Concentration consecutive reaction

For the consecutive reactions 2A B and 2B C, concentrations were measured as functions of residence time in a CSTR. In all experiments, C o = 1 lb moPfF. Volumetric flow rate was constant. The data are tabulated in the first three columns. Check the proposed rate equations,... 

Present research is devoted to investigation of application of luminol reactions in heterogeneous systems. Systems of rapid consecutive reactions usable for the determination of biologically active, toxic anions have been studied. Anions were quantitatively converted into chemiluminescing solid or gaseous products detectable on solid / liquid or gas / liquid interface. Methodology developed made it possible to combine concentration of microcomponents with chemiluminescence detection and to achieve high sensitivity of determination. 

The formation of resins, tarry matter by consecutive reaction, is prevalent in organic reactions. Figure 3-13a shows the time variations in the concentrations of A, B, and C as given by these equations. The concentration of A falls exponentially, while B goes through a maximum. Since the formation rate of C is proportional to the concentration of B, this rate is initially zero and is a maximum when B reaches its maximum value. 

Consecutive reactions involving one first-order reaction and one second-order reaction, or two second-order reactions, are very difficult problems. Chien has obtained closed-form integral solutions for many of the possible kinetic schemes, but the results are too complex for straightforward application of the equations. Chien recommends that the kineticist follow the concentration of the initial reactant A, and from this information rate constant k, can be estimated. Then families of curves plotted for the various kinetic schemes, making use of an abscissa scale that is a function of c kit, are compared with concentration-time data for an intermediate or product, seeking a match that will identify the kinetic scheme and possibly lead to additional rate constant estimates. 

The procedure for solving the relations between concentrations has been used in kinetic studies of complex catalytic reactions by many authors, among the first of them being Jungers and his co-workers 17-20), Weiss 21, 22), and others [see, e.g. 23-25a). In many papers this approach has been combined with the solution of time dependencies, at least for some of the single reactions. Also solved were some complicated cases [e.g. six-step consecutive reaction 26,26a) 3 and some improvements of this time-elimination procedure were set forth 27). The elimination of time is... 

Competition reactions ad eosdem, 106 ad eundem, 105 (See also Reactions, trapping) Competitive inhibitor, 92 Complexation equilibria, 145-148 Composite rate constants, 161-164 Concentration-jump method, 52-55 Concurrent reactions, 58-64 Consecutive reactions, 70, 130 Continuous-flow method, 254—255 Control factor, 85 Crossover experiment, 112... 

At a fixed temperature, a single, reversible reaction has no interior optimum with respect to reaction time. If the inlet product concentration is less than the equilibrium concentration, a very large flow reactor or a very long batch reaction is best since it will give a close approach to equilibrium. If the inlet product concentration is above the equilibrium concentration, no reaction is desired so the optimal time is zero. In contrast, there will always be an interior optimum with respect to reaction time at a fixed temperature when an intermediate product in a set of consecutive reactions is desired. (Ignore the trivial exception where the feed concentration of the desired product is already so high that any reaction would lower it.) For the normal case of bin i , a very small reactor forms no B and a very large reactor destroys whatever B is formed. Thus, there will be an interior optimum with respect to reaction time. 

Consecutive Reactions. The prototypical reaction is A B C, although reactions like Equation (6.2) can be treated in the same fashion. It may be that the first reaction is independent of the second. This is the normal case when the first reaction is irreversible and homogeneous (so that component B does not occupy an active site). A kinetic study can then measure the starting and final concentrations of component A (or of A and A2 as per Equation (6.2)), and these data can be used to fit the rate expression. The kinetics of the second reaction can be measured independently by reacting pure B. Thus, it may be possible to perform completely separate kinetic studies of the reactions in a consecutive sequence. The data are fit using two separate versions of Equation (7.8), one for each reaction. The data will be the experimental values of for one sum-of-squares and b ut for another. 

Figure 2.S. Concentrations of reactant, intermediate, and product for a consecutive reaction mechanism for different rate constants.

