Kinetics first-order rate constant

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 kinetics of the nitration of benzene, toluene and mesitylene in mixtures prepared from nitric acid and acetic anhydride have been studied by Hartshorn and Thompson. Under zeroth order conditions, the dependence of the rate of nitration of mesitylene on the stoichiometric concentrations of nitric acid, acetic acid and lithium nitrate were found to be as described in section 5.3.5. When the conditions were such that the rate depended upon the first power of the concentration of the aromatic substrate, the first order rate constant was found to vary with the stoichiometric concentration of nitric acid as shown on the graph below. An approximately third order dependence on this quantity was found with mesitylene and toluene, but with benzene, increasing the stoichiometric concentration of nitric acid caused a change to an approximately second order dependence. Relative reactivities, however, were found to be insensitive... 

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. 

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... 

The reaction displays simple first-order kinetics, with the observed first-order rate constant being equal to kik2l(k i + k. ... 

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. 

Not surprisingly, we find that the relaxation is a first-order process with rate constant A , + A i. It is conventional in relaxation kinetics to speak of the relaxation time T, which is the time required for the concentration to decay to Me its initial value. In Chapter 2 we found that the lifetime defined in this way is the reciprocal of a first-order rate constant. In the present instance, therefore,... 

The isomerization of A to B yielded kinetic data that conformed to a first-order rate law. but the apparent first-order rate constant depended on the initial concentration of A. The authors propose competing unimolecular and bimolecular processes, and they show that the system reduces to a first-order expression when the equilibrium constant K is unity that is,... 

If the equilibrium is suddenly displaced, the results obtained in Chapter 3 show that the re-equilibration process will follow first-order kinetics. It is customary in this field to refer to r, the relaxation time, which is defined as reciprocal of the first-order rate constant for re-equilibration. In this case, we have... 

Photolysis of all brominated dibenzodioxins investigated occurs very fast in n-hexane. The rate of degradation of all compounds follows a good first-order kinetic scheme. In Table 4 the calculated first order rate constants k are summarised along with the quantum-yields. The corresponding results for three brominated dibenzofurans are also included. 

Figure 2. Inhibition of eel AChE by ANTX-A(S) - the secondary plot. P, the first-order rate constant which was the rate of inhibition at that ANTX-A(S) concentration obtained from the primary plot (insert). The intercept on the 1/P axis is 1/k and the intercept on the 1/[I] axis is -1/K. Figure insert Progressive irreversible inhibition of eel AChE by ANTX-A(S). The inactivation followed first-order kinetics. ANTX-A(S) concentrations, xg/mL (A) 0.083 ( ) 0.166 (o) 0.331 ( ) 0.497 (V) 0.599 ( ) control. Each point represents the mean of 3 or 4 determinations.

It is possible to distinguish between direct and indirect nOes from their kinetic behavior. The direct nOes grow immediately upon irradiation of the neighboring nucleus, with a first-order rate constant, and their kinetics depend initially only on the intemuclear distance r" indirect nOes are observable only after a certain time lag. We can thus suppress or enhance the indirect nOe s (e.g., at He) by short or long irradiations, respectively, of Ha- a long irradiation time of Ha allows the buildup of indirect negative nOe at He, while a short irradiation time of Ha allows only the direct positive nOe effects of Ha on He to be recorded. 

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. 

E I is a kinetic chimera Kj and kt are the constants characterizing the inactivation process kt is the first-order rate constant for inactivation at infinite inhibitor concentration and K, is the counterpart of the Michaelis constant. The k,/K, ratio is an index of the inhibitory potency. The parameters K, and k, are determined by analyzing the data obtained by using the incubation method or the progress curve method. In the incubation method, the pseudo-first-order constants /cobs are determined from the slopes of the semilogarithmic plots of remaining enzyme activity... 

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). 

Soil models tend to be based on first-order kinetics thus, they employ only first-order rate constants with no ability to correct these constants for environmental conditions in the simulated environment which differ from the experimental conditions. This limitation is both for reasons of expediency and due to a lack of the data required for alternative approaches. In evaluating and choosing appropriate unsaturated zone models, the type, flexibility, and suitability of methods used to specify needed parameters should be considered. 

The metalloalkyne complex Ru ( )-CH=CH(CH2)4C CH Cl(CO)(P,Pr3)2 exhibits behavior similar to that of cyclohexylacetylene (Scheme 10).40 Thus, it reacts with OsHCl(CO)(P Pr3)2 to give the hydride-vinylidene derivative (P Pr3)2 (CO)ClRu ( )-CH=CH(CH2)4CH=C OsHCl(CO)(P,Pr3)2, which evolves in toluene into the heterodinuclear-pi-bisalkenyl complex (P Pr3)2(CO)ClRu (is)-CH=CH(CH2)4CH=CH-( ) OsCl(CO)(P,Pr3)2. Kinetic measurements between 303 and 343 K yield first-order rate constants, which afford activation parameters ofAH = 22.1 1.5, kcal-mol-1 andAS = -6.1 2.3 cal-K 1-mol 1. The slightly negative value of the activation entropy suggests that the insertion of the vinylidene ligand into the Os—H bond is an intramolecular process, which occurs by a concerted mechanism with a geometrically highly oriented transition state. 

This technique is readily adaptable for use with the generalized additive physical approach discussed in Section 3.3.3.2. It is applicable to systems that give apparent first-order rate constants. These include not only simple first-order irreversible reactions but also irreversible first-order reactions in parallel and reversible reactions that are first-order in both the forward and reverse directions. The technique provides an example of the advantages that can be obtained by careful planning of kinetics experiments instead of allowing the experimental design to be dictated entirely by laboratory convention and experimental convenience. 

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. 

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]. 

An estimate of the rate enhancement associated with the intramolecular phosphorylation can be made by using isopropyl p-nitrophenyl methyl-phosphonate as a model for the covalent intermediate formed in the initial step of the reaction of cycloheptaamylose with bis (p-nitrophenyl) me thy 1-phosphonate. The first-order rate constant for the alkaline hydrolysis of isopropyl p-nitrophenyl methylphosphonate at pH 9.86 can be obtained from the data of van Hooidonk and Groos (1970) kun = 1.4 X 10-5 sec-1. This value may be compared with the maximal rate constant for the reaction of cycloheptaamylose with bis(p-nitrophenyl) methylphosphonate— k2 = 1.59 X 10-1 sec-1 at pH 9.86—which must be a minimal value for the rate of the intramolecular phosphorylation. This comparison implies a kinetic acceleration of at least 104 which is similar to rate enhancements associated with the formation of cyclic phosphates from nucleoside phosphate diesters. 

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) ... 

Limiting Kinetics. In some instances first-order rate constants (kQbs) give a less than first-order dependence on the reactant in large excess, and (3) no longer applies. Instead, in for example the Co(phen)33+ oxidation of PCu(I), (4) holds,... 

Reactivity differences between 2P + 2S photoexcited Cu and Ag atoms have also been observed with CHi (59). For example,comparative matrix quenching kinetic measurements for Cu and Ag atoms in solid CHi show that the first order rate constant is considerably larger for Cu Fig.7. Detailed studies on the Cu system... 

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