Pseudo-first order kinetics

Another case in which pseudo-first order kinetics is often observed is a catalytic reaction. If one species is a catalyst, it is not consumed, so its concentration does not change (A + 

B gives P + B). If we let B be the catalyst, then [B] always equals [B]o, even if B is not in excess. Applying the same concepts expressed with regard to Eq. 7.37 allows us to solve for fcobs and therefore k. We will encounter examples of this kind of kinetic behavior when we examine general acid-base catalysis in Chapter 9. 

Pseudo-first order kinetics is actually the most common form of kinetics used when determining the kinetic order of a reactant. For example, a linear dependence of upon [B]o 

Since large excesses of ii were used relative to i, a pseudo-first order kinetic treatment was appropriate. 

If path B were operative, the kobs values would include [/ ], and we would expect a four-fold increase in the concentration of ii to directly give a four-fold increase in the A bs value. Hence, the experiment given to distinguish Path A from Path B was actually designed to distinguish first order kinetics from pseudo-first order kinetics, thereby supporting either a unimolecular or bimolecular mechanism, respectively. It is important to stress that pseudo-first order kinetics, despite the first order in the name, will usually represent bimolecular or even more complex reaction mechanisms. 

If the concentration of species B (for example) is large relative to A, it will remain essentially unchanged during the course of the reaction, and the rate expression 23-6 is simplified to 23-10, a form of equation 23-1. The reaction is said to be run imder pseudo-first-order conditions  

Once the first-order behavior with respect to [A] has been verified, the reaction can be nm with varying concentrations of B (B still in large excess over A). A graph of /cobsd function of [B] should be linear the slope is the rate constant k. For large variations in [B], resulting in large variations in fcobsd/ h is 

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In classical kinetics, intemiolecular exchange processes are quite different from the uniniolecular, first-order kinetics associated with intramolecular exchange. However, the NMR of chemical exchange can still be treated as pseudo-first-order kinetics, and all the previous results apply. One way of rationalizing this is as... 

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... 

Decomposition of diphenoylperoxide [6109-04-2] (40) in the presence of a fluorescer such as perylene in methylene chloride at 24°C produces chemiluminescence matching the fluorescence spectmm of the fluorescer with perylene was reported to be 10 5% (135). The reaction follows pseudo-first-order kinetics with the observed rate constant increasing with fluorescer concentration according to = k [flr]. Thus the fluorescer acts as a catalyst for peroxide decomposition, with catalytic decomposition competing with spontaneous thermal decomposition. An electron-transfer mechanism has been proposed (135). 

For those pesticides that are cometabolized, ie, not utilized as a growth substrate, the assumption of first-order kinetics is appropriate. The more accurate kinetic expression is actually pseudo-first-order kinetics, where the rate is dependent on both the pesticide concentration and the numbers of pesticide-degrading microorganisms. However, because of the difficulties in enumerating pesticide-transforming microorganisms, first-order rate constants, or half-hves, are typically reported. Based on kinetic constants, it is possible to rank the relative persistence of pesticides. Pesticides with half-hves of <10 days are considered to be relatively nonpersistent pesticides with half-hves of >100 days are considered to be relatively persistent. 

Even if the peak behavior fits well for a given apparent desorption order, the real kinetic situation may be a different one. As a rate controlling step in a second-order desorption, random recombination of two particles is assumed most frequently. However, should the desorption proceed via a nonrandom recombination of neighboring particle pairs into an ordered structure, the resulting apparent first-order desorption kinetics is claimed to be possible (36). The term pseudo-first-order kinetics is used in this instance. Vice versa, second-order kinetics of desorption can appear for a nondissociative adsorption, if the existence of a dimer complex is necessary before the actual desorption step can take place (99). A possibility of switching between the apparent second-order and first-order kinetics by changing the surface coverage has also been claimed (60, 99, 100). 

