Rate-determining step Arrhenius plot

Pai Vemeker and Kannan [1273] observe that data for the decomposition of BaN6 single crystals fit the Avrami—Erofe ev equation [eqn. (6), n = 3] for 0.05 < a < 0.90. Arrhenius plots (393—463 K) showed a discontinuous rise in E value from 96 to 154 kJ mole-1 at a temperature that varied with type and concentration of dopant present Na+ and CO2-impurities increased the transition temperature and sensitized the rate, whereas Al3+ caused the opposite effects. It is concluded, on the basis of these and other observations, that the rate-determining step in BaN6 decomposition is diffusion of Ba2+ interstitial ions rather than a process involving electron transfer. 

Finally, yet another issue enters into the interpretation of nonlinear Arrhenius plots of enzyme-catalyzed reactions. As is seen in the examples above, one typically plots In y ax (or. In kcat) versus the reciprocal absolute temperature. This protocol is certainly valid for rapid equilibrium enzymes whose rate-determining step does not change throughout the temperature range studied (and, in addition, remains rapid equilibrium throughout this range). However, for steady-state enzymes, other factors can influence the interpretation of the nonlinear data. For example, for an ordered two-substrate, two-product reaction, kcat is equal to kskjl ks + k ) in which ks and k are the off-rate constants for the two products. If these two rate constants have a different temperature dependency (e.g., ks > ky at one temperature but not at another temperature), then a nonlinear Arrhenius plot may result. See Arrhenius Equation Owl Transition-State Theory van t Hoff Relationship... 

They therefore concluded that several different rate-determining steps were involved in the deposition. Figure 3.6 shows the dependence of the deposition rate on the concentration of the reactants (Cd, thiourea, ammonia, and pH—the last varied through introduction of ammonium ion) (a) as well as an Arrhenius plot of the deposition (b) for the CdS deposition. From the kinetic data, they deduced the hydroxide-complex-decomposition mechanism, given earlier in Eqs. (3.50) and (3.51) and, more specifically, as... 

The rate constant, k, for most elementary chemical reactions follows the Arrhenius equation, k = A exp(— EJRT), where A is a reaction-specific quantity and Ea the activation energy. Because EA is always positive, the rate constant increases with temperature and gives linear plots of In k versus 1 IT. Kinks or curvature are often found in Arrhenius plots for enzymatic reactions and are usually interpreted as resulting from complex kinetics in which there is a change in rate-determining step with temperature or a change in the structure of the protein. The Arrhenius equation is recast by transition state theory (Chapter 3, section A) to... 

The Arrhenius plot shown in Figure 5A represents a rate determining step during the H/D exchange with an apparent activation energy of Eapp=55 kJ/mol. According to the mechanism proposed above, the selectivity is determined in the subsequent mechanisms following the adsorption. 

The characteristic Arrhenius plots predicted by this approach have been reported on a number of occasions for reactions involving the transfer of a proton to or from a carbon atom in the rate-determining step (Hulett, 1964 Caldin and Kasparian, 1965 and references there cited). It is also encouraging to find that the difference between the rates observed at the lower temperatures and those calculated at the same temperatures from the linear portion of the Arrhenius plot are always consistent with reasonable values for the barrier width, 2a. However, concurrent reaction via two different mechanisms having different activation energies (see p. 123) has been considered to account for some of the observations previously interpreted in terms of the tunnel effect (Jones, 1965). 

The effect of temperature on the catalytic reaction is most easily determined with Arrhenius plots. Such plots of the turnover rate, or of the rate of individual steps in the catalytic reaction (e.g., kacyiation, kdegiycosyiation) can be very useful in comparisons between the catalytic reaction in the cryosolvent at subzero temperature and the reaction under normal conditions. 

Figure 2B. Arrhenius plot for the reaction of fi-galactosidase with p-nitro-phenyl-fi-D-galactoside in 60% dimethyl sulfoxide, pH 7.0. Rate-determining step is formation of the galactose-enzyme intermediate. (18)...

The form of Eq. 98 is typical of equations of processes involving simultaneous surface reactions and volume diffusion. Thus it may be believed that at low concentrations of oxidant, the oxidation process is the rate-limiting step, and that at high concentrations, the supply of the oxidant to the surface is the rate-determining step. Information about the rate-determining step can also be obtained from the value of activation energy for dissolution calculated from Arrhenius-type plots of etch-rate data at different temperatures, and from the effect of stirring on etch rates (see also Sec.2.2). 

It is perhaps noteworthy that the use of the term anti-Arrhenius behavior in such reaction systems is probably inappropriate or misleading. When one says that the rate constants, k, follow anti-Arrhenius behavior, it apparently means that k corresponds to a reaction step that has negative energy of activation and by definition and physical reality, energy of activation can never be negative for any elementary reaction step. The apparent anti-Arrhenius plots are obtained when the rate constants used to construct the Arrhenius plots are the functions of various rate and equilibrium constants for various irreversible and reversible reaction steps in the overall reactions. It is almost certain for most micellar-mediated reactions that micellar effects on reaction rates are not caused by the decrease or increase in the energy of activation for the rate-determining steps of these reactions. For example, reported anti-Arrhenius behavior of reaction rate ... 

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