Rate laws pseudo-first-order reactions

The demetalation kinetics of ZnTTP by an acidic aqueous phase have also been reported [61]. In this study, ZnTTP was considered to adsorb at the interface producing Zn and free base porphyrin by proton attack. The demetalation kinetics of ZnTTP were analyzed as a pseudo-first-order reaction, because the proton concentration in the aqueous phase was in large excess. The rate law was found to be described by... 

A mechanism for a pseudo-first-order reaction involving the hydrolysis of substrate S catalyzed by acid HA that is consistent with the observed rate law rs = kohscs, is as follows ... 

Figure 8.14 The reaction of A and B, with B greatly in excess is a second-order reaction, but it follows a kinetic rate law for a first-order reaction. We say it is pseudo first-order reaction. The deviation from linearity at longer times occurs because the concentration of B (which we assume is constant) does actually change during reaction, so the reaction no longer behaves as a first-order reaction...

When RH is in large excess, the triplet state undergoes pseudo first-order reaction to form QH and R, so an integrated rate-law plot of ln[3Q ] against t gives a straight line of slope -k (Figure 10.13). 

A-3 Rate Laws for Second-Order and Pseudo-First-Order Reactions... 

Hydrogen peroxide, cuprum perchloride, and perchloric acid were used as acceptors in aqueous solutions. The experimentally observed process of hydrated electron decay in solutions of these three substances obeyed the first-order reaction law. Kinetic characteristics of observed processes were calculated by the method of the least squares using 15-20 photo-oscillograms. Values of rate constants of corresponding pseudo-first order reactions are shown in Table I. There one can see also values of bimolecular rate constants calculated on the basis of above data. The rate constant does not vary occasionally within some limits but it changes monotonously with the variation of concentration. This may mean that some process of the decay of the intermediates was not taken into consideration. It was shown in earlier work (J), that we had satisfactory agreement with the experiment supposing that the process was the mono-molecular intermediates decay. 

The experimental results in aqueous and ammonium solutions show that the process of intermediates decay in the presence of acceptors follows a first-order law. However, a proportionality between the calculated rate constant of the pseudo-first order reaction and the concentration is not observed. Under these conditions no influence of dose rate on the kinetics of intermediates decay is found, so recombination interactions play a rather small role. By kinetic treatment of the results, satisfactory agreement with experimental data can be obtained by supposing that the intermediates disappear in a monomolecular decay which simultaneously proceeds with scavenger reactions. 

The mass balance with diffusion and first-order chemical reaction, given by (24-12), is classified as a frequently occurring second-order linear ordinary differential equation (i.e., ODE) with constant coefficients. It is a second-order equation because diffusion is an important mass transfer rate process that is included in the mass balance. It is linear because the kinetic rate law is first-order or pseudo-first-order, and it is ordinary because diffusion is considered only in one coordinate direction—normal to the interface. The coefficients are constant under isothermal conditions because the physicochemical properties of the fluid don t change... 

The reaction was followed by observing the imine formation spectrophotometrically under conditions where the total glycine concentration was much greater than that of pyridinealdehyde. In this case, the reaction could be described by the rate law for a first-order reversible reaction. (This is an example of a pseudo first-order reaction.) The assumption was then made that the reaction in the forward direction was also first order with respect to glycine, and a second-order rate constant was obtained by dividing the first-order constant by the total glycine concentration. This second-order rate constant varied with the glycine concentration in the manner shown in Table P7-7 [35]. 

Pseudo-First-Order Reactions Under certain circumstances, second-order reactions can sometimes be approximated as first-order reactions. For example, consider a second-order reaction that depends on the concentrations of two different reactants (each to the first order). If one of the reactant concentrations is much larger than the other reactant concentration, then it will remain essentially constant (only slightly depleted) during the reaction process while the concentration of the other reactant is fully consumed. In this situation, the second-order rate law can be rewritten as a pseudo-first-order rate law. As an example, consider a second-order reaction that is first order with respect to two reactants A and B. The rate law for this reaction is... 

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. 

