Kinetics pseudo-first-order rate

Kinetic measurements were performed employii UV-vis spectroscopy (Perkin Elmer "K2, X5 or 12 spectrophotometer) using quartz cuvettes of 1 cm pathlength at 25 0.1 C. Second-order rate constants of the reaction of methyl vinyl ketone (4.8) with cyclopentadiene (4.6) were determined from the pseudo-first-order rate constants obtained by followirg the absorption of 4.6 at 253-260 nm in the presence of an excess of 4.8. Typical concentrations were [4.8] = 18 mM and [4.6] = 0.1 mM. In order to ensure rapid dissolution of 4.6, this compound was added from a stock solution of 5.0 )j1 in 2.00 g of 1-propanol. In order to prevent evaporation of the extremely volatile 4.6, the cuvettes were filled almost completely and sealed carefully. The water used for the experiments with MeReOj was degassed by purging with argon for 0.5 hours prior to the measurements. All rate constants were reproducible to within 3%. 

The intermediate diphenylhydroxymethyl radical has been detected after generation by flash photolysis. Photolysis of benzophenone in benzene solution containing potential hydrogen donors results in the formation of two intermediates that are detectable, and their rates of decay have been measured. One intermediate is the PhjCOH radical. It disappears by combination with another radical in a second-order process. A much shorter-lived species disappears with first-order kinetics in the presence of excess amounts of various hydrogen donors. The pseudo-first-order rate constants vary with the structure of the donor with 2,2-diphenylethanol, for example, k = 2 x 10 s . The rate is much less with poorer hydrogen-atom donors. The rapidly reacting intermediate is the triplet excited state of benzophenone. 

The initial anhydride concentration was about 3 x 10 M, and the amine concentration was much larger than this. The reaction was followed spectrophoto-metrically, and good first-order kinetics were observed hence, the reaction is first-order with respect to cinnamic anhydride. It was not convenient analytically to use the isolation technique to determine the order with respect to allylamine, because it is easier to observe the cinnamoyl group spectrophotometrically than to follow the loss of amine. Therefore, the preceding experiment was repeated at several amine concentrations, and from the first-order plots the pseudo-first-order rate constants were determined. These data are shown in Table 2-1. Letting A represent... 

Considering the attention that we have given in this chapter to concentrationtime curves of complex reactions, it may seem remarkable that many kinetic studies never generate a comprehensive set of complicated concentration-time data. The reason for this is that complex reactions often can be studied under simplified conditions constituting important special cases for example, whenever feasible one chooses pseudo-first-order conditions, and then one studies the dependence of the pseudo-first-order rate constant on variables other than time. This approach is amplified below. 

The concentration of monomers in the aqueous phase is usually very low. This means that there is a greater chance that the initiator-derived radicals (I ) will undergo side reactions. Processes such as radical-radical reaction involving the initiator-derived and oligomeric species, primary radical termination, and transfer to initiator can be much more significant than in bulk, solution, or suspension polymerization and initiator efficiencies in emulsion polymerization are often very low. Initiation kinetics in emulsion polymerization are defined in terms of the entry coefficient (p) - a pseudo-first order rate coefficient for particle entry. 

It may be noted that the pseudo-first-order rate law for an Sn2 reaction in the presence of a large excess of Y [Eq. (10.2)] is the same as that for an ordinary SnI reaction [Eq. (10.3)]. It is thus not possible to tell these cases apart by simple kinetic... 

The successive equilibria are characterized by K12 and K23, respectively, and when Kl2 (often denoted K0) cannot be directly determined, it may be estimated from the Fuoss equation (3), where R is the distance of closest approach of M2+ and 1/ (considered as spherical species) in M OH2 Um x) +, e is the solvent dielectric constant, and zM and zL are the charges of Mm+ and Lx, respectively (20). Frequently, it is only possible to characterize kinetically the second equilibrium of Eq. (2), and the overall equilibrium is then expressed as in Eq. (4) (which is a general expression irrespective of mechanism). Here, the pseudo first-order rate constant for the approach to equilibrium, koba, is given by Eq. (5), in which the first and second terms equate to k( and kh, respectively, when [Lx ] is in great excess over [Mm+]. When K0[LX ] <11, koba - k,K0[Lx ] + k.it and when K0[LX ] > 1, fc0bs + k l. Analogous expressions apply when [Mm+] is in excess. 

