Rate-determining step, definition

To clarify the mechanism of reaction of P-450, it is crucial to characterize the reactive intermediates in the rate-determining step. Definitive evidence for an electron-transfer mechanism (C in Scheme 2) for the 7V-demethylation of N,N-dimethylanilines has been obtained by direct observation of the reduction of the high-valent species responsible for P-450 catalysis [96]. For peroxidase, an oxoferryl porphyrin 7r-radical cation, compound I ([(P)Fe =0] "), has been well characterized as the species equivalent to the proposed active intermediate of P-450 [97-103]. Compound I of horseradish peroxidase (HRP) can be readily generated by chemical oxidation of HRP [100-103]. The involvement of the electron-transfer process of compound I in the oxidation of several amines catalyzed by HRP was... 

Much of the kinetic work has been concerned with the oxidation of isopropyl alcohol to acetone in aqueous sulphuric or acetic acids. The rate-determining step definitely involves the breaking of a carbon-hydrogen bond, as isopropyl alcohol is oxidised 6-7 times faster than its 2-deutero derivative . At all acidities, the rate of oxidation shows a first-order dependence on both the concentration of HCr04 and the alcohol, but the dejiendence on [H] varies. In dilute acidic solution the rate is proportional to [H] , to [H] in more concentrated solution and to Ho in 20-60% aqueous sulphuric acid . These observations are consistent with two mechanisms (i) a bimolecular electron transfer process (218) ,... 

These similarities indicate that the mechanism for (188) is apparently exactly the same as that for (135) except that the attack of water occurs on a sulfonyl group in (188), instead of on a sulfinyl group as in (135), and that a proton transfer is also part of the rate-determining step of the spontaneous hydrolysis of cr-disulfones. It may be recalled that in the case of the spontaneous hydrolysis of sulfinyl sulfones we determined that the purpose of the proton transfer was either to assist the attack of a water molecule on the substrate (136) or to assist the departure of the ArSOz group (137), but could not make a definite decision between the two alternatives from the information available. Thus the mechanism for the spontaneous hydrolysis of cr-disulfones is either as in (189) (where attack of water on a sulfonyl group is aided by the removal of a... 

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... 

Chronopotentiometry, galvanostatic transients, 1411 as analytical technique, 1411 activation overpotential, 1411 Clavilier, and single crystals, 1095 Cluster formation energy of, 1304 and Frumkin isotherm, 1197 Cobalt-nickel plating, 1375 Cold combustion, definition, 1041 Cole-Cole plot, impedance, 1129, 1135 Colloidal particles, 880, 882 and differential capacity, 880 Complex impedance, 1135 Computer simulation, 1160 of adsorption processes, 965 and overall reaction, 1259 and rate determining step, 1260... 

These mechanistic patterns, which are of course fundamental to all aspects of organic chemistry, will be discernible in the syntheses that are discussed. Although space limitations preclude explicit discussion in most instances, the reader can, by consideration of the mechanism of ring closure, identify the nature of the bond-forming steps. Frequently, the order in which the steps occur is considerably less certain and relatively few of the synthetic methods have been subjected to the definitive mechanistic studies that would be required to determine relative rates, specify the position of participating equilibria, or even identify rate-determining steps. 

Photolysis of allyl iodide in thiophene gives a mixture of 2-allyl- (63.8%) and 3-allyl-(36.2%) thiophenes (77JOC1570). This is in contrast to homolytic phenylation, where almost exclusive 2-phenylation takes place (Section 3.14.2.9). It has been suggested that the rate-determining step in the allyl substitution reaction has a small but definite charge-transfer character. 

There is some confusion about the various theoretical and experimental distinctions between the Sjj 1 and SN 2 mechanisms. Since molecularity is the number of molecules necessarily undergoing covalency change during the rate determining step (Ingold, 1969), the unimolecular reaction (SN 1) involves rate determining heterolysis of the R—X bond (kx, Fig. 2) without assistance from nucleophilic attack. This definition is independent of the nature of the first intermediate, which in many cases is probably a contact ion pair rather than a free (i.e. symmetrically solvated) carbocation (see... 

In Fig. 8 the calorimetric curve of a typical miniemulsion polymerization for 100-nm droplets consisting of styrene as monomer and hexadecane as hydrophobe with initiation from the water phase is shown. Three distinguished intervals can be identified throughout the course of miniemulsion polymerization. According to Harkins definition for emulsion polymerization [59-61], only intervals I and III are found in the miniemulsion process. Additionally, interval IV describes a pronounced gel effect, the occurrence of which depends on the particle size. Similarly to microemulsions and some emulsion polymerization recipes [62], there is no interval II of constant reaction rate. This points to the fact that diffusion of monomer is in no phase of the reaction the rate-determining step. 

In this case, the apparent activation energy is not equal to the activation energy of the rate-determining step. By definition, the activation energy for elementary step 2 equals... 

These rate determining steps are discussed in detail in Chapter 5. Using the relation between the flux J and the change in core radius given in equations (5.36) and (5.37) with the definitions of the fluxes for mass and heat transfer equations (5.27), (5.28), (5.31), (5.32) (with equations (5.33) and (5.34)), it is possible to determine the time dependence of conversion, Xb ... 

Although Eqs. 4D and 5D look similar, the transition from one to the other is by no means trivial and is the subject of detailed discussion later. Here we shall limit ourselves to a brief discussion of two points. First, the charge on the particle z, which appears in Eq. 4D has been dropped from Eq. 5D, since it is tacitly assumed that electrode reactions occur by the transfer of one electron at a time. Tlius, for any rate-determining step, the value of z is always taken as unity. Second, the parameter P, called the symmetry factor, has been introduced. By definition it can take values from zero to unity,... 

Now we come to the concept of quasi-equilibrium. If there is a distinct rate-determining step in a reaction sequence, then all other steps before and after it must be effectively at equilibrium. This comes about because the overall rate is, by definition, very slow compared to the rate at which each of the other steps could proceed by itself, and equilibrium in these steps is therefore barely disturbed. To see this better, consider the specific example given earlier for chlorine evolution. Assume, for the sake of argument, that the values of the exchange current density i for steps 8F and 9F are 250 and 1.0 mA/cm, respectively. Assume now that we apply a current density of 0.5 mA/cm. We can calculate the overpotential corresponding to each step in the sequence, using Eq. 6E, namely... 

Although catalysis in electrochemical reactions was probably first specifically recognized by Frumkin at a conference in Leningrad in 1939, a first and perceptive definition of electrocatalysis seems to have been by Busing and Kauzmann in 1952 (72) in terms of the ability of various electrode surfaces to promote the velocity of the rate-determining step of the reaction. In this respect, their definition preceded the common use of this term in North America in the 1960s by some years, when it was applied to the activities of fuel-cell electrodes by Liebhafsky (7i). 

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