Pseudo-First-Order Reaction Conditions

The ions or cluster ions are thermalized by collisions with an inert carrier gas (usually helium), although often argon or even nitrogen is employed. Neutral reactant gas is added through a reactant gas inlet at an appropriate location downstream in the flow tube, and allowed to react with the injected ions. Rate coefficients, k, are determined by establishing pseudo-first-order reaction conditions in which the reactant ion concentration is small compared to the reactant neutral concentration. Bimolecular rate coefficients, k, are obtained from the slope of the natural logarithm of the measured signal intensity, /, of the reactant ion versus the flow rate (2b of reactant gas 45,48-50... 

Surprisingly, despite requiring two analyte molecules to produce one S2 molecule, the kinetics of the chemiluminescent reaction are first order with respect to the sulfur compound. This can be explained if every H2S or CH3SH molecule is consumed in the reaction and every S atom recombines to form S2, through the use of an excess of OCIO to maintain pseudo-first-order reaction conditions [81]. The limit of detection for this analysis was found to be 3 ppbv for H2S. 

In order to ensure that the process takes place, a powerful oxidant Z (to ensure the irreversibility of the complication), but electro inactive (at least in the potential region of interest), must be present in solution at concentrations normally much higher than that of Ox, in order to guarantee pseudo-first-order reaction conditions. 

R = Et) were hydrolysed in micellar solutions of the prepared ketoximes under pseudo-first-order reaction conditions.In the alkaline hydrolysis of / -nitrophenyl ethyl chloromethylphosphonate (254), micellar catalysis by cetylpyridinium bromide is much reduced when KCl and KBr are present. ... 

Kinetic Studies. Although it was not possible to measure the ozonation rates for dialkylmercurials by the techniques described earlier, the alkylmercuric halides reacted slowly enough at 0°C that quite good rate plots were obtained. These plots, performed by an IBM 1620 computer and on concentration data obtained under pseudo-first-order reaction conditions, yielded the relative rate data listed in Table III. These data suggested the two general relative-rate sequences illustrated by sequences 16 and 17 (see p. 88). 

Substitution of cyclooctatetraene in (COT)Fe(CO)3 by phosphorus-containing ligands in decalin has been studied under pseudo-first-order reaction conditions. The observed rate constant is given by the relation... 

Molybdenum-catalyzed epoxidations of cyclohexene under pseudo first-order reaction conditions showed the highest rate, of the investigated tertiary alkyl hydroperoxides (Figure 1), with TBHP. 

It would be convenient to assume that a large excess of reagent R originally present (C ) is instantaneously mixed with sample material (A), so that the pseudo-first-order-reaction conditions prevailed and, hence, rate equation (2.47) could be used, but this is seldom the case in a real FIA system. [If it were the case, then the position of the maximum t/(response)/i/L = 0 in Fig. 2.29 would not change with the concentration of the injected sample ] Thus, for theoretical prediction of the fractional conversion in a FIA system, a correct reaction rate equation must be selected, and the value of the reaction constant must be known. 

In applying most kinetic methods, experimental parameters are usually set so as to ensure pseudo-first-order reaction conditions, which is why only this type of reaction is dealt with here for simplicity. 

The pseudo-first-order reaction condition is very widely used, but it is seldom mentioned in textbooks. Although many reactions have second-order or more complex rate laws, the experimental kineticist wishes to optimize experiments by taking advantage of the first-order rate law b ause it imposes the fewest restrictions on the conditions required to determine a reliable rate constant The trick is to use the pseudo-first-order condition. 

Use of the isolation or pseudo-order technique. This approach is discussed in Chapter 2, where it was shown how a second-order reaction could be converted to a pseudo-first-order reaction by maintaining one of the reactant concentrations at an essentially eonstant level. The same method may be usefully applied to eomplex reactions. In this way, for example. Scheme XI can be studied under conditions such that it functions as Scheme IX. A corollary that must be kept in mind is that a reaction system that is observed to behave in accordance with (as an example) Scheme IX may actually be more complex than it appears to be, if an unsuspected reactant is present under pseudo-order conditions. 

Emmert and Pigford (E2) have studied the reaction between carbon dioxide and aqueous solutions of monoethanolamine (MEA) and report that the reaction rate constant is 5400 liter/mole sec at 25°C. If it is assumed that MEA is present in excess, the reaction may be treated as pseudo first-order. This pseudo first-order reaction has been recently used by Johnson et al. (J4) to study the rate of absorption from single carbon dioxide bubbles under forced convection conditions, and the results were compared with their theoretical model. 

