Intrinsic first-order rate constant

As shown in Figure 13.2, the intrinsic first-order rate constant of NO reduction increases linearly with the vanadium content whereas the intrinsic first-order rate constant for the oxidation of SO2 increases more than linearly with the vanadia content. This is consistent with the identification of the active sites for reduction... 

All the polymers show marked catalytic effects on the decarboxylation in the water solvent. In the polymer environment the intrinsic first-order rate constant k2 can be 103-fold greater than the pseudo-first-order rate constant in the aqueous solvent alone (B and E, respectively, in Table X). 

The irreversible, first-order reaction of gaseous A lo B occurs in spherical catalyst pellets with a radius of 2 mm. For this problem, the molecular diffusivity of A is 1.2 X 10" cm s and the Knudsen diffusivity is 9 X 10 " cm s. The intrinsic first-order rate constant determined from detailed laboratory measurements was found to be 5.0 s . The concentration of A in the surrounding gas is 0.01 mol L . Assume the porosity and the tortuosity of the pellets are 0.5 and 4, respectively. 

Figure 14. Intrinsic first-order rate constant over a potassium poison-doped V2O5 on Ti02 catalyst and a WO3/V2O5 on Ti02 catalyst as a function of the atomic ratio K V [NO], = [NH3], = [SO2], = 1000 ppm [O2], =2% [H2O], = 8% balance N2 GHSV = 15OOGh T = 575 K (adapted from Ref. 118).

The fast phase of the reaction, i, is equal to the sum of all four intrinsic first-order rate constants, defining the rate of formation of E-S and the decay of E. The substrate concentration dependence of the rate is a straight line with a slope equal to and an intercept equal to i + 7 2 + k-2 - The slow phase defines the rate of decay of E-S and the rate of formation of E-X, and the rate of slow decay of E if it is noticeably biphasic. The substrate concentration dependence of the slow reaction approximates a hyperbola with an apparent defined by... 

Reactions catalyzed by hydrogen ion or hydroxide ion, when studied at controlled pH, are often described by pseudo-first-order rate constants that include the catalyst concentration or activity. Activation energies determined from Arrhenius plots using the pseudo-first-order rate constants may include contributions other than the activation energy intrinsic to the reaction of interest. This problem was analyzed for a special case by Higuchi et al. the following treatment is drawn from a more general analysis. ... 

Samples 1-4 correspond to VPO treated in steam for 92, 312h, in N2 and activated base catalysts, respectively, k, are pseudo-first-order rate constants for the disappearance of butane. The constants are measured in a microreactor on a larger amount ( 1 g) of catalyst at 633 K. k (intrinsic) are based on the BET surface area. 

In a typical experiment, the sample is a solution (e.g., in benzene) of both the ferf-butoxyl radical precursor (di-tert-butylperoxide) and the substrate (phenol). The phenol concentration is defined by the time constraint referred to before. The net reaction must be complete much faster than the intrinsic response of the microphone. Because reaction 13.23 is, in practical terms, instantaneous, that requirement will fall only on reaction 13.24. The time scale of this reaction can be quantified by its lifetime rr, which is related to its pseudo-first-order rate constant k [PhOH] and can be set by choosing an adequate concentration of phenol, according to equation 13.25 ... 

Case C is illustrated in Scheme 4.2, where Iq is the diffusional second-order rate constant for the formation of the pair (M. .. Q) from separated M and Q, k i is the first-order backward rate constant for this step, kR is the first-order rate constant for the reaction of (M. .. Q) to form products 3, and km (= 1/%) is the rate constant for intrinsic de-excitation of M. If the interaction between M and Q is weak, the fluorescence characteristics of the pair M. .. Q are the same as those of M (Scheme 4.2). 

The intrinsic inertness of the peptide bond is demonstrated by a study of the chemical hydrolysis of N-benzoyl-Gly-Phe (hippurylphenylalanine, 6.37) [67], a reference substrate for carboxypeptidase A (EC 3.4.17.1). In pH 9 borate buffer at 25°, the first-order rate constant for hydrolysis of the peptide bond ( chem) was 1-3 x 10-10 s-1, corresponding to a tm value of 168 y. This is a very slow reaction indeed, confirming the intrinsic stability of the peptide bond. Because the analytical method used was based on monitoring the released phenylalanine, no information is available on the competitive hydrolysis of the amide bond to liberate benzoic acid. 

The optical rotation of the mixture approaches zero (a racemic mixture) over time, with apparent first-order kinetics. This observation was supported by the semi-log plot [ln(a°D/ aD) vs time], which is linear (Figure 1). It has been shown that this racemization process does in fact follow a true pseudo-first-order rate equation, the details of which have been described by Eliel.t30 Therefore, these processes can be described by the first-order rate constant associated with them, which reflects precisely the intrinsic rate of racemization. Comparison of the half-lives for racemization under conditions of varying amino acid side chain, base, and solvent is the basis for this new general method. 

Metalloenzyme is represented by E(Mg2 ), C is chelator, E(Mg2 C) represents chelator reversibly bound to the metalloenzyme with dissociation constant KD and with characteristic enhancement of the protein fluorescence, and k is the first-order rate constant for irreversible formation of inactive protein P and the cation-chelator complex, Mg2+C. Values of both Kd and k may vary according to the nature of the chelator, the nature of the metal ion (if other cations can replace Mg2 ), and the intrinsic stability of the cation-chelator complex, as well as pH, temperature, and protein concentration. 

Km measurements, where V,nax has units of mass x time-1. The definition of intrinsic clearance as Vmax x Xm-1 should not be confused with the historically prevalent calculation of ksl (the first-order rate constant of decay of concentration in plasma), calculated from kel = Vmax/Xm, where Vmax is the zero-order rate of plasma concentration decay observed at high concentrations and Xmax is the concentration of plasma at half-maximal rate of plasma level decay. 

Consider a species A whose removal from the atmosphere can be expressed as a first-order reaction, that is, RA = —kAcA. If the removal of A is the result of reaction with background species B, then kA can be a pseudo-first-order rate constant that includes the concentration of B in it. The intrinsic rate constant is given by the Arrhenius expression kA = Aq exp(—Ea/RT). 

Table 11.6 Pseudo-First-Order Rate Constants and Intrinsic Activity of the Catalysts Applied...

Matsumoto et al. [24] investigated to the stability of aspirin in mixtures of aspirin and PCC at various temperatures and humidities. They calculated the intrinsic rate constants of aspirin hydrolysis from the relationship between the apparent first-order hydrolysis rate constant and the amount of water adsorbed at each temperature. The apparent first-order rate constant of aspirin and the amount of adsorbed water in the heated mixture of PCC and aspirin at different temperatures are listed in Table 1. It was suggested that the apparent first-order decomposition rate constants of aspirin in the heated mixtures were closely related to the amount of adsorbed water. 

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