Rate constants, conversion factors

The usefulness of a technique is not, of course, related solely to the maximum time resolution or observable rate constant other factors such as versatility, precision, convenience of operation and availability can all be important. The stopped-flow method, for instance, which is the most widely used of all, owes its popularity to its adaptability, speed and convenience, robustness, and wide availability it is suited not to the fastest reactions but to those with rate constants less than about 10 M s . Conversely, fluorescencequenching methods are applicable only to very fast reactions, for which however they are very powerful and flash techniques, uniquely, can follow changes down to 10 s. The availability of commercial equipment, and its cost, may also be important, especially where sophisticated electronic instrumentation is required. 

For example, the rate constant of the collinear reaction H -f- H2 has been calculated in the temperature interval 200-1000 K. The quantum correction factor, i.e., the ratio of the actual rate constant to that given by CLTST, has been found to reach 50 at T = 200 K. However, in the reactions that we regard as low-temperature ones, this factor may be as large as ten orders of magnitude (see introduction). That is why the present state of affairs in QTST, which is well suited for flnding quantum contributions to gas-phase rate constants, does not presently allow one to use it as a numerical tool to study complex low-temperature conversions, at least without further approximations such as the WKB one. ... 

Do not infer from the above discussion that all the catalyst in a fixed bed ages at the same rate. This is not usually true. Instead, the time-dependent effectiveness factor will vary from point to point in the reactor. The deactivation rate constant kj) will be a function of temperature. It is usually fit to an Arrhenius temperature dependence. For chemical deactivation by chemisorption or coking, deactivation will normally be much higher at the inlet to the bed. In extreme cases, a sharp deactivation front will travel down the bed. Behind the front, the catalyst is deactivated so that there is little or no conversion. At the front, the conversion rises sharply and becomes nearly complete over a short distance. The catalyst ahead of the front does nothing, but remains active, until the front advances to it. When the front reaches the end of the bed, the entire catalyst charge is regenerated or replaced. 

The above explanation of autoacceleration phenomena is supported by the manifold increase in the initial polymerization rate for methyl methacrylate which may be brought about by the addition of poly-(methyl methacrylate) or other polymers to the monomer.It finds further support in the suppression, or virtual elimination, of autoacceleration which has been observed when the molecular weight of the polymer is reduced by incorporating a chain transfer agent (see Sec. 2f), such as butyl mercaptan, with the monomer.Not only are the much shorter radical chains intrinsically more mobile, but the lower molecular weight of the polymer formed results in a viscosity at a given conversion which is lower by as much as several orders of magnitude. Both factors facilitate diffusion of the active centers and, hence, tend to eliminate the autoacceleration. Final and conclusive proof of the correctness of this explanation comes from measurements of the absolute values of individual rate constants (see p. 160), which show that the termination constant does indeed decrease a hundredfold or more in the autoacceleration phase of the polymerization, whereas kp remains constant within experimental error. 

Kinetic Term The designation kinetic term is something of a misnomer in that it contains both rate constants and adsorption equilibrium constants. For thfe cases where surface reaction controls the overall conversion rate it is the product of the surface reaction rate constant for the forward reaction and the adsorption equilibrium constants for the reactant surface species participating in the reaction. When adsorption or desorption of a reactant or product species is the rate limiting step, it will involve other factors. 

If the standard potential of the A/B couple, B, is known independently, we obtain the rate constant kc for decomposition of the transient intermediate B. If not, kc can be obtained when the following conditions are achieved. Upon increasing the mediator concentration, while keeping the excess factor, y = C /Cp, constant, the system tends to pass from kinetic control by the forward electron transfer step to control by the follow-up reaction (Figure 2.21). An ideal situation would be reached if the available concentration range would allow perusal of the entire intermediary variation between the two limiting situations. More commonly encountered situations are when it is possible to enter the intermediary zone coming from the forward electron transfer control zone or, conversely, to pass from the intermediary zone to the follow-up reaction control zone. In both cases the values of ke and Ke /kc can... 