Calculation of kinetic parameters - In the experiments carried out in the single autoclave the H2 pressure was not maintained and the consumption of H2 controlled the conversion of AcOBu, which could be described by pseudo-first order rate constant. In the activity tests performed in SPR16 the conversion of AcOBu increased linearly up to ca. 50 % with reaction time. Initial reaction rates were calculated from AcOBu conversion vs. reaction time dependence, the initial concentration of substrate and the amount of catalyst or the amount of promoters in 1 g of catalyst. 

In the experiments carried out, the rate of hydrogenation was first order with respect to [C=C] from 30 to 90% conversion. Pseudo first order rate constants (k ) were determined for experiments over a range of conditions in order to measure the effect of different reaction parameters. The maximum hydrogenation rate constant recorded in this study was an order of magnitude less than the rate of H2 mass transfer10 and so gas uptake measurement reflected the inherent chemically controlled kinetics of the system. 

The overall study showed that the rate of reaction has a first order dependence on both hydrogen concentration and total [Ir] (up to certain limiting hydrogen and catalyst concentrations) and an inverse dependence on the nitrile concentration. The observed kinetic dependence of the pseudo first order rate constant (k ) for the hydrogenation of C=C in NBR may be summarized by the expression show in Equation (1). 

The following values of the pseudo first-order rate constant /cx have been reported by Subbotin, Antonov, and Etlis [Kinetics and Catalysis, 7 (183), 1966]. 

IR kinetic measurements on Cr(CO)5(N2) were a particular technological triumph (99) because not only were the strong vc—o bands observed but also the very weak (2240 cm J) and natural abundance vnCo bands were detected. The compound Cr(CO)5(N2) decayed at 25°C with a pseudo-first order rate constant of 1.7 second-1. Thus, Cr(CO)5(H2) and Cr(CO)5(N2) have similar thermal stabilities, and it has been one of the great surprises of the Miilheim work (96-99) to find how long-lived unstable molecules can be. 

Kinetic theory indicates that equation (32) should apply to this mechanism. Since the extent of protonation as well as the rate constant will vary with the acidity, the sum of protonated and unprotonated substrate concentrations, (Cs + Csh+), must be used. The observed reaction rate will be pseudo-first-order, rate constant k, since the acid medium is in vast excess compared to the substrate. The medium-independent rate constant is k(), and the activity coefficient of the transition state, /, has to be included to allow equation of concentrations and activities.145 We can use the antilogarithmic definition of h0 in equation (33) and the definition of Ksh+ in equation (34) ... 

In the 1988-1999 period, almost all absolute kinetic studies of carbenic reactions employed LFP with UV detection. Carbenes that contain a UV chromophore (e.g., PhCCl) are easily observed, and their decay kinetics during reaction can be readily followed by LFP.11 However, alkyl, alkylhalo, and alkylacyloxycarbenes are generally transparent in the most useful UV region. To follow their kinetics, Jackson et al. made use of the ylide method, 12 in which the laser-generated carbene (2) is competitively captured by (e.g.) pyridine, forming a chromophoric ylide (3, cf. Scheme 1). The observed pseudo first order rate constants (kobs) for the growth of ylide 3 at various concentrations of pyridine are monitored by UV spectroscopy, and obey Eq. 1. 

By lifting the simplifying restrictions, the kinetic observations can be examined in more detail over much wider concentration ranges of the reactants than those relevant to pseudo-first-order conditions. It should be added that sometimes a composite kinetic trace is more revealing with respect to the mechanism than the conventional concentration and pH dependencies of the pseudo-first-order rate constants. Simultaneous evaluation of the kinetic curves obtained with different experimental methods, and recorded under different conditions, is based on fitting the proposed kinetic models directly to the primary data. This method yields more accurate estimates for the rate constants than conventional procedures. Such an approach has been used sporadically in previous studies, but it is expected to be applied more widely and gain significance in the near future. 

What is the value of the pseudo first-order rate constant k l We calculate the pseudo first-order rate constant k by assuming that the reaction obeys first-order kinetics. Accordingly, we write from Equation (8.24) ... 

