First-order kinetic analysis

This pseudo-first-order kinetic analysis is generally applied regardless of the experimental system used. 

Figure 5. First order kinetic analysis of conversion rate data on the MY720-DDS system cured Isothermally at 177 C and 153 C.

Figure 6. First order kinetic analysis of the rate of hydroxyl group appearance of 177 C.

Fig. 6. First-order kinetic analysis for a reaction consuming a substrate A. Plot of logarithm of relative consumption (in the present plot, ratio of initial concentration of substrate A and concentration of A at a given time).

Under these conditions, rate constant k obtained by the first-order kinetic analysis does not reflect the reactivity of a photocatalyst k contains diffusion constant of a substrate and surface area of a substrate (strictly speaking, area of the diffusion layer on the photoirradiated active surface). 

Examination of these data clearly shows that none of the three compounds Is as effective as terbufos In the jar test. Perhaps the most Interesting aspect of this data Is the relative soil efficacy of the second compound compared to the first. The substitution of a methyl group for a hydrogen between the two sulfur atoms greatly enhances the soil activity of this molecule. Quantitation of the relative soil stability of these three molecules as measured by the bioassay data are collected in Table 5 using a pseudo first order kinetic analysis of the data. 

A more extensive investigation, using mass spectrometry with molecular beam sampling, and first order kinetic analysis for the measurement of —dln[03]/dr in the presence of excess [Br], gave ko= (7 1) X 10 cm mol s at 298 K. The same method has been used for the rate constant of the more rapid Cl + O3 reaction. 

FIGURE 2. a) Kinetic traces of the time-course of P-700 photooxidation. The trace of T3 is the mean of 6 individual measurements, while the trace of B3 is the mean of 24 individual measurements. b) First-order kinetic analysis of the traces in Fig.2.a,. B3 gives a higher rate constant (5.5 s ) than T3 (4.3 s ). 

A mass spectrometric discharge flow study gives for the rate constant k = 2.8 x lO exp -450 + 400 cal mol /RT) cm molecule s , corresponding to a value of 1.3 x 10 molecule s" at 300 K. In this study, [o], F and [of] were all monitored, and conditions ranged from excess O to excess F. The F atom concentration tends to remain consteint even with excess O, because of the regeneration of F atoms in the subsequent decomposition of OF. Hence a pseudo-first order kinetic analysis can be applied ( ). ... 

General first-order kinetics also play an important role for the so-called local eigenvalue analysis of more complicated reaction mechanisms, which are usually described by nonlinear systems of differential equations. Linearization leads to effective general first-order kinetics whose analysis reveals infomiation on the time scales of chemical reactions, species in steady states (quasi-stationarity), or partial equilibria (quasi-equilibrium) [M, and ]. 

The relationship of this type of model to a tme differential analysis has been discussed for the case of linear equiHbrium and first-order kinetics (74,75). A minor extension of this work leads to the foUowing relations for a bed section in which dow rates of soHd and Hquid are constant. For the number of theoretical trays,... 

A detailed study of the solvolysis of L has suggested the following mechanism, with the reactivity of the intermediate M being comparable to that of L. Evidence for the existence of steps ki and k 2 was obtained fiom isotopic scrambling in the sulfonate M when it was separately solvolyzed and by detailed kinetic analysis. Derive a rate expression which correctly describes the non-first-order kinetics for the solvolysis of L. 

With two of the concentrations in large excess, the fourth-order kinetic expression has been reduced to a first-order one, with considerable mathematical simplification. The experimental design in which all the concentrations save one are set much higher, so that they can be treated as approximate constants, is termed the method of flooding (or the method of isolation, since the dependence on one reagent is thereby isolated). We shall consider the method of flooding further in Section 2.7. Here our concern is with the data analysis it should be evident that the same treatment suffices for first-order and pseudo-first-order kinetics. 

If the method of analysis responds to A (or A2), the change follows pseudo-first-order kinetics. The value of Zt /tB] is k (or k2). On the other hand, if one monitors the buildup of P, then both rate constants contribute. We can write... 

M aqueous solutions of iodopentaminecobalt(lll) decompose with first-order kinetics at 45 °C with = 6.0x 10" sec 10" M solutions decompose faster after an initial induction period at the normal rate. Product analysis shows the fast decomposition to be a mixture of a redox process leading to iodine and substitution leading to aquopentaminecobalt(iri) and iodide. Addition of sodium iodide (to 10 M) accelerates the decomposition and... 

Analogously, by assuming first order kinetics with respect to the other organic components, a product distribution analysis can be performed. The reaction rates of steps (l)-(5) in scheme (Figure 12.2) are expressed as... 

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.

Although we cannot clearly determine the reaction order from Figure 3.9, we can gain some insight from a residual plot, which depicts the difference between the predicted and experimental values of cA using the rate constants calculated from the regression analysis. Figure 3.10 shows a random distribution of residuals for a second-order reaction, but a nonrandom distribution of residuals for a first-order reaction (consistent overprediction of concentration for the first five datapoints). Consequently, based upon this analysis, it is apparent that the reaction is second-order rather than first-order, and the reaction rate constant is 0.050. Furthermore, the sum of squared residuals is much smaller for second-order kinetics than for first-order kinetics (1.28 X 10-4 versus 5.39 xl0 4). 

The kinetic trace due to (c) at different CO pressures shows its lifetime is dependent on the pressure of CO above the solution. Analysis of the kinetic trace data of this intermediate under constant CO pressure shows that its decay follows first-order kinetics and allows calculation of the bimolecular rate constant for its reaction with CO ... 

RP-HPLC found application in the monitoring of the alkali hydrolysis kinetics of alkali-clearable azo disperse dyes containing a fluorosulphonyl group. The chemical structures of dyes included in the experiments are shown in Fig. 3.85. Samples for RP-HPLC analysis were neutralized to pH 4.0 - 4.5 with diluted HC1 mixed with five volumes of ACN and injected without any other sample preparation step. Separation was carried out in an ODS column at ambient temperature. The isocratic mobile phase consisted of ACN-water (80 20, v/v) and dyes were detected at their absorption maxima. HPLC measurements indicated that dyes are easily hydrolysed under relatively mild alkaline conditions, and the hydrolysis follows a pseudo first-order kinetics [148],... 

Aqueous PB solutions are well-behaved klnetlcally with the five op s studies, as evidenced by excellent pseudo-first-order kinetics and mass balance between OP and PNP at the reaction termination. Our kinetic analysis confirms that reactions (2) through (6) adequately describe PB reactivity, judged by the good agreement of calculated kjjQQ values with literature values. 

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