Kinetic Plots

Figure 4 Reaction kinetics plot showing the use of a differential method of rate determination of PP-N6-PP-g-AA ternary blend. Source Ref. 47.

The inhibition analyses were examined differently for free lipase in a batch and immobilised lipase in membrane reactor system. Figure 5.14 shows the kinetics plot for substrate inhibition of the free lipase in the batch system, where [5] is the concentration of (S)-ibuprofen ester in isooctane, and v0 is the initial reaction rate for (S)-ester conversion. The data for immobilised lipase are shown in Figure 5.15 that is, the kinetics plot for substrate inhibition for immobilised lipase in the EMR system. The Hanes-Woolf plots in both systems show similar trends for substrate inhibition. The graphical presentation of rate curves for immobilised lipase shows higher values compared with free enzymes. The value for the... 

The initial rate constant values related to 10 mg of the metal film catalyst obtained from the kinetic plots (analogous to those represented in Fig. 15) diminishes by about one order of magnitude as a consequence of nickel film preexposure to atomic hydrogen (i.e. after transformation into... 

Determination of M . The end group concentration can be determined from Mn. However, M determinations permit only a control of the kinetic plots obtained by other methods. They are not suffidently accurate to allow unambiguous determinations of reaction orders. 

Since high temperatures and a nitrogen atmosphere are necessary to obtain measurable rates of polyesterification and to remove the reaction water, a loss of volatile reactants can hardly be avoided, especially in early stages of polyesterification. In the last stages, the decrease of the concentration of the volatile reactants can be of the same order of magnitude as their concentration. Consequently, the ultimate points of the kinetic plot have possibly no significance. 

The kinetics of alkylation by triphenylmethyl compounds have been studied. Hart and Cassis353 found that the alkylation of phenol and o-cresol by triphenylmethyl chloride in o-dichlorobenzene gave non-linear kinetic plots which were, however, rendered linear by presaturation of the reaction mixture with hydrogen chloride, precise third-order kinetics, equation (182)... 

Since there is inherent in reactions which give low selectivities, the possibility that non-competitive conditions are responsible, Olah and Overchuck359 have measured directly the rates of benzylation, isopropylation, and fer/.-butylation of benzene and toluene with aluminium and stannic chlorides in nitromethane at 25 °C. Apparent second-order rate coefficients were obtained (assuming that the concentration of catalyst remains constant), but it must be admitted that the kinetic plots showed considerable departure from second-order behaviour. The observed rate coefficients and kreh values determined by the competition method are given in Table 88, which seems to clearly indicate that the competitive ex-... 

The rate of the reaction in various buffer solutions, covering the pH range 4-8, was determined, and in hydrogen phosphate-dihydrogen phosphate buffers the rate at constant pH decreased as the concentration of dihydrogen phosphate increased. Similarly, with acetic acid-acetate and phosphoric acid-dihydrogen phosphate buffers the rate was inversely dependent upon the concentration of the molecular acid in addition, with the latter buffer, the kinetic plots showed an unexplained departure from linearity after 50 % reaction. 

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. 

Fig. 17. Kinetic plots showing a linear dependence on irradiation time (305 nm) of the absorbance ratios and AgJ " (O) and a linear dependence on...

Two additional characteristics of the inhibition of mineral absorption by phenolic acids were observed. The inhibition of both P0 absorption (27) and K+ absorption (31, 32) was reversed when the phenolic acid was removed from the absorption solution. Harper Balke (32) found this reversibility to be dependent upon pH the lower the pH, the less the reversal. Also, kinetic plots of the inhibition of mineral absorption showed that the phenolic acids did not competitively inhibit either P0 (26, 28) or K+ (31) absorption. Rather, ferulic acid inhibited PO -absorption in a noncompetitive (26) or uncompetitive (28) manner and jr-hydroxybenzoic acid inhibited K+ absorption in an uncompetitive manner (31). 

Although etch rate data for a particular polymer film yielded straight-line kinetic plots, the data from one film to another for any given polymer exhibited considerable scatter this is indicated by the large standard deviations in Tables I and II. Because of the scatter, the cause of which is under investigation, the etch rate data reported here have only semiquantitative significance. 

Figure 5. Typical kinetic plots for 0(3P)-induced weight loss in various polybutadienes and polyalkenamers.

Figures 8 and 9 show the first order kinetic plots for the isomerization and crosslinking reactions, respectively. In the data analysis the area of the isoimide peak was measured between consistent limits chosen to exclude any contribution from the 1775 cm imide band. These data were generated by measuring the area of the appropriate peak in a baseline corrected spectrum and ratioing this area to that of a reference peak (which was invarient during the experiment) in the same spectrum. This concentration indicative number was then ratioed to the concentration ratio observed on the initial scan. Plots of the log of the ratio of the concentration of the functionality at time "t" to the concentration of the functionality at t = 0 were then constructed. In order to insure that the trends in the data were not artifacts of this procedure or of the baseline correction routine, we also plotted the data in terms of peak intensity in absorbance units and observed the same trends but with more scatter in the data.

