annamalai Hopper, 1993) as follows ... 

Estimation of Rates of Individual Steps and Determination of the Rate Controlling Step... 

Some quantities associated with the rates and mechanism of a reaction are determined. They include the reaction rate under given conditions, the rate constant, and the activation enthalpy. Others are deduced reasonably directly from experimental data, such as the transition state composition and the nature of the rate-controlling step. Still others are inferred, on grounds whose soundness depends on the circumstances. Here we find certain features of the transition state, such as its polarity, its stereochemical arrangement of atoms, and the extent to which bond breaking and bond making have progressed. 

Many experimental criteria have been suggested for identification of the rate-controlling step. The majority are based on curve fitting to idealized rate laws and are unreliable. The two best methods are the so-called interruption test and the determination of the dependence of (he rate on particle. size. 

It will be noted that properties of the barrier-to-electron transfer do not enter into the determination of b for chemically controlled rate-determining steps provided the quasiequilibrium hypothesis applies adequately to the steps prior to the ratecontrolling one, which may not always be the case. This means practically that the exchange rate in the pre-rate-determining steps must be at least 10 times the net velocity of the rate-controlling step at all overpotentials. 

Many other mathematical methods have been proposed to analyze non-isothermal kinetic data to determine unequivocally the exact kinetic model using functional forms of < (a) or /(a) of the rate-controlling step (154). Criado (155) found that it was impossible in the Coats and Redfern method to distinguish between an interface chemical reaction-controlled mechanism (R3) and the Jander diffusion mechanism (D3). Bagchi and Sen (156) also demonstrated the inadequacy of the Coats and Redfern method in identifying unambiguously the rate-controlling mechanism of the dehydroxylation of Mg(OH)2. 

Thus, the first approach to CdS nanoparticle synthesis in both the outer and inner surfaces of the lipid vesicles seems to have been found. The main factors that control the sizes of the CdS nanoparticles in the inner cavities of the lipid vesicles were determined and some attempts to determine the nature of the rate-controlling step in the process of CdS particle growth in these cavities were also undertaken. 

The figure shows the linearized concentration profiles of dissolved oxygen (in the form of O atoms) and of metal A. At the reaction front, both concentrations are quite small, as long as the oxidation reaction is sufficiently fast. Their value corresponds to the saturation concentration of the formed oxide. The displacement rate of the reaction front lies between two limiting cases, determined by the rate controlling step of the oxidation reaction ... 

In a study of oxidation resistance over the range 1200—1500°C an activation energy of 276 kj/mol (66 kcal/mol) was determined (60). The rate law is of the form 6 = kT + C the rate-controlling step is probably the diffusion of oxygen inward to the SiC—Si02 interface while CO diffuses outwards. 

The first equation was derived by assuming that the rate-controlling step is the reaction of one molecule of adsorbed C02 with two molecules of dissociated adsorbed hydrogen. The second equation, which correlates almost as well, is based on the assumption that the rate-determining step is the reaction of one molecule of adsorbed C02 with two molecules of adsorbed hydrogen. This indicates that, in this particular case, it was not possible to prove reaction mechanisms by the study of kinetic data. 

Irreversible Unimolecular Reactions. Consider the irreversible catalytic reaction A P of Example 10.1. There are three kinetic steps adsorption of A, the surface reaction, and desorption of P. All three of these steps must occur at exactly the same rate, but the relative magnitudes of the three rate constants, ka, and kd, determine the concentration of surface species. Suppose that ka is much smaller than the other two rate constants. Then the surface sites will be mostly unoccupied so that [S] Sq. Adsorption is the rate-controlling step. As soon as a molecule of A is absorbed it reacts to P, which is then quickly desorbed. If, on the other hand, the reaction step is slow, the entire surface wiU be saturated with A waiting to react, [ASJ Sq, and the surface reaction is rate-controlling. Finally, it may be that k is small. Then the surface will be saturated with P waiting to desorb, [PS] Sq, and desorption is rate-controlling. The corresponding forms for the overall rate are ... 

In general, the overall reaction process may comprise several individual steps, as shown in Figure 3.24. It could be seen that these steps pertain to (i) mass transfers of reactants and the products between the bulk of the fluid and the external surface of the solids (ii) transport of reactants and the products within the pores of the solid and (iii) chemical reaction between the reactants in the fluid and those in the solid. In order to be able to determine the rate-controlling step and to ascertain whether more than a single step should be consid-... 

Very few references are available on the determination of the rate constant for each step of electron charge transfer in the reaction M2+ + 2e -> M(s), i.e., M2+ + e -> M+, M+ + c" -> M(s). Earlier studies are mostly related to two-electron charge transfer reactions either at M2+/Hg(dme), M2+/metal amalgam, or redox couple/Pt interfaces. Even in these studies, the kinetic parameters have been determined assuming that one of the two steps of the reaction is much slower and is in overall control of the rate of reaction in both... 

The rate-controlling step is the elementary reaction that has the largest control factor (CF) of all the steps. The control factor for any rate constant in a sequence of reactions is the partial derivative of In V (where v is the overall velocity) with respect to In k in which all other rate constants (kj) and equilibrium constants (Kj) are held constant. Thus, CF = (5 In v/d In ki)K kg. This definition is useful in interpreting kinetic isotope effects. See Rate-Determining Step Kinetic Isotope Effects... 

It is often the situation that most reaction steps in a mechanism are fast, while a single step is much slower than the other. In this situation, the slow step is called the rate limiting step (RLS) or the rate controlling step as it determines the rate of the overall reaction. 

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