Elementary reactions kinetic isotope effect

An elementary reaction or step (in a chemical process) for which the rate constants are altered by an isotopic substitution in substrate, product, or solvent. See Kinetic Isotope Effect Solvent Isotope Effect... 

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... 

Ab initio methods provide the information needed in Equations (25) and (26) to calculate the rate constants and kinetic isotope effect of gas phase reaction as well as surface reactions. For example. Table 6 shows calculated activation energies and frequency factors for some elementary reactions involving atoms and radicals. The theoretical and experimental results agree with each very well. For detailed discussions on the relevant... 

Secondary isotope effects can sometimes be observed when vibrations of the reactive bond are coupled to nearby bonding involving isotopically substituted atoms. They are always very small and require very precise kinetic analysis. Sometimes it is possible to carry out reactions with and without substitution, using a differential technique (for instance using the two cuvettes of a spectrophotometer). The following elementary description of the kinetic isotope effect will provide some insight in terms of the theory of absolute reaction rates. For more profound treatments and references to fundamentals the texts mentioned above must be consulted (see also Westheimer, 1961 Jencks, 1969). 

The rate constants, kn, obtained at all pH values studied, were effectively identical. For anions lie and 2ie, the rate of reactions with O2 showed no significant change as the pH was decreased from 2 to 1. These were the first indications that the reaction is zero-order in [H+], namely, pH-independent. Solvent kinetic-isotope effect experiments were carried out in D2O at D+ concentrations corresponding to pH values of 2 and 7.2. The rate remained unchanged when the solvent H2O was replaced by D2O. That provided a second line of evidence that even at pH 2, well below the pAfa = 4.7 of protonated superoxide (HO2 ), proton transfer (PT) occurs after rate-limiting electron transfer to O2 (ETPT mechanism), rather than via concerted proton-electron transfer (CPET) [61-65], in which an electron and proton are transferred simultaneously in a single elementary step—see Sect. 12.3.2. 

When a standard solvent is rq>laced by deuterated one, for example, H2O by D2O, we have the isotope effect by solvent with a complex character. The kinetic isotope effect is characteristic of proton transfer reactions. It depends on the following factors type of the dissociated bond, change in enthalpy, and character of the elementary step of proton transfer (adiabatic or tunneling). For the adiabatic character of the reaction, the isotope effect is maximum for the thamally neutral reaction. The main contribution to the isotope effect is made by the difference in zero energies AE of stretching vibrations of the A—and A—D bonds. The kyjko values are presented below, the effect is due to ASq only for different types of A—bonds (T= 298 K). 

For skeletal isomerization of a nonlabeled and a monolabeled substrate at 240° C, the kinetic isotope effect (KIE) of the forward reaction is 0.80. For the reverse reaction, the KIE is 2. Determine the thermodynamic isotope efiect (TIE), assuming that such reactions are elementary ones. 

The investigation of enzymatic processes accompanied by a proton transfer, especially with the help of the kinetic isotope effect, is quite interesting from two complementary points of view. Firstly, it is essential to study the applicability of the quantum-mechanical theory of an elementary act to this very important class of biochemical processes, and thus create a certain experimental basis for further application and development of the theory for analyzing biological phenomena. Secondly, enzymatic reactions are found to be more convenient, to a certain extent, than ordinary chemical homogeneous reactions for the verification of certain concepts of the theory. 

Thus, the above analysis shows that the regularities of the kinetic isotope effect in enzymatic hydrolysis reactions confirm the basic results of the quantum-mechanical theory of an elementary act and contradict the results of the bond-stretching model. The concepts of the quantum-mechanical theory are found to be useful for discussing some specific aspects of the action of enzymes. Hence it is important to discuss the general corollaries of the theory as applied to enzymatic reactions and other biological processes. Some aspects of this problem will be discussed in the following section. 

One of the most important branches of theoretical organic chemistry deals specifically with the determination of these parameters. It should be noted that they cannot, with rare exceptions, be determined by experimental methods. Indeed, studying of reaction kinetics and isotopic effects, analysis of various correlational relationships of the steric structure of reaction products etc. give data which allow only indirect conclusions as to the overall reaction pathway since they all are invariably based on the studies of only the initial and the final state of every elementary step of the reaction. This situation may remind one of the black box direct access to the information therein is impossible, it can be deduced only through a comparison between the input and the output data. 

We have shown in this and the previous paragraph that methane formation occurs preferentially at a kinetic condition where the rate of CO dissociation is slow compared to methanation. This is the situation at nonreactive metals such as Ni or Pd and also at the dense (111) terraces of the fcc-type metals. So methane formed in excess to ASF distribution should not be sensitive to H/D isotope exchange. On the other hand, C2 formation occurs on sites with efficient CO dissociation, and a slow rate of C hydrogenation and chain growth termination. So in the slow elementary reaction steps of the FT reaction, hydrogen atom transfer plays an important role, which results in the observed inverse isotope effect [44, 45]. 

Discussions and studies of reaction mechanisms attempt to analyse the way in which a compound A is transformed into a compound B. Varying degrees of sophistication are attached to the phrase reaction mechanism but the aim is generally to define the reaction in terms of elementary steps and stereochemistry. In solution chemistry, the structures of compounds A and B will be known and mechanistic information may be deduced from kinetic studies, solvent effects, stereochemistry, isotopic labelling, and other slight structural modifications. 

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