INITIAL RATE PHASE

Initial Rate Assumption. The entire reaction progress curve, or at least a substantial portion of it, is typically required to accurately determine the rate constant for a first-order or second-order reaction. Nonetheless, one can frequently estimate the rate constant by measuring the velocity over a brief period (known as the initial rate phase) where only a small amount of reactant is consumed. This leads to a straight-line reaction progress curve see Fig. 6) which is drawn as a tangent to the initial reaction velocity. 

The relationship between reaction velocity and enzyme concentration (in the absence of self-association of the enzyme) should also be adjusted such that reaction rate is linearly related to catalyst concentration, [Etotai]- Initial rates typically fail to obtain if [Etotai] = 0-01 [Ajmitiai where [Ajinitiai is the initial substrate concentration. As a general rule, the substrate concentration will not have changed more than 5-10% of its value over the initial rate phase of the reaction. This rule-of-thumb applies only to thermodynamically favorable reactions, and investigators are well advised to limit substrate consumption to well below 5%. 

It was Henri who first proposed that enzyme catalysis depended on the formation of a transient complex of enzyme and substrate, followed by the breakdown i.e., chemical conversion) of bound substrate into product. Nonetheless, credit for derivation of the rate expression for the initial rate phase of one-substrate enzyme-catalyzed reactions is given to Michaelis and Menten. Both treatments gave the same general result ... 

The initial-rate phase may quickly end if one or more products accumulate to concentrations approaching the respective inhibition constants. In these cases, one may seek to minimize this problem by including an auxiliary enzyme (a) to remove product(s) or (b) to regenerate the substrate concentration. Ideally, the auxiliary enzyme should have a lower value for the product of the primary reaction than the corresponding value for the primary enzyme. See Chemical Kinetics ATP/GTP regeneration... 

Figure 1. Plot of the change in product concentration as a function of time of reaction. The initial rate phase corresponds to the early linear region, and a tangent to this early region has a slope corresponding to the initial reaction velocity. (For a detailed description of how one obtains rate constants using the initial rate assumption. See Chemical Kinetics.)...

INITIAL RATE PHASE Substrate dissociation rate,... 

Oxidation. The chlorine atom [22537-15-17-initiated, gas-phase oxidation of vinyl chloride yields 74% formyl chloride [2565-30-2] and 25% CO at high oxygen [7782-44-7], O2, to CI2 ratios it is unique among the chloro olefin oxidations because CO is a major initial product and because the reaction proceeds by a nonchain path at high O2/CI2 ratios. The rate of the gas-phase reaction of chlorine atoms with vinyl chloride has been measured (39). 

Table 3-11 gives the initial rate data [-d(B2Hg)/dt] reported for the gas phase reaetion of diborane and aeetone at 114°C BjHg -i-dMejCO —> 2(Me2CHO)2BH. If a rate expression is of the form Rate = PmcjCO determine n, m, and k. 

Mukherjee studied the gas phase equilibria and the kinetics of the possible chemical reactions in the pack-chromising of iron by the iodide process. One conclusion was that iodine-etching of the iron preceded chromis-ing also, not unexpectedly, the initial rate of chromising was controlled by transport of chromium iodide. Neiri and Vandenbulcke calculated, for the Al-Ni-Cr-Fe system, the partial pressures of chlorides and mixed chlorides in equilibrium with various alloys and phases, and so developed for pack aluminising a model of gaseous transport, solid-state transport, and equilibria at interfaces. 

A second way to simplify the behavior of a reaction is the method of initial rates. In this method, we measure the rate at the very beginning of the reaction for different concentrations. A set of experiments is done, changing only one initial concentration each time. Instead of measuring the concentration at many different times during the reaction, we make just one measurement for each set of concentrations. The reaction orders can be evaluated from the relationships between the changes in concentration and the changes in initial rates. We illustrate how this works using a gas-phase reaction of H2 with NO 2H2(g) -b 2NO(g) N2(g) + 2H2 0(g)... 

To check if this liquid-phase reaction is not controlled by diffusion, the reaction is repeated with different weights of catalysts. A linear correlation is found between the initial rate of reaction and the weight of catalyst, indicating that the rate is not controlled by external or internal diffusion. 