In the atomic resonance absorption spectrometric (ARAS) adaptation of the methods, atomic species are spectroscopically monitored as a function of time. H [7,9], D- [7,10], O- [7,11], N- [12], Cl- [13] and I-atom [14] reactions have been studied. Beer s law holds if absorbance, (ABS), is kept low, and then (ABS) s -ln(I/Io) (I and Iq are transmitted and incident intensities of the resonance light, respectively) is proportional to the atomic concentration. If the decay of atom A is controlled by a bimolecular reaction, A + R, where R is the stable reactant molecule, then the decay rate is pseudo-first-order provided [R] [A]. Because (ABS) is proportional to [A], observation of (ABS)t is sufficient to determine the decay constant. Values for kbini for each experiment are then determined by dividing the decay constant by [R]. The results from many experiments are usually displayed as Arrhenius plots. If a reaction is pressure dependent, experiments can also be carried by varying total density. Termolecular reactions can therefore be studied. In certain cases, chemical isolation is not possible, and numerical chemical simulations of the... 

The reaction temperature was set to 50 C, and helium was used as the inert carrier gas (inlet pressure 50 kPa). From the obtained chromatographic data, the reaction rate constants were directly accessible by assuming a pseudo-first-order reaction law for the ring-closing metathesis (RCM). The contact time Af of the reactant on the catalytically active column was determined to be only 1.75 s, which corresponds to a reaction rate constant of 0.54 s and an activation barrier AG (323 k) of 81 kj mol . The high activity of the permanently bonded polymeric Grubbs second-generation catalyst is corroborated by the activation barrier determined for the formation of Af-trifluoroacetamide-3-pyrroline. 

Kinetic Anaiysis Kinetic studies were conducted by measuring the rate of TCE degraded over time and is modeled based on the pseudo-first-order reaction rate law ... 

The effective rate law correctly describes the pressure dependence of unimolecular reaction rates at least qualitatively. This is illustrated in figure A3,4,9. In the lunit of high pressures, i.e. large [M], becomes independent of [M] yielding the high-pressure rate constant of an effective first-order rate law. At very low pressures, product fonnation becomes much faster than deactivation. A j now depends linearly on [M]. This corresponds to an effective second-order rate law with the pseudo first-order rate constant Aq ... 

The experiments were perfonued in a static reaction cell in a large excess of N2 (2-200 bar). An UV laser pulse (193 mu, 20 ns) started the reaction by the photodissociation of N2O to fonu O atoms in the presence of NO. The reaction was monitored via the NO2 absorption at 405 mu using a Hg-Xe high-pressure arc lamp, together with direct time-dependent detection. With a 20-200-fold excess of NO, the fonuation of NO2 followed a pseudo-first-order rate law ... 

The integrated form of the rate law for equation 13.4, however, is still too complicated to be analytically useful. We can simplify the kinetics, however, by carefully adjusting the reaction conditions. For example, pseudo-first-order kinetics can be achieved by using a large excess of R (i.e. [R]o >> [A]o), such that its concentration remains essentially constant. Under these conditions... 

Direct-Computation Rate Methods Rate methods for analyzing kinetic data are based on the differential form of the rate law. The rate of a reaction at time f, (rate)f, is determined from the slope of a curve showing the change in concentration for a reactant or product as a function of time (Figure 13.5). For a reaction that is first-order, or pseudo-first-order in analyte, the rate at time f is given as... 

Flooding and Pseudo-First-Order Conditions For an example, consider a reaction that is independent of product concentrations and has three reagents. If a large excess of [BJ and [CJ are used, and the disappearance of a lesser amount of A is measured, such flooding of the system with all components butM permits the rate law to be integrated with the assumption that all concentrations are constant except A. Consequentiy, simple expressions are derived for the time variation of A. Under flooding conditions and using equation 8, if x happens to be 1, the time-dependent concentration... 

The conditions chosen make the reaction appear to be first-order overall, although the reaction is really not first-order overall, unlessjy and happen to be 2ero. If a simple exponential is actually observed over a reasonable extent (at least 90—95%) of decay the assumptions are considered vaUdated and is obtained with good precision. The pseudo-first-order rate constant is related to the k in the originally postulated rate law by... 

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