Kinetic concentration method

Many enzymes, which transform two different substrates to one or two product(s), could be characterized using equation (8.1), if the concentration of one substrate is high enough to saturate the enzyme. If the two substrate molecules bind to the enzyme independently from each other, the calculated KM values will reflect the affinity of the substrate to the complex of the other substrate molecule and the enzyme. Further, the Vj ax " ill characterize the rate of the reaction at the excess concentrations of both substrates (the enzyme is saturated by both substrates). However, this could be just a coarse approximation, and there are kinetic analytical methods for a more exact characterization of such two-substrate enzymic reactions, which could run on different ways e.g. random Bi-Bi, ping-pong Bi Bi mechanisms (Keleti, 1986 Fersht, 1985 Segel, 1975 Comish-Bowden, 1995). 

On the other hand, electrode kinetic studies are at a disadvantage compared with investigations of homogeneous kinetics because concentrations are not uniform and surface concentrations can rarely be measured directly (optical methods can sometimes provide direct measurement of the product concentration [1]). This means that the converse situation to that in classical homogeneous kinetics exists in electrode kinetics concentration information needs to be inferred from reaction rates. 

For the former case (Equation (3)), which is environmentally more relevant for low contamination situations, the rate obeys first-order kinetics with respect to substrate and biomass (second-order overall), whereas in the latter case (Equation (4)), the kinetics have a first-order relationship to biomass but are independent of substrate concentration. Methods for measuring of biomass, B, have varied widely, and, for studies involving mixed populations, in which only a fraction of the organisms can degrade the substrate, a means for quantifying the responsible fraction is not available. 

Various types of possible interactions between reactions are discussed. Some of them are united by the general idea of chemical reaction interference. The ideas on conjugated reactions are broadened and the determinant formula is deduced the coherence condition for chemical interference is formulated and associated phase shifts are determined. It is shown how interaction between reactions may be qualitatively and quantitatively assessed and kinetic analysis of complex reactions with under-researched mechanisms may be performed with simultaneous consideration of the stationary concentration method. Using particular examples, interference of hydrogen peroxide dissociation and oxidation of substrates is considered. 

It is common knowledge that when intermediate products are highly reactive particles, a stationary mode is set in the system in a short time. In this mode concentration of active intermediate compounds is accepted as stationary, i.e. the difference in rates of their accumulation and consumption is very low compared with the reaction rates. Thus, the intermediate product concentration in the conjugated reaction may be determined by the method of stationary concentrations. On the other hand, kinetics of conjugated reactions may be described by an expression deduced from the determinant equation (2.25) not using the stationary concentration method. 

Basing on the mechanism suggested and with the help of the stationary concentration method, the following kinetic equation of the reaction rate was deduced ... 

On the other hand, the determinant equation (5.28) allows the study of complex reaction kinetics with incompletely studied mechanisms neglecting the assumptive stationary concentration method. Let us assume that the most probable mechanism of methane oxidation to methanol with hydrogen peroxide is unknown. Then equations (5.29) and (5.30) should be presented in the form that discloses the conjugation mechanism of these two reactions ... 

Finally, concordant results have been obtained from a kinetic study of the iodination of acetophenone and acetone at very low iodine concentration (Verny-Doussin, 1979). The procedure used is similar to that followed for the determination of equilibrium constants for enol formation by the kinetic-halogenation method, i.e. second-order rate constants were measured under conditions such that halogen additions to enol and enolate are rate-limiting (43). Under these conditions, the experimental kn-values can be expressed by... 

Recently, the present author (Toullec and Verny-Doussin, 1980) obtained a concordant value for the equilibrium constant of (65 L = H) for [83, n — 3] from kinetic data on amine-catalysed iodination of acetone at low iodine concentrations. The principle of this determination is similar to that described for estimation of the keto-enol equilibrium constants by the kinetic halogenation method (see p. 48). At low iodine concentrations ( 10-6 mol dm-3), the enamine pathway is preferred [see (61)] and iodination of the enamine is rate-limiting. Rate measurements, in a pH range in which only the monoprotonated and diprotonated forms of the diamine exist, made it possible to determine the second-order rate constants k u which include the equilibrium constants, for interconversion of the ketone and protonated enamine... 

