First-order rate constant of reaction

TABLE 2 Logarithms of first order rate constants of reactions of the tested compounds with 4-nitrobenzylpyridine (log k jgp) and sums of Hammett a values (la). 

First order rate constants of reactions between the organophosphorus compounds and 4-nitrobenzylpyridine (in min" ). 

The table below gives first-order rate constants for reaction of substituted benzenes with w-nitrobenzenesulfonyl peroxide. From these data, calculate the overall relative reactivity and partial rate factors. Does this reaction fit the pattern of an electrophilic aromatic substitution If so, does the active electrophile exhibit low, moderate, or high substrate and position selectivity ... 

The observed first-order rate constant of the overall reaction is Kkn o ... 

The rate of MV formation was also dependent on pH. The bimolecular rate constant, as calculated from the first order rate constant of the MV build-up and the concentration of colloidal particles, was substantially smaller than expected for a diffusion controlled reaction Eq. (10). The electrochemical rate constant k Eq. (9) which largely determines the rate of reaction was calculated using a diffusion coefficient of of 10 cm s A plot of log k vs. pH is shown in Fig. 24. 

In early work on the effect of potential on ET reactions [76], Solomon and Bard showed that an ET reaction between Fe(CN)g in an aqueous phase and 7,7,8,8-tetra-cyanoquinodimethane (TCNQ) in 1,2-dichloroethane (DCE) could be promoted by judiciously adjusting the potential drop across the ITIES, using tetraphenylarsonium cation as a potential determining ion. In a similar period, Selzer and Mandler [77] reported a study of the ET reaction between aqueous IrClg and Fc in a NB phase, without any potential determining ion in either phase. A first-order rate constant of 0.013 cm s was obtained... 

In the case of 0-pipettes, the collection efficiency also decreases markedly with increasing separation. The situation becomes more complicated when the transferred ion participates in a homogeneous chemical reaction. For the pseudo-first-order reaction a semiquantita-tive description is given by the family of dimensionless working curves calculated for two disks (Fig. 6) [23]. Clearly, at any separation distance the collection efficiency approaches zero when the dimensionless rate constant (a = 2kr /D, where k is the first-order rate constant of the homogeneous ionic reaction) becomes 1. 

At any time the reactor contains 2 m3 of fluid. The feed and effluent rates remain constant at 3.3 m3/ksec. Does the response of the system approximate that of any simple ideal reactor What conversion level is expected if the reaction has a first-order rate constant of 15 sec -... 

Values of pA"R for the addition of water to carbocations to give the corresponding alcohols. The equilibrium constants KR (m) were determined as the ratio Hoh/ h> where fcHOH (s 1) is the first-order rate constant for reaction of the carbocation with water and H (m 1 s ) is the second-order rate constant for specific acid-catalyzed cleavage of the alcohol to give the carbocation.9,12 13... 

To impress you, enzymologists often tell you how much faster their enzyme is than the uncatalyzed reaction. These comparisons are tricky. Here s the problem Suppose we know that the reaction S — P has a first-order rate constant of 1 X 10 3 min 1 (a half-life of 693 min). When an enzyme catalyzes transformation of S to P, we have more than one reaction ... 

By combining (1), (3) and (4), expressions (5) and (6) are obtained. These, or similar, equations readily explain why first-order rate constants of micelle-assisted bimolecular reactions typically go through maxima with increasing surfactant concentration if the overall reactant concentration is kept constant. Addition of surfactant leads to binding of both reactants to micelles, and this increased concentration increases the reaction rate. Eventually, however, increase in surfactant concentration dilutes the reactants in the micellar pseudophase and the rate falls. This behavior supports the original assumption that substrate in one micelle does not react with reactant in another, and that equilibrium is maintained between aqueous and micellar pseudophases. 

Other 4-nitrophenyl esters have also been reported to be substrates of various hydrolases. For example, 4-nitrophenyl hexanoate (7.19) was hydrolyzed by bovine serum albumin [39], The affinity of the substrate for the macromolecule was found to be high (Km/n = 0.040 mM, where n is the number of sites), but the reaction itself was slow ( = 5 10-3 s-1, where k2 is the first-order rate constant of the formation of the phenol product from the enzyme-substrate complex). Another ester, 4-nitrophenyl pivalate (7.20), was hydrolyzed by cytoplasmic aldehyde dehydrogenase at a maximum velocity ca. 1/3 and an affinity ca. 1/20 those of the acetate [40], However, the rate-limiting steps were different for the two substrates, namely acylation of the enzyme for the pivalate, and acyl-enzyme hydrolysis for the acetate (see Chapt. 3). 

Similar to the diffusion controlled CrE mechanism (Sect. 2.4.1) the preceding chemical reaction (2.108) is characterized by the eqnilibrinm constant K=, where kf and kb are the first-order rate constants of the forward and backward cliemical reactions, respectively. The surface CrE mechanism is represented by (2.92) and the following differential eqnations ... 

First-order rate constant of forward reaction, s ... 

In water, carbofuran reacted with OH radicals at a first-order rate constant of 2.2 x 10 /M-sec (Mabury and Crosby, 1996a). Benitez et al. (2002) reported an apparent pseudo-first-order rate constant ranging from 5.1 x 10to 19.5 x lO Vsec for the reaction of carbofuran with ozone in water. When ozone and UV radiation was used to study the degradation kinetics, the pseudo-first-order rate constant was 22.8 x 10 Vsec. Similarly, the oxidation of carbofuran by Fenton s reagent and UV radiation ranged from 17.2 x 10 to >200 x lO Vsec. 

Figure 2. Kinetic plot of pseudo-first-order rate constant for reaction of paraoxon (kohc) versus concentration of added sodium perborate at 27.5 oc avvarious pH in 0.1 mol dm borate buffer.

In Equation 18, K and ka are the equilibrium constant and first-order rate constant for Reactions 16 and 17, respectively. The constants ka and K may be evaluated by using Equation 18 and the data given in columns 1 and 2 of Table V. The procedure involves obtaining l/ka and K from the intercept and the ratio of intercept to slope in the linear plot of l/k vs. l/(H+) and leads to ka = 3.2 x KT3 seer1 and K = 4.7. The excellent agreement between theory and experiment may be seen by comparing the experimental and calculated values of k given in Table V. 

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