One of the typical features of a (pseudo)-first order reaction is that a plot of the logarithm of the advancement of the reaction versus time (Fig. 2B) should give straight lines. However we observed deviation from linearity before the first half-life, in spite of the fact that another characteristic features of (pseudo)-first order reactions, namely that plots of the extent of reaction versus time were independant of the initial concentration (Fig. 3), was verified. We therefore investigated whether variation occured in the reaction conditions as a function of time. 

In Illustrations 8.3 and 8.6 we considered the reactor size requirements for the Diels-Alder reaction between 1,4-butadiene and methyl acrylate. For the conditions cited the reaction may be considered as a pseudo first-order reaction with 8a = 0. At a fraction conversion of 0.40 the required PFR volume was 33.5 m1 2 3, while the required CSTR volume was 43.7 m3. The ratio of these volumes is 1.30. From Figure 8.8 the ratio is seen to be identical with this value. Thus this figure or equation 8.3.14 can be used in solving a number of problems involving the... 

When the reaction scheme involves first- or pseudo- first-order reactions, fast enough for pure kinetic conditions to be achieved D/k concentration profile of B is squeezed within a thin reaction layer adjacent to the electrode surface as represented in Figure 2.31 (bottom diagram). Starting from the electrode surface, the following relationships apply. 

As we have seen earlier, even third-order reactions can be reduced to pseudo-first-order reactions by keeping the concentrations of all species except A constant and in great excess compared to A. This technique of using pseudo-first-order conditions is by far the most common technique for determining rate constants. Not only does it require monitoring only one species, A, as a function of time, but even absolute concentrations of A need not be measured. Because the ratio [A]/[A]0 appears in Eq. (T), the measurement of any parameter that is proportional to the concentration of A will suffice in determining k l7, since the proportionality constant between the parameter and [A] cancels out in Eq. (T). For example, if A absorbs light in a convenient... 

A more detailed LSV study [58, 89] resulted in the conclusion that the kinetics, under all conditions, could not be described by the simple eCej, scheme. It was proposed that the reaction order in anthracene anion radical (AN- ) varies between 1 and 2 and the reaction order in phenol is greater than 1. A complex mechanism was also indicated from DCV measurements [89]. At a phenol concentration of 10 mM, values of dEpj d log v were in all cases close to that expected for a reaction second order in An-, i.e. 19.5mV decade-1 under the conditions of the experiments. The process is fast enough under these conditions for it to be expected to fall well within the KP zone. That this is the case was indicated by the fact that d p/dlog v was linear over a reasonably wide range of v (10— 1000 mV s-1). The highest value of the slope, observed at a phenol concentration of 100mM, was still significantly lower than 29.3 mV decade -1 predicted for a pseudo-first-order reaction. 

In a micrometer-sized droplet, a diffusion time of FeCp-X in the droplet is very short ( 1 s) so that diffusion of FeCp-X in the droplet is not the rate-determining step. The total amount of Fe(III) produced in the water phase is much larger than that of FeCp-X in the droplets, and the electrolysis is continued during the IF measurement. Therefore, the ratedetermining step is not bulk electrolysis of Fe(II) in water. When the rate-determining step is ET between FeCp-X in the droplet and Fe(III) in water (discussed later), the reaction rate can be analyzed on the basis of a pseudo-first-order reaction at t 10 s (Fe(III) concentration [Fe(III)] = 0.2 mM). [FeCp-X( )]0 is given as in Eq. 2 under the boundary condition of [FeCp-X]0 = [FeCp-X(0)]o at t = 0,... 

For the general case of trialkoxysilanes, although the hydrolysis reaction is reversible, under the conditions employed it may be considered as three consecutive, irreversible pseudo-first-order reactions shown in the following equations ... 

Wulff and collaborators, for instance, reported the preparation of TSA imprinted beads for the hydrolysis of carbonate and carbamate [61, 62], exploiting the amidine (33) functional monomer previously developed by the same group and successfully applied to the bulk format [63]. The polymers were prepared using a suspension polymerisation that produced beads with sizes in the range 8-375 pm, depending on the polymerisation conditions. The pseudo-first order reaction rate of the imprinted beads (Tyrrp/ soin) was enhanced by a factor of 293 for the carbonate hydrolysis and 160 for the carbamate, when compared with the background. 

Biodegradation can be described as a second order reaction (Equation la) which, under conditions of constant competent biomass, simplifies to a pseudo first-order reaction (Equation lb). 

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