Unusual reactivities of mechano-radicals have been reported in a few instances. To explain the pseudo first-order kinetics and the high yield of linear block copolymers formed during the mechanochemical degradation of a mixture of... 

With two of the concentrations in large excess, the fourth-order kinetic expression has been reduced to a first-order one, with considerable mathematical simplification. The experimental design in which all the concentrations save one are set much higher, so that they can be treated as approximate constants, is termed the method of flooding (or the method of isolation, since the dependence on one reagent is thereby isolated). We shall consider the method of flooding further in Section 2.7. Here our concern is with the data analysis it should be evident that the same treatment suffices for first-order and pseudo-first-order kinetics. 

In experiments with [sulfone]o = 3.15 x 10 5 M and excess N2H4, the reaction follows pseudo-first-order kinetics. Values of k vary with [N2H4]. Formulate the rate law and evaluate the constants therein ... 

If the method of analysis responds to A (or A2), the change follows pseudo-first-order kinetics. The value of Zt /tB] is k (or k2). On the other hand, if one monitors the buildup of P, then both rate constants contribute. We can write... 

Experiments with [ArH] [Hg] followed pseudo-first-order kinetics. Plots of 1 /k versus 1/tArH] were linear. Interpret this information in terms of a reaction scheme, and show how the intercept and slope of the plot are related to the kinetic constants. 

Proton inventory technique. 21.9-220 Pseudo-first-order kinetics, 16 Pulse-accelerated-flow method. 255 Pulse radiolysis, 266-268 Pump-probe technique. 266... 

The rate of the reaction with most reagents is proportional to the concentration of NO2, not to that of other species. When the reagent produces this ion in small amounts, the attack is slow and only active substrates can be nitrated. In concentrated and aqueous mineral acids the kinetics are second order first order each in aromatic substrate and in nitric acid (unless pure nitric acid is used in which case there are pseudo-first-order kinetics). But in organic solvents, such as nitromethane, acetic acid, and CCI4, the kinetics are first order in nitric acid alone and zero order in aromatic substrate, because the rate-determining step is formation of NOj and the substrate does not take part in this. 

Example 4.3 Suppose a pure monomer polymerizes in a CSTR with pseudo-first-order kinetics. The monomer and pol5Tner have different... 

The fact that the rate of silanization is influenced by the moisture content of the sUica supports the mechanism wherein a hydrolysis step is involved. The reaction follows pseudo first-order kinetics. Figure 29.1 shows the mechanism of the primary reaction. 

Figure 1. Time-resolved profiles of cations from the + C2H6 reaction at 2.0-eV collision energy. The decay of CDj and the formation of C2H5 and CD3CH2 cations follow pseudo-first-order kinetics. Reprinted from [38] with permission from Elsevier.

Pectins were incubated in buffered medium in mild alkaline conditions (pH 8.5 to 11.2) at room temperature, leading to both demethylation and P-elimination. At higher pHs p-elimination had increased initial speed but soon plateaued. Demethylation was slower but proceeded until completion. It followed a (pseudo)-first order kinetics with respect to concentration of methylesterified carboxyl groups. A rate constant of 27.2 9.0 moT 1 min was calculated after correction for the pH variation during the course of the reaction. 

In mild alkaline conditions, highly methylated pectin was demethylated following a (pseudo)-first order kinetics with respect to the concentration of methoxylated galacturonate moieties. Investigation in this pH range, where the initial concentration of methylesters was higher than the initial concentration of OH ions, was complicated by the necessity to use a buffer. This led to deviations from the theoretical behavior as the concentration of OH ions still varied in proportions which could not be neglected in the equations of the kinetics. However these deviations could be accounted for be the pH variation, and the pH variation itself predicted from the amount of liberated methanol. The constant we found was similar to previously reported data (Scamparini Bobbio, 1982). 