When a heptane solution of 5-Br-PADAP and an aqueous solution of Ni " " were stirred, the ligand in the organic phase was continuously consumed according to the complexation, but there was no extraction of the complex. The complex formed was completely adsorbed at the interface. On the other hand, in a toluene system the complex was extracted very slowly (Fig. 6). The complexation mechanism in the two solvent systems could be analyzed by taking into account the interfacial adsorption of the ligand. The next equation was derived for the initial rate of the consumption of HLq in the heptane system ... 

The above result was used as a ground-stone of the well known kinetic method of detection which was initially proposed by Myasnikov [75] more than 30 years ago. Above paper dealt with experimental comparison of the change of relative concentration of CH3 radicals in gaseous phase using the stationary values of electric conductivity and initial rate of its change. The experiment yielded perfect coincidence of the measured values. Using methyl radicals as example of adsorption it was established that the resolution of this method was better than 10 particles per cubic centimeter of the ambient volume [75, 76]. 

Figure 4.3 Product progress curves for an enzyme-catalyzed reaction in the absence (closed circles) and presence open circles) of an inhibitor at a concentration that reduces the reaction rate by 50%. Inset The initial velocity phase of these progress curves.

Note that the initial linear phase is observed only in sites containing a single contaminant. For sites contaminated with mixtures of contaminants there is a decreasing rate of removal from the beginning of the project due to the different volatility of the components. The more volatile constituents are extracted with a higher rate from all the phases, and as a consequence the total VOC content of extracted air decreases constantly with time. This effect should be considered during the design phase. 

Table 1 illustrates the effect of hydrogen pressure on the selectivity to MIBK based on the initial rate of MIBK production and the rate of IPA production. Palladium gives very high selectivity to MIBK, typically in excess of 93% with the selectivity improving significantly with decreasing pressure. This result is of particular importance since the CD process for MIBK production is carried out at relatively low pressure (< IMPa). In contrast, alternative one-step processes for MIBK production are carried out in the liquid phase in trickle-bed reactors at pressures as high as 10 MPa. 

The following initial rate data [ —d(B2H6)/ dt] were reported for the gas-phase reaction of diborane and acetone at 114 °C. 

The kinetics and mechanisms of the C —> G transition in a concentrated solution of PS-fr-PI in the PS-selective solvent di-n-butyl phthalate was studied [137,149]. An epitaxially transformation of the shear-oriented C phase to G, as previously established in melts [13,50,150], was observed. For shallow quenches into G, the transition proceeds directly by a nucleation and growth process. For deeper quenches, a metastable intermediate structure appears, with scattering and rheological features consistent with the hexag-onally perforated layer (PL) state. The C -> G transition follows the same pathways, and at approximately the same rates, even when the initial C phase is not shear-oriented. 

The reduction steps on active Co sites are strongly affected by activated hydrogen transferred from promoter metal particles (Pt and Ru). Several indications for the existence and importance of hetero-bimetallic centers have been obtained.63 [Cp Co(CO)2] in the presence of PEt3 and Mel catalyzes the carbonylation of methanol with initial rates up to 44 mol L 1 h 1 before decaying to a second catalytic phase with rates of 3 mol L 1 h-1.64 HOAc-AcOMe mixtures were prepared by reaction of MeOH with CO in the presence of Co(II) acetate, iodine, and additional Pt or Pd salts, e.g., [(Ph3P)2PdCl2] at 120-80 °C and 160-250 atm.65... 

Substituting expressions (Eq. 78) for and w2(q) into relationships Eqs. 73 and 74 we get a closed set of kinetic equations describing radical copolymerization in the framework of the simplest model in hand. The values of the rates of initiation in phases 1 and 2 entering in Eq. 74 are determined as follows... 

X-ray powder diffractometry can be used to study solid state reactions, provided the powder pattern of the reactant is different from that of the reaction product. The anhydrous and hydrated states of many pharmaceutical compounds exhibit pronounced differences in their powder x-ray diffraction patterns. Such differences were demonstrated earlier in the case of fluprednisolone and carbamazepine. Based on such differences, the dehydration kinetics of theophylline monohydrate (CvHgN H20) and ampicillin trihydrate (Ci6H19N304S 3H2O) were studied [66]. On heating, theophylline monohydrate dehydrated to a crystalline anhydrous phase, while the ampicillin trihydrate formed an amorphous anhydrate. In case of theophylline, simultaneous quantification of both the monohydrate and the anhydrate was possible. It was concluded that the initial rate of this reaction was zero order. By carrying out the reaction at several... 

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