Figure 1. Reaction rate of the decrease of double bonds, conversion and swelling degree as a function of time. Insert Kinetic plot of swelling degree versus reaction time (silicone acrylate lb values from [3,4])...

Fig. 3.2 First-order kinetic plots for microwave (MW) and thermal (A) activation of the imidization reaction.

P sh2+ va ues to be calculated from the kinetic plots by curve-fitting 258 for instance, the quite reasonable value of —1.038 0.090 was obtained for [16]. The resulting linear kinetic plots according to equation (54), i.e. assuming full substrate protonation, are shown in Fig. 15. 

A.G. Sykes I agree with Dr. Sutin that a 16% effect is small. Recent work has however shown that in our experiments the Cr binds at two or more sites on the plastocyanin (analyses confirm that there is attachment of one Cr per molecule of protein), and it is necessary therefore for us to elaborate on the original Farver and Pecht results. Our evidence is based on detailed kinetic studies with redox partners such as Co(phen>3 + when kinetic plots are found to be biphasic. It is concluded that the Cr attached at... 

Fz -wre 7. First-order kinetic plots for the quenching of 2P <— 2S photoexcited Cu tjS ln CHh at 10-12 K. Identical experimental conditions were used with Cu/CHt Ag/CHh 1/104. (Reproduced from Ref. 59. Copyright American... 

Figure 2. Second-order kinetic plot for the reaction of CO at subatmospheric pressures with Mn(CO)k(CCHsOAlBrBr2) in toluene solution (19)...

Fig. 7.3 Kinetic plots for nC and 14C in the reaction of labeled methyl iodide with N,N-dimethyl- -toluidine in methanol at 30°C. (CR is the count rate (cpm) for the reactant fraction and CP the count rate for product fraction) (After Axelsson, B. S. et. al. J. Am. Chem. Soc. 109, 7233 (1987))...

The plot of ln(ki/k2) vs. AH2, named the kinetic plot , is a straight line with a slope m = l/RTg and an intercept q = (—AHi/RT ff). Hence the unknown value of the affinity of A for 1 can be determined. However the assumption of negligible entropy effects cannot be applied in a large number of cases, and thus, in 1993, Fenselau and co-workers ° ° suggested a means to overcome this limitation, which was later refined by Wesdemiotis and co-workers. Assuming that... 

The data for the reactions of potassium cyanide with benzyl halides at 85 C and 25 C are summarized in Tables I-III and graphical representations of these data are shown in Figures 1-3. The reactions carried out at 85 C were followed to 70% completion, while those at 25 C were followed to 50% completion. In general, excellent first-order kinetic plots were obtained. Each point on the graphs represents an average of at least three kinetic determinations. It is interesting to note that in the absence of added water (solid-liquid phase transfer catalysis), the rates of benzyl halide disappearance were more accurately described by zero-order kinetics. 

Fig. 1.3 Second-order kinetic plot for decay of RefCO) obtained by flash photolysis of 120 pM RejlCOlm with 10 mM CO in isooctane. (CO slows further reactions of RelCO) ) At X = 535 nm, the molar absorbance coefficient, 8m of Re(CO)5 is 1.0 x lO lVf cm". Since therefore from Beer-Lambert law (Df-Df) = [A]e ,l, where D s are optical absorbances and 1 is the path length (10 cm), the slope of Fig. 1.3 is 2k/s and 2k therefore equals (5.3 x lO KlO lflO) = 5.3 x lO M- s". Ref. 25. Reproduced with permission of the Journal of the American Chemical Society. 1982, American Chemical Society.

Fig. 6.7 First-order kinetic plot for ATRP experiments with MMA in the presence of macroligand Me3o(4Bpy7)e.

Figure 26. A kinetic plot on air oxidation of a-pinene using Co(III)-HMS as the catalyst rmder atmospheric pressure at 100 °C [ 15].

Figure 1. Pseudo-first-order kinetic plot of - n(A -Ao)/ A -Ag) versus time for production of p-nitrophenolate from reaction of sodium perborate at various concentrations with EPMP at 27.5 oc, pH = 8.

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.

Fig. 4 Semilogarithmic kinetic plot for the NMP of styrene (St) initiated by Bloc Builder (left), Mn and PDI values vs conversion plot at different polymerization temperatures right). (Reprinted with permission from [49]. Copyright (2006) John Wiley Sons, Inc.)...

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