Pseudo-first order kinetics was assumed to interpret the experimental data. Fig. 5.4-36 shows that the fit of the experimental data using first order-kinetics is acceptable. However, a systematic deviation is observed in the curve obtained at 110 C. This indicates inadequacy of the first-order kinetics, which is inappropriate from the view of theory. On the other hand, the kinetic equation seems to describe the... 

Pseudo-first order kinetics with respect to lactose implies (at constant hydrogen pressure) that the mass balance of lactose becomes... 

Where k =Ek j. The concentration ratio expressed with the aid of lactose conversion (X) is Cqa/ca=1-X. A series of first-order test plots were prepared and they revealed that lactose obeys pseudo-first order kinetics very well. 

Let us now consider the situation where [/] [E], We have here a situation that is analogous to our discussion of pseudo-first-order kinetics in Appendix 1. When [/] E in equilibrium binding studies, the diminution of [/]f due to formation of El is so insignificant that we can ignore it and therefore make the simplifying assumption that [/]f = [/]T. Combining this with the mass balance Equations (A2.1) and (A2.2), and a little algebra, we obtain... 

The stirred experiment of Figure 1(b) is more typical in that all concentrations behave as expected (reagent decreasing with pseudo-first order kinetics products monotonically increasing intermediate undergoing well-behaved rise and fall concentration). We have performed kinetic analyses of the data in Figure 1(b) according to the equations ... 

For some organic compounds, such as phenols, aromatic amines, electron-rich olefins and dienes, alkyl sulfides, and eneamines, chemical oxidation is an important degradation process under environmental conditions. Most of these reactions depend on reactions with free-radicals already in solution and are usually modeled by pseudo-first-order kinetics ... 

A great many reactions follow first-order kinetics or pseudo first-order kinetics over certain ranges of experimental conditions. Among these are many pyrolysis reactions, the cracking of butane, the decomposition of nitrogen pen-toxide (N205), and the radioactive disintegration of unstable nuclei. 

In aqueous solution the water concentration may be considered constant, so the reverse reaction follows pseudo first-order kinetics. The data below on this reaction have been taken from Emanuel and Knorre. Use them to determine the values of both first-order rate constants. 

For the case where all of the series reactions obey first-order irreversible kinetics, equations 5.3.4, 5.3.6, 5.3.9, and 5.3.10 describe the variations of the species concentrations with time in an isothermal well-mixed batch reactor. For series reactions where the kinetics do not obey simple first-order or pseudo first-order kinetics, the rate expressions can seldom be solved in closed form, and it is necessary to resort to numerical methods to determine the time dependence of various species concentrations. Irrespective of the particular reaction rate expressions involved, there will be a specific time... 

Vaidyanathan and Doraiswamy [Chem. Eng. Sci., 23 (537), 1966] have studied the catalytic partial oxidation of benzene in a composition range where the reactions of interest all follow pseudo first-order kinetics. The pertinent stoichiometric equations are... 

Since the second reaction rate constant is orders of magnitude greater than the first at temperatures near room temperature, the first reaction may be regarded as the rate controlling step. Since ethanol is used as the solvent, the reaction will follow pseudo first-order kinetics. The rate of this liquid phase reaction can be expressed as... 

Aqueous solutions of (z))-penicillamine are comparatively stable at pH 2-4, and it degrades slowly by first order or pseudo-first order kinetics in aqueous solutions. A 3% solution of penicillamine hydrochloride stored under nitrogen in a sealed container at 20 °C decomposed to the extent of about 10% per year [2]. 

Fig. 5 shows the time dependence of the solid-state ion exchange process. The process has pseudo first order kinetics in the investigated conversion range for both (i) the distribution and crystallinity loss of the CdCl2 salt and (ii) the formation of new Cd,H-Y phase. The rate constant obtained for the decay of... 

Irradiation of DMDAF in benzene solution at room temperature generates a transient intermediate that appears within the rise-time of the laser and decays by a pseudo first-order kinetic path with a half-life of 51 ns. The optical spectrum of the intermediate is essentially the same as that observed in the low temperature irradiation experiment. 

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