In searching to formulate a mechanism of CuInSc2 phase formation by one-step electrodeposition from acid (pH 1-3) aqueous solutions containing millimolar concentrations of selenous acid and indium and copper sulfates, Kois et al. [178] considered a number of consecutive reactions involving the formation of Se, CuSe, and Cu2Se phases as a pre-requisite for the formation of CIS (Table 3.2). Thermodynamic and kinetic analyses on this basis were used to calculate a potential-pH diagram (Fig. 3.10) for the aqueous Cu+In-i-Se system and construct a distribution diagram of the final products in terms of deposition potential and composition ratio of Se(lV)/Cu(ll) in solution. 

The consecutive reaction will be triggered by too long exposure of already chlorinated product in an environment with a high density of chlorine radicals. Accordingly, controls over residence time, concentration profiles and efficient heat transfer have the potential to cope with such a problem. 

Consecutive Reactions that are other than First-Order. For consecutive reactions that are not first-order, closed form analytical solutions do not generally exist. This situation is a consequence of the nonlinearity of the set of differential equations involving the time derivatives of the various species concentrations. A few two-member sequences have been analyzed. Unfortunately, the few cases that have been... 

When consecutive reactions take place within a porous catalyst, the concentrations of A and V within the pellet will be significantly different from those prevailing at the external surface. The intermediate V molecules formed within the pore structure have a high probability of reacting further before they can diffuse out of the pore. 

The authors chose pyruvic acid as their model compound this C3 molecule plays a central role in the metabolism of living cells. It was recently synthesized for the first time under hydrothermal conditions (Cody et al., 2000). Hazen and Deamer carried out their experiments at pressures and temperatures similar to those in hydrothermal systems (but not chosen to simulate such systems). The non-enzymatic reactions, which took place in relatively concentrated aqueous solutions, were intended to identify the subsequent self-selection and self-organisation potential of prebiotic molecular species. A considerable series of complex organic molecules was tentatively identified, such as methoxy- or methyl-substituted methyl benzoates or 2, 3, 4-trimethyl-2-cyclopenten-l-one, to name only a few. In particular, polymerisation products of pyruvic acid, and products of consecutive reactions such as decarboxylation and cycloaddition, were observed the expected tar fraction was not found, but water-soluble components were found as well as a chloroform-soluble fraction. The latter showed similarities to chloroform-soluble compounds from the Murchison carbonaceous chondrite (Hazen and Deamer, 2007). 

Figure 3. Conversion of DBT in vitro by lysate prepared from IGTS8 cells with assay protein concentration of 5 mg/ml. The data represents concentrations of DBT (circles), HPBS (diamonds), and HBP (squares). The data fitting represents a consecutive reaction model with kx = 0.2/min, and k2 = 0.05/min. Figure extracted from Ref [53].

The concentration profile of a simple 1 1 reaction is always easy to draw because product is formed at the expense of the reactant, so the rate at which reactant is consumed is the same as the rate of product formation. No such simple relation holds for a consecutive reaction, because two distinct rate constants are involved. Two extreme cases need to be considered when dealing with a consecutive reaction when k(i) > k(2) and when k(i) < k(2). We shall treat each in turn. 

Figure 8.20 Schematic graph of concentration against time ( a concentration profile ) for a consecutive reaction for which k( ) > k(2). Note the maximum in the concentration of the intermediate, B. This graph was computed with k(2) being five times slower than k(i)...

Fig. 2. Concentration and temperature profiles in a DSC measurement of a consecutive reaction.

Older hydrolysis processes applied concentrated inorganic acids such as H2SO4 and mild temperature (100-120 °C) to minimize the undesired consecutive reactions [49]. The recovery and reconcentration of the acid catalyst from the product mixture turned out to be difficult and expensive. Modern processes are therefore based on diluted acid and higher temperatures (180-220 °C) [49]. 

We derive the new concept by using a chemical example based on absorption data. First, consider a consecutive reaction A—with rate constants k and fe, where the absorption at one particular wavelength was recorded as a function of time. Let s say our task is to determine the molar absorptivities of species A, B and C at this wavelength, knowing all individual concentrations at all reaction times. 

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