Reaction rate-controlling step

Reaction rate Controlling step Equations Notes... 

The equations of combiaed diffusion and reaction, and their solutions, are analogous to those for gas absorption (qv) (47). It has been shown how the concentration profiles and rate-controlling steps change as the rate constant iacreases (48). When the reaction is very slow and the B-rich phase is essentially saturated with C, the mass-transfer rate is governed by the kinetics within the bulk of the B-rich phase. This is defined as regime 1. 

Chemistry. Free-radical nitrations consist of rather compHcated nitration and oxidation reactions (31). When nitric acid is used in vapor-phase nitrations, the reaction of equation 5 is the main initiating step where NO2 is a free radical, either -N02 or -ON02. Temperatures of >ca 350° are required to obtain a significant amount of initiation, and equation 5 is the rate-controlling step for the overall reaction. Reactions 6 and 7 are chain-propagating steps. 

These reactions occur as low as 200°C. The exact temperature depends on the specific hydrocarbon that is nitrated, and reaction 8 is presumably the rate-controlling step. Reaction 9 is of minor importance in nitration with nitric acid, as indicated by kinetic information (32). 

Absorption of Nitrogen Oxides. There have been numerous studies and reports on the reaction mechanisms and rate-controlling steps for the absorption of nitrogen oxides into water (43—46). The overall reaction to form nitric acid may be represented by equation 14, where Ai/298 K kJ/mol ofNO consumed. 

Reaction 1 is the rate-controlling step. The decomposition rate of pure ozone decreases markedly as oxygen builds up due to the effect of reaction 2, which reforms ozone from oxygen atoms. Temperature-dependent equations for the three rate constants obtained by measuriag the decomposition of concentrated and dilute ozone have been given (17—19). 

Equation 20 is the rate-controlling step. The reaction rate of the hydrophobes decreases in the order primary alcohols > phenols > carboxylic acids (84). With alkylphenols and carboxylates, buildup of polyadducts begins after the starting material has been completely converted to the monoadduct, reflecting the increased acid strengths of these hydrophobes over the alcohols. Polymerization continues until all ethylene oxide has reacted. Beyond formation of the monoadduct, reactivity is essentially independent of chain length. The effectiveness of ethoxylation catalysts increases with base strength. In practice, ratios of 0.005—0.05 1 mol of NaOH, KOH, or NaOCH to alcohol are frequendy used. 

As we have seen, a consequence of the formation of porous oxide is that the rate-controlling step reverts to that of a phase boundary reaction and... 

This paper surveys the field of methanation from fundamentals through commercial application. Thermodynamic data are used to predict the effects of temperature, pressure, number of equilibrium reaction stages, and feed composition on methane yield. Mechanisms and proposed kinetic equations are reviewed. These equations cannot prove any one mechanism however, they give insight on relative catalyst activity and rate-controlling steps. Derivation of kinetic equations from the temperature profile in an adiabatic flow system is illustrated. Various catalysts and their preparation are discussed. Nickel seems best nickel catalysts apparently have active sites with AF 3 kcal which accounts for observed poisoning by sulfur and steam. Carbon laydown is thermodynamically possible in a methanator, but it can be avoided kinetically by proper catalyst selection. Proposed commercial methanation systems are reviewed. 

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. 

In other instances, reaction kinetic data provide an insight into the rate-controlling steps but not the reaction mechanism see, for example, Hougen and Watson s analysis of the kinetics of the hydrogenation of mixed isooctenes (16). Analysis of kinetic data can, however, yield a convenient analytical insight into the relative catalyst activities, and the effects of such factors as catalyst age, temperature, and feed-gas impurities on the catalyst. 

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. 

For most real systems, particularly those in solution, we must settle for less. The kinetic analysis will reveal the number of transition states. That is, from the rate equation one can count the number of elementary reactions participating in the reaction, discounting any very fast ones that may be needed for mass balance but not for the kinetic data. Each step in the reaction has its own transition state. The kinetic scheme will show whether these transition states occur in succession or in parallel and whether kinetically significant reaction intermediates arise at any stage. For a multistep process one sometimes refers to the transition state. Here the allusion is to the transition state for the rate-controlling step. 

The strong emphasis placed on concentration dependences in Chapters 2-5 was there for a reason. The algebraic form of the rate law reveals, in a straightforward manner, the elemental composition of the transition state—the atoms present and the net ionic charge, if any. This information is available for each of the elementary reactions that can become a rate-controlling step under the conditions studied. From the form of the rate law, one can deduce the number of steps in the scheme. In most cases, further information can be obtained about the pattern in which parallel and sequential steps are arranged. 

Note that two H+ and one CU ions are formed. The rate-controlling step may be a bimolecular reaction of the intermediates so formed note that the composition of its transition state does, indeed, conform to the data ... 

