Rate-determining step of a reaction

Chemical reactivity differences may be calculated if for the transition state of a rate-determining step of a reaction a structural model can be given which is describable by a force field with known constants. We give only two examples. Schleyer and coworkers were able to interpret quantitatively a multitude of carbonium-ion reactivities (63, 111) in this way. Adams and Kovacic studied the pyrolysis of 3-homoadamantylacetate (I) at 550 °C and considered as transition state models the two bridgehead olefins II and III (112). From kinetic data they estimated II to be about 2 kcal mole-1 more favourable than III. 

Thus, if an O-H(D) bond is broken during the rate-determining step of a reaction, there is a difference in the rates of the two reactions, the magnitude of which varies with the nature of the TS. If the proton being transferred is bound equally between two atoms in the TS,then the effect is maximized, whereas if the TS is product- or reactant-like, primary isotope effects closer to one will be observed. 

It should be noted that the rate-determining step of a reaction changes with substrate concentration, since the rate is proportional to kcat at saturating concentrations of substrate, and to kcdt/KM at low concentrations. When a step is said to be rate-determining and the reaction conditions are not stated, the reaction is usually at saturating substrate concentrations. 

Suppose the activated complex T of the rate-determining step of a reaction, starting from gaseous A and B, is (AaBb) and that it occupies tt sites on the surface. Under the conditions of the reaction this surface may be partially covered by adsorbed A, adsorbed B, or both. Let us suppose that a fraction dA is covered by /lads, each A molecule occupying ta sites, and that a fraction dB is covered by Bada, each B occupying tb sites. A fraction 6f = 1 — dA — 6B of the surface is empty. 

The kinetic isotope effect was introduced in Chapter 19. If a bond to deuterium is formed or broken in the rate-determining step of a reaction, the deuterated compound will react more slowly, usually by a factor of about 2-7. This effect is particularly valuable when C-H bonds are being formed or broken. In Chapter 22 we told you that the rate-determining step in the nitration of benzene was the attack of the electrophile on the benzene ring. This is easily verified by replacing the hydrogen atoms round the benzene ring with deuteriums. The rate of the reaction stays the same. 

Who are rate-determining-step players Kinetics can yield information about the rate-determining step of a reaction. At a constant temperature, the concentration of a particular reactant is changed and the effect on the rate of reaction is noted. For example, a reaction that is second order in compound A would quadruple its rate if the concentration of A were doubled. If the reaction were first order in A, the rate would double if the A concentration were doubled. In this way the kinetic order with respect to each reactant is determined. These kinetic orders can then be compared to that expected for the slow step of a postulated mechanism. Often, however the kinetic order can easily fit several possibilities. 

What is the rate-determining step of a reaction Give an everyday analogy to illustrate the meaning of rate determining. ... 

The identification of a rate law provides valuable insight into the reaction mechanism, the sequence of elementary steps by which a reaction takes place. The aim is to identify the reaction mechanism by constructing the rate law that it implies. This procedure may be simplified by identifying the rate-determining step of a reaction, the slowest step in a sequence that determines the overall rate. Thus, if the proposed mechanism is A B followed by B C, and the former is much faster than the latter, then the overall rate of the reaction will be equal to the rate of A B, for once B is formed, it immediately converts into C. 

Activation parameters such as entropy or volume of activation, and to a lesser degree the enthalpy of activation, also provide mechanistic information. Entropies and enthalpies of activation are obtained from measurements of the rate constant for a reaction over a range of temperatures. Whether the rate-determining step of a reaction is unimolecular or bimolecular can have a significant effect on these parameters. 

Deuterium isotope effects have been widely used to demonstrate that bonds to hydrogen are broken in the rate-determining step of a reaction. The presence of a... 

Let us first determine which species are the key ones in a rate equation. For all rate equations we are interested in the species involved in the rate determining step. The rate determining step of a reaction is usually the slow part of the reaction, or if a reaction has several slow steps, the rate determining step is the slowest step. 

Section 5.17 A P C—D bond is broken more slowly in the E2 dehydrohalogenation of alkyl halides than a p C—H bond. The ratio of the rate constants / h/ d is a measure of the deuterium isotope effect and has a value in the range 3-8 when a carbon-hydrogen bond breaks in the rate-determining step of a reaction. 

Recall that Eqs. 8.48 and 8.50 are called BrDnsted linear free energy relationships. If an acid or base is involved in the rate-determining step of a reaction, the rate of that reaction should depend upon the strength of the acid or base. Hence, a Bronsted correlation is often found. Eqs. 8.51 and 8.52 relate the rate constants for an acid- or base-catalyzed reaction, respectively, to the pfC, of the acid or conjugate acid of the base. The sensitivity of an acid-catalyzed reaction to the strength of the acid is a, whereas the sensitivity of a base-catalyzed reaction to the strength of the base is p. The a and p reaction constants indicate the extent of proton transfer in the transition state. In Chapter 9 we explore the use of these two equations in much more detail, and we apply them in Chapters 10 and 11. 

The rate-determining step of a reaction is the step with the highest-energy transition state. It may or may not be the same as the product-determining step. For example, in the Sn2 reaction it is the same, but in the SnI reaction it is not. 

It is important to be certain you understand the source of the rate increase for the sulfide compound. Intramolecular reactions often have a large rate advantage over inter-molecular reactions because there is no need for the nucleophile and substrate to find each other in solution. Intramolecular assistance in the rate-determining step of a reaction is called anchimeric assistance. Once again, it is important not to be put off by the elaborate name. The concept is quite simple Intramolecular nucleophiles are often more effective displacing agents than intermolecular nucleophiles. What is somewhat more difHcult to anticipate is that an intramolecular displacement by a very weak, but perfectly situated nucleophile can often compete effectively with intermolecular reactions. 

Elementary Reactions and Molecularity 526 The Rate-Determining Step of a Reaction Mechanism 527... 

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