Reactants rate-determining step

Fig. 1. The rate-determining step in the neutral hydrolysis of paramethoxy-phenyl dichloroacetate. In the reactant state (a) a water molecule is in proximity of the carbonyl carbon after concerted proton transfer to a second water molecule and electron redistribution, a tetrahedral intermediate (b) is formed.

Until now we have been discussing the kinetics of catalyzed reactions. Losses due to volatility and side reactions also raise questions as to the validity of assuming a constant concentration of catalyst. Of course, one way of avoiding this issue is to omit an outside catalyst reactions involving carboxylic acids can be catalyzed by these compounds themselves. Experiments conducted under these conditions are informative in their own right and not merely as means of eliminating errors in the catalyzed case. As noted in connection with the discussion of reaction (5.G), the intermediate is stabilized by coordination with a proton from the catalyst. In the case of autoprotolysis by the carboxylic acid reactant, the rate-determining step is probably the slow reaction of intermediate [1] ... 

The goal of a kinetic study is to establish the quantitative relationship between the concentration of reactants and catalysts and the rate of the reaction. Typically, such a study involves rate measurements at enough different concentrations of each reactant so that the kinetic order with respect to each reactant can be assessed. A complete investigation allows the reaction to be described by a rate law, which is an algebraic expression containing one or more rate constants as well as the concentrations of all reactants that are involved in the rate-determining step and steps prior to the rate-determining step. Each concentration has an exponent, which is the order of the reaction with respect to that component. The overall kinetic order of the reaction is the sum of all the exponents in the... 

Kinetic data provide information only about the rate-determining step and steps preceding it. In the hypothetical reaction under consideration, the final step follows the rate-determining step, and because its rate will not affect the rate of the overall reaction, will not appear in the overall rate expression. The rate of the overall reaction is governed by the second step, which is the bottleneck in the process. The rate of this step is equal to A2 multiplied by the molar concentration of intermediate C, which may not be directly measurable. It is therefore necessary to express the rate in terms of the concentrations of reactants. In the case under consideration, this can be done by recognizing that [C] is related to [A] and [B] by an equilibrium constant ... 

Notice that specific acid catalysis describes a situation in which the reactant is in equilibrium with regard to proton transfer, and proton transfer is not rate-determining. On the other hand, each case that leads to general acid catalysis involves proton transfer in the rate-determining step. Because of these differences, the study of rates as a function of pH and buffer concentrations can permit conclusions about the nature of proton-transfer processes and their relationship to the rate-determining step in a reaction. 

The details of proton-transfer processes can also be probed by examination of solvent isotope effects, for example, by comparing the rates of a reaction in H2O versus D2O. The solvent isotope effect can be either normal or inverse, depending on the nature of the proton-transfer process in the reaction mechanism. D3O+ is a stronger acid than H3O+. As a result, reactants in D2O solution are somewhat more extensively protonated than in H2O at identical acid concentration. A reaction that involves a rapid equilibrium protonation will proceed faster in D2O than in H2O because of the higher concentration of the protonated reactant. On the other hand, if proton transfer is part of the rate-determining step, the reaction will be faster in H2O than in D2O because of the normal primary kinetic isotope effect of the type considered in Section 4.5. 

Formation of the n-complex can be reversible. The partitioning of the n-complex forward to product or back to reactants depends on the ease with which the electrophile can be eliminated relative to a proton. For most electrophiles, it is easier to eliminate the proton, in which case the formation of the n-complex is essentially irreversible. Formation of the (T-complex is least likely to be reversible for the electrophiles in group A in Scheme 10.1, whereas those in group C are most likely to undergo reversible n-complex formation. Formation of the n-complex is usually, but not always, the rate-determining step in... 

TWo types of rate expressions have been found to describe the kinetics of most aromatic nitration reactions. With relatively unreactive substrates, second-order kinetics, first-order in the nitrating reagent and first-order in the aromatic, are observed. This second-order relationship corresponds to rate-limiting attack of the electrophile on the aromatic reactant. With more reactive aromatics, this step can be faster than formation of the active electrq)hile. When formation of the active electrophile is the rate-determining step, the concentration of the aromatic reactant no longer appears in the observed rate expression. Under these conditions, different aromatic substrates undergo nitration at the same rate, corresponding to the rate of formation of the active electrophile. 