Adding up the steps in a mechanism must yield the net chemical reaction rapid reactions may follow the rate-controlling step. 

Also, the rates of the propagation steps are equal to one another (see Problem 8-4). This observation is no surprise The rates of all the steps are the same in any ordinary reaction sequence to which the steady-state approximation applies, since each is governed by the same rate-controlling step. The form of the rate law for chain reactions is greatly influenced by the initiation and termination reactions. But the chemistry that converts reactant to product, and is presumably the matter of greatest importance, resides in the propagation reactions. Sensitivity to trace impurities, deliberate or adventitious, is one signal that a chain mechanism is operative. 

The decomposition of acetaldehyde has Eq. (8-6) as the rate-controlling step, this being the one (aside from initiation and termination) whose rate constant appears in the rate law. In the sequence of reactions (8-20)—(8-23), the same reasoning leads us to conclude that the reaction between ROO and RM, Eq. (8-22), is rate-controlling. Interestingly, when Cu2+ is added as an inhibitor, rate control switches to the other propagating reaction, that between R and O2, in Eq. (8-21). The reason, of course, is that Cu2+ greatly lowers [R ] by virtue of the new termination step of reaction (8-30). 

This expression suggests a rate-controlling step in which RM reacts with an intermediate. If so, [Int] °c [RM] /2. To be consistent with this, the initiation step should be first-order in [RM] and the termination step second-order in [Int]. Since O2 is not involved in the one propagation step deduced, it must appear in the other, because it is consumed in the overall stoichiometry. On the other hand, given that one RM is consumed by reaction with the intermediate, another cannot be introduced in the second propagation step, since the stoichiometry [Eq. (8-3)] would disallow that. Further, we know that the initiation and propagation steps are not the reverse of one another, since the system is not well-behaved. From this logic we write this skeleton ... 

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. 

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 ... 

Bimolecular Reactions. Models of surface-catalyzed reactions involving two gas-phase reactants can be derived using either the equal rates method or the method of rate-controlling steps. The latter technique is algebraically simpler and serves to illustrate general principles. 

An analytical solution is possible when the reaction is first order e.g., a reaction of the form A —> P with adsorption as the rate-controlling step. Then Equation (10.3) becomes... 

It is not clear why QAS and inaidazolium salt yield fevoiable results in DMC catalyz i polymerizations. One possible reason is that since the oi uoic phase reaction is the rate controlling step, the total carbon number of the quaternary salt which participates in the... 

If mechanism (A) applied the Cr(VI)+V(IV) system would be anomalous when compared with the Cr(VI) + Fe(II) and Ce(IV) + Cr(III) reactions which have similar rate laws and Cr(V) -> Cr(IV) transformations as rate-controlling steps. Apart from this there are other good reasons for rejecting mechanism (+). At 25 °C, K is 10 ° and k is 0.56 l.mole sec , allowing At2 to be calculated as... 

Scheme B) is considered unlikely on the grounds that, at the low concentrations of U(V) involved, the latter would disappear by oxidation with Fe(ni) rather by dismutation. The hydrogen-ion dependence suggests that the rate-controlling step between Fe(irf) and U([V) can be visualised in terms of a series of competitive reactions of hydrolysed species of both reactants viz.

Oxidation of isopropyl alcohol (H2R) by chromic acid has been studied in det ai by Westheimer and Novick , and it was found that acetone (R) is formed nearly quantitatively. The reaction proved to be first order with respect to hydrogen chromate and second order with respect to hydrogen ions. Measurements using 2-deutero-2-propanol under identical conditions as those for the oxidation of ordinary isopropyl alcohol showed the rate of reaction to be of that with the hydrogen compound. This fact is considered to prove that the secondary hydrogen atom is removed in the rate-controlling step and that the assumption of hydride-ion abstraction can be excluded. The data are consistent with the following mechanism... 

The theoretical approach involved the derivation of a kinetic model based upon the chiral reaction mechanism proposed by Halpem (3), Brown (4) and Landis (3, 5). Major and minor manifolds were included in this reaction model. The minor manifold produces the desired enantiomer while the major manifold produces the undesired enantiomer. Since the EP in our synthesis was over 99%, the major manifold was neglected to reduce the complexity of the kinetic model. In addition, we made three modifications to the original Halpem-Brown-Landis mechanism. First, precatalyst is used instead of active catalyst in om synthesis. The conversion of precatalyst to the active catalyst is assumed to be irreversible, and a complete conversion of precatalyst to active catalyst is assumed in the kinetic model. Second, the coordination step is considered to be irreversible because the ratio of the forward to the reverse reaction rate constant is high (3). Third, the product release step is assumed to be significantly faster than the solvent insertion step hence, the product release step is not considered in our model. With these modifications the product formation rate was predicted by using the Bodenstein approximation. Three possible cases for reaction rate control were derived and experimental data were used for verification of the model. 

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