The PPC, required by the FDA Guideline, is a sample of the test material that contains a concentration of endotoxin that is double the labeled sensitivity of the LAL reagent.The PPC must be tested with each sample in a Limits test or kinetic LAL assay to ensure that a result is valid and free of interference. The most accurate and reliable technique is the hot spike method that requires adding 10 pi of endotoxin standard to the reaction vessel (tube or well) before addition of LAL. The gel clot method requires the addition of 10 pi of 20 A to the reaction mixture. Kinetic methods require the addition of 10 pi of a standard, 10 times greater than the spike concentration, to the wells or tubes designated as PPCs. Only inhibition is seen in gel-clot Limits tests, whereas both inhibition and enhancement are seen in kinetic LAL methods. 

Sm(III) dissociation from the polyelectrolytes occurred by multiple first-order processes. To determine the number of first-order processes and estimate rate constants and the concentration of metal dissociating by each process in the reaction, a kinetic spectrum method was used (75). The kinetic spectrum H(k,t) is defined as the following distribution function ... 

Because the rate of creation of supersamration in reactive crystallization is dependent on the reaction kinetics, control of particle size can be difficult because slowing down the reaction is often difficult or undesirable. For compounds with fast crystallization kinetics, traditional methods such as reduced concentration and temperamre may help, but the range of improvement may not be significant. 

The effect of pore size on the kinetics of sorption of large molecules on carbon has been studied. Rapid breakthrough and low-concentration factors of organic compounds have been attributed to slow sorption kinetics (Yous-sefi and Faust, 1980). McCreary and Snoeyink (1980) report that sorptive capacity decreased with increasing-molecular-weight fractions, and that humic acid was slower to attain equilibrium than the smaller fulvic acid. Slow sorption kinetics particularly hamper column-concentration methods, and the choice of proper flow rate is important. 

Neiman (117) worked out an interesting kinetic tracer method for determining the reaction kinetics from variations in radioactivity and concentration of intermediates with time. When a substance A is converted into X, and then X is converted into B (A X -> B), then the concentration and specific radioactivity of X may be determined at any time by labeling A or X and adding the labeled substance to the reactant mixture. The rates of formation and consumption kx follow the equation... 

Greiner [148] has reported detailed quantitative rate data for a series of HO transfer reactions (see Table 14) studied by the kinetic spectroscopic method. The source of HO radicals was the far ultraviolet flash photolysis of HjO, rather than H Oj which was found to undergo rapid reaction with HO to yield HOj radicals. The concentration of HO was monitored by their absorption at 3090 A. 

The automation or semi-automation of a conventional manual method by FIA often results in a decrease in the number and level of interferents. Thus, in the FIA version of the determination of cyanide by the classical reaction with barbituric acid/chloramine T, nitrite and sulphide pose no Interference at concentrations ten times as high as that of the analyte, which is otherwise adversely affected by the presence of both interferents in the manual method [48], The greater tolerance to foreign species in FIA methods can be generally attributed to their kinetic character, so that undesirable side reactions scarcely have the opportunity to develop to an appreciable extent in such a short interval as the residence time. The tolerance to extransous species is even more remarkable in kinetic FIA methods based on the measurement of a reaction rate (stopped-flow). Optimization of FIA systems as regards selectivity is a relatively simple task on account of their enormous versatility. 

The following kinetic equation, based on the scheme above, can be obtained using the steady-state concentrations method and assuming reaction (VII. 1)... 