An interesting question then arises as to why the dynamics of proton transfer for the benzophenone-i V, /V-dimethylaniline contact radical IP falls within the nonadiabatic regime while that for the napthol photoacids-carboxylic base pairs in water falls in the adiabatic regime given that both systems are intermolecular. For the benzophenone-A, A-dimethylaniline contact radical IP, the presumed structure of the complex is that of a 7t-stacked system that constrains the distance between the two heavy atoms involved in the proton transfer, C and O, to a distance of 3.3A (Scheme 2.10) [20]. Conversely, for the napthol photoacids-carboxylic base pairs no such constraints are imposed so that there can be close approach of the two heavy atoms. The distance associated with the crossover between nonadiabatic and adiabatic proton transfer has yet to be clearly defined and will be system specific. However, from model calculations, distances in excess of 2.5 A appear to lead to the realm of nonadiabatic proton transfer. Thus, a factor determining whether a bimolecular proton-transfer process falls within the adiabatic or nonadiabatic regimes lies in the rate expression Eq. (6) where 4>(R), the distribution function for molecular species with distance, and k(R), the rate constant as a function of distance, determine the mode of transfer. 

Intersection region, but small enough so that It may be neglected In calculating the height of the potential barrier (Hab Eth) Under these conditions the rate constant for the conversion of the precursor to the successor complex Is Independent of the magnitude of the electronic coupling and depends only on the nuclear factor... 

Using the various simplifications above, we have arrived at a model for reaction 11.9 in which only one step, the chemical conversion occurring at the active site of the enzyme characterized by the rate constant k3, exhibits the kinetic isotope effect Hk3. From Equations 11.29 and 11.30, however, it is apparent that the observed isotope effects, HV and H(V/K), are not directly equal to this kinetic isotope effect, Hk3, which is called the intrinsic kinetic isotope effect. The complexity of the reaction may cause part or all of Hk3 to be masked by an amount depending on the ratios k3/ks and k3/k2. The first ratio, k3/k3, compares the intrinsic rate to the rate of product dissociation, and is called the ratio of catalysis, r(=k3/ks). The second, k3/k2, compares the intrinsic rate to the rate of the substrate dissociation and is called forward commitment to catalysis, Cf(=k3/k2), or in short, commitment. The term partitioning factor is sometimes used in the literature for this ratio of rate constants. 

All of the kinetic resolutions described above have been characterized in terms of yields and ee values of the recovered substrate and the product. In principle the efficiency of a kinetic resolution can also be described by the selectivity factor S [lu], the ratio of the rate constants for the reactions of the enantiomers of the substrate with the catalyst. For a Pd-catalyzed kinetic resolution of an allylic substrate obeying first-order kinetics in regard to the reaction of the substrate with the catalyst (unimolecularity) S can be calculated according to Eq. (1), which contains as variables the conversion (c) and the ee value of the substrate (ee ). 

Analogous parahydrogen conversion and deuterium exchange reactions, catalyzed by NH2, have been observed in liquid ammonia (Wilmarth and Dayton, 61). The kinetics are of the same form as those of the OH -cat-alyzed reaction in water and the mechanism is open to similar interpretations. The NH2 -catalyzed reaction is much faster, its rate constant at —50° being 10 times that of the OH -catalyzed reaction at 100°. The assumption of equal frequency factors for the two reactions leads to a calculated activation energy for the NH2 -catalyzed reaction of about 10 kcal. This low value has been attributed to the much greater base strength of NH2 relative to OH . The results provide some support for the hydride ion mechanism. 

Divalent counterions Kinetic measurements using mono- and bifunctional initiators and Ba++ as the counterion in THF were reported by Mathis and Francois (37 ), who applied adiabatic calorimetry. At -7o°C no termination is found and conversion follows first order with respect to monomer concentration. The rate constants do not depend on the concentration of living ends, indicating the absence of free anions. The rate constants are smaller by a factor of 2o as compared with those measured with monovalent counterions. However, they are smaller by a factor of 3 only, compared with those calculated for chains which are intramolecular ly associated (Na+, counterion). The activation energy for PMMA Ba in THF is equal to that for monovalent counterions, but the frequency exponent is smaller by about 1.5 units, reflecting the fact that the transition state for the dianionic ion pair has higher steric requirements. 

Assuming a fast pre-equilibrium with respect to k<-at, Km is essentially the dissociation constant of the encapsulated neutral substrate. The specificity factor k JKj can be used to compare the efficiency of hydrolysis by 1 for the two substrates. This constant corresponds to the second-order proportionality constant for the rate of conversion of the pre-formed host-guest complex to the product. Interestingly, 69 and 72 have specificity factors of 0.37 and 0.50 m s, respectively, showing that the more hydrophobic 72 is more efficiently hydrolyzed by 1. 

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