This argument can be extended to consecutive reactions having a rate-determining step. - P The composition of the transition state of the rds is given by the rate equation. This composition includes reactants prior to the rds, but nothing following the rds. Thus, the rate equation may not correspond to the stoichiometric equation. We will consider several examples. In Scheme IV a fast acid-base equilibrium precedes the slow rds. 

In contrast to the influence of velocity, whose primary effect is to increase the corrosion rates of electrode processes that are controlled by the diffusion of reactants, temperature changes have the greatest effect when the rate determining step is the activation process. In general, if diffusion rates are doubled for a certain increase in temperature, activation processes may be increased by 10-100 times, depending on the magnitude of the activation energy. 

Rate constant The proportionality constant in the rate equation for a reaction, 288 Rate-determining step The slowest step in a multistep mechanism, 308 Rate expression A mathematical relationship describing the dependence of reaction rate upon the concentra-tion(s) of reactant(s), 288,308-309 Rayleigh, Lord, 190... 

If the rate-determining step were not a surface reaction but adsorption of competing reactants, we should obtain from the corresponding equations the expression which is formally identical with Eq. (15), in which, however, the relative reactivity is given by the expression S = fc dsA/ adsB. On the basis of data on competitive reactions only, these two cases cannot there-... 

STRATEGY Construct the rate laws for the elementary reactions and combine them into the overall rate law for the decomposition of the reactant. If necessary, use the steady-state approximation for any intermediates and simplify it by using arguments based on rapid pre-equilibria and the existence of a rate-determining step. 

Reactions with molecular species above the arrow e.g. RIO) involve subsequent reactions with these species to produce the indicated products. In most cases the reactants shown to the left of the arrow participate in the slowest or rate-determining step]. The CH3O radical formed in Rll then follows reaction R7. The H02 radical formed in RIO is the other member of the family and is linked with HO in a variety of chain reactions. These radicals are produced following HO attack on hydrocarbons or by photodissociation of oxygenated hydrocarbons such as formaldehyde (RIO) and acetaldehyde ... 

The solvent may be a reactant. If an O—H bond of the solvent is broken in the rate-determining step, there will be a primary isotope effect. If the molecules involved are D2O or D3O+ there may also be a secondary effect caused by the O—D bonds that are not breaking. 

For many reaction mechanisms, the rate-determining step occurs after one or more faster steps. In such cases the reactants in the early steps may or may not appear in the rate law. Furthermore, the rate law is likely to depart from simple first- or second-order behavior. Fractional orders, negative orders, and overall orders greater than two, all are signals that a fast first step is followed by a slow subsequent step. 

To see if the proposed mechanism predicts the correct rate law, we start with the rate-determining step. The second step in this mechanism is rate-determining, so the overall rate of the reaction is governed by the rate of this step Rate — 2[Br ][H2 ] This rate law describes the rate behavior predicted by the proposed mechanism accurately, but the law cannot be tested against experiments because it contains the concentration of Br atoms, which are intermediates in the reaction. As mentioned earlier, an intermediate has a short lifetime and is hard to detect, so it is difficult to make accurate measurements of its concentration. Furthermore, it is not possible to adjust the experimental conditions in a way that changes the concentration of an intermediate by a known amount. Therefore, if this proposed rate law is to be tested against experimental behavior, the concentration of the intermediate must be expressed in terms of the concentrations of reactants and products. 

By utilizing this we can now express the coverages of all the relevant intermediates and the overall rate in terms of equilibrium constants of the steps in quasi-equilibrium, the pressures of the reactants and the products, and the rate constant of the rate-determining step. 

Kinetics of chemical reactions at liquid interfaces has often proven difficult to study because they include processes that occur on a variety of time scales [1]. The reactions depend on diffusion of reactants to the interface prior to reaction and diffusion of products away from the interface after the reaction. As a result, relatively little information about the interface dependent kinetic step can be gleaned because this step is usually faster than diffusion. This often leads to diffusion controlled interfacial rates. While often not the rate-determining step in interfacial chemical reactions, the dynamics at the interface still play an important and interesting role in interfacial chemical processes. Chemists interested in interfacial kinetics have devised a variety of complex reaction vessels to eliminate diffusion effects systematically and access the interfacial kinetics. However, deconvolution of two slow bulk diffusion processes to access the desired the fast interfacial kinetics, especially ultrafast processes, is generally not an effective way to measure the fast interfacial dynamics. Thus, methodology to probe the interface specifically has been developed. 

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