The concept of employing reaction-rate parameters to determine the initial analytical concentration of reactants dates back over 50 to 60 years to the early literature in biochemistry, radiochemistry, and gas-phase diffusion furthermore, among all the analyses performed in all the laboratories around this country, the number carried out by kinetic-based methods probably exceeds that carried out by thermodynamic methods and direct instrumental measurement combined. This comes as a surprise at first, until one considers the large numbers of enzymatic and other determinations done on multi-channel autoanalyzers used in clinical laboratories. Most of these rapid automated instruments use kinetic methods. 

In order to determine the initial concentration of a desired species by kinetic-based methods, the rate of the chemical reaction must be measured by monitoring the concentration of at least one of the reactants or products as a function of time. Chemical methods (titration) or physical methods (spectrophotometry or conductivity) can be employed. If chemical methods are used, the rates of reaction must be quite slow or, if the reaction has suitable properties, quenching methods can be utilized when some reaction occurs at a significantly fast rate. Continuous measurement of the reaction rate is possible by physical, but not by chemical, methods the reaction rates observable are limited only by the response times of the instruments. 

Another modification of the catalytic kinetic spectrophotometric method has been established for the determination of iodine using the principle that potassium periodate oxidize rhodamine B (RhB) to discolor and 1 has a catalytic effect on the reaction. The absorbance difference (AA) is linearly related with the concentration of iodine in the range of 0 - 2.6 pg/mL and fits the equation AA = 0.1578 C(C pg/mL) + 0.0052, with a regression coefficient of 0.9965. The detection limit of the method is 7.10 ng/mL. The method was used to determine iodine in kelp, potato, tap water, and rain water samples. The relative standard deviation of 13 replicate determinations was 1.81-2.10%. The recovery of the standard addition of the method was 96.2-99.2% (Zhaiet al., 2010). 

Several kinetic spectrophotometric methods have been developed for selenium determination. The catalytic effect of Se(IV) on the reduction of thionine by sulfide ions has been explored. The reaction is monitored spectrophotometrically by following the decrease in absorbance at 598 nm, and the method has an LOD of 5ngml . Another method is based on the catalytic effect of selenium on the oxidation of methyl yellow by hydrogen peroxide in a nitric acid medium. It is monitored by the loss of the red color of methyl yellow. The method is extremely sensitive, with the possibility of measuring concentrations of 0.2ngml . Selenium can be also determined based on its effect on the oxidation reaction of methyl orange with bromate in acidic media. 

In the application of chemical kinetics, a formal kinetic evaluation method has been proposed (Schmid and Sapunov, 1982). An operation scheme is illustrated in Fig. 5.16 it uses two properties of c/t curves as decision criteria, called invariance I and invariance II. These properties concern the linear transformation capability of first- and second-order reactions. Kinetic curves with various initial concentrations Cj o can be superimposed over arbitrary standard curves (cj o)s by multiplying ordinates by ratios (cj o)s/Ci,o tbe case... 

Sorption kinetics Permeation methods Concentration-distance curves... 

Let us carry out a check of the steady-state principle. For this purpose, let us calculate the time dependence of the end product formation rate from the relationships obtained by accurate solving the direct kinetic problem (see Table 2.1). Next, let us compare the result with the calculations from obtained formula (2.9). The corresponding plots represented in Fig. 2.17 show that the behaviour of the both curves coincide after less than 0.5 s at given values of the rate constants satisfying the condition ki > k. This indicates applicability of the steady-state concentration method to the considered model of the consecutive reaction. 

The steady-state concentration method is widely used for an analysis of kinetic mechanisms of complex reactions. In particular, this method plays an important... 

The rate constant and the exponents (orders of reaction) can be determined in the usual way using, for instance, initial rate data or the excessive concentration method (Levenspiel 1972). From the power law thus determined, one may postulate a L-H rate expression that in turn can be verified kinetically up to a certain point. As discussed in Chapter 2, it may suffice just to use the power law rate expression in some cases. 

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