Bertole et al.u reported experiments on an unsupported Re-promoted cobalt catalyst. The experiments were done in a SSITKA setup, at 210 °C and pressures in the range 3-16.5 bar, using a 4 mm i.d. fixed bed reactor. The partial pressures of H2, CO and H20 in the feed were varied, and the deactivation, effect on activity, selectivity and intrinsic activity (SSITKA) were studied. The direct observation of the kinetic effect of the water on the activity was difficult due to deactivation. However, the authors discuss kinetic effects of water after correcting for deactivation. The results are summarized in Table 1, the table showing the ratio between the results obtained with added water in the feed divided by the same result in a dry experiment. The column headings refer to the actual experiments compared. It is evident that adding water leads to an increase in the overall rate constant kco. The authors also report the intrinsic pseudo first order rate-coefficient kc, where the overall rate of CO conversion rco = kc 6C and 0C is the coverage of active... 

The pseudo first-order rate constants, obs, are obtained by least-squares fits of the measured peak height increase of the relevant coalesced oxygen-17 signal as a function of time to the modified McKay equation (7, 67, 68). The kinetics can be studied by manipulation of... 

Fig. 16 (A) Typical decay of anisole cation radical in the presence of added NO-, showing the fit to first-order kinetics (smooth curve). (AN+- generated from the 355-nm irradiation of 0.2 m anisole and 0.3 m MeOPyNOF in acetonitrile.) (B) Plot of the pseudo-first-order rate constant against the concentration of added N02. (C) Similar to (B), but with added pyridine or 2.6-lutidine.

A kinetic analysis of Schemes 4.2 and 4.3 shows that, in all cases, it is valid to consider a pseudo-first order rate constant kq [Q] and that three main cases should be considered ... 

Figure 1. Competition kinetics for the Ru(NH2)62y reduction of Co([14 aneNk)-(0H,)0 Reactions at 25°C, pH 2, and n = 0.1(NaClO,). Individual pseudo-first-order rate constants were determined from the exponential (to four half-lives) decay of Co([14]aneN,)(OH2)022 absorbance at 360 nm. Reactions were performed by mixing a solution containing Ru(NH2)62 and Co([14]aneNh)(OHt) -(1 X I 3 M) with a solution saturated in 02(1.2 X 10 3 in an Aminco stopped-...

To understand the pharmacokinetic relevance of the proxibarbal-valofan equilibrium, the kinetics and thermodynamics of the reaction were carefully examined in aqueous and biphasic media. The various pseudo-first-order rate constants shown in Fig. 11.19 were determined in the pH range of 6.7 - 8.0... 

It has already been mentioned that in the absence of added water the reaction kinetics follows a pseudo zero-order rate profile the rate-controlling step under these conditions appears to involve the complexation of the crown in the organic phase with the salt in the solid phase. In contrast to this, in the presence of small quantities of water the reaction kinetics follows a pseudo first-order rate profile. Thus it appears that the water facilitates the interaction between the crown and the salt by forming an omega phase since the displacement process now becomes the rate-controlling step. The phase region where the displacement process actually takes place is not certain at this juncture. 

Since the equilibrium quotient K is small, a nonnueleophilic base is added to the reaction mixture to react with liberated protons and drive the reaction to completion (left to right). Using an excess of ROH then ensures simple unidirectional pseudo first-order (rate constant Atj) kinetics ... 

If the reactants are oppositely charged, the collision complex in (5.18) takes the form of an outer-sphere complex with discernable stability. For the outer sphere redox reaction between Co(NH3)jL"+ and Fe(CN)g, L being a series of pyridine or carboxylate derivatives, saturation kinetics are observed, with the pseudo first-order rate constant (/ obs)> Fe(II) in excess, being given by... 

In a dehydration reaction (Scheme 12.4), the IR band of the formamide carbonyl group at 1684 cm in (7) decreased and eventually converted to the isonitrile band at 2150 cm in (8) (Fig. 12.8). In a separate example (Scheme 12.5), the conversion of the IR band from the carbonate carbonyl group in (9) to the IR band of the carbamide carbonyl group in (10) can be monitored to assure the reaction completion (Fig. 12.9). Based on FTIR analysis, the reaction time course can be analyzed by integrating peak areas of the IR bands from the starting resin and the product. From the point of view of kinetics, the side reaction product formation can be excluded if the pseudo first order rates of the starting material consumption and the product formation are identical. 

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