Plots of kinetic data

The commonly used linearized plots of kinetic data are a usable initial guide to determining the mechanism. 

The differential (rate) forms are (1.16), (1.18) and (1.20), and the corresponding integrated forms are (1.17), (1.19) (or (1.19a)) and (1.21). The designations [A]q and [A], represent the concentrations of A at zero time and time /. Linear plots of [A], In [A], or [A], vs time therefore indicate zero-, first, or second order dependence on the concentration of A. The important characteristics of these order reactions are shown in Fig. 1.1. Notwithstanding the appearance of the plots in 1.1 (b) and 1.1 (c), it is not always easy to differentiate between first-and second-order kinetics.Sometimes a second-order plot of kinetic data might be mistaken for successive first-order reactions (Sec. 1.6.2) with similar rate constants. 

Figure 1 Is a plot of kinetic data according to equation (1) for reaction of EPMP with various concentrations of PB at pH ...

Secondary plots of kinetic data are used to obtain various rate constants and other kinetic parameters such as and Vmax- To simply the analysis, one choses a algebraic transform of the rate equation that allows the observed data to be graphed in a hnear format. 

The Eyring equation is usually used in the logarithmic form (6) to have a linear plot of kinetic data. The intercept gives the AS value and the slope gives the APP value ... 

FIGURE 5.5 Linear plot of kinetic data for a second-order reaction. 

Figs.3 4 are the plots of kinetic data of for steamed and equilibrium catalysts respectively. It is very clear from the Figs.3 4 that all the catalysts exhibit 1st order behavior with respect to the concentration of coke up to about 5 minutes of reaction time. The deviation from the 1 st order behavior becomes significant after about 6 minutes of reaction time. The concentration of coke at which the deviation from the 1st order behavior takes place is termed as critical coke concentration (C ). 

Fig. 3. p-Glucosidase inhibition shown by Lineweaver-Burk plot (reproduced from [2]). Lineweaver-Burk plot of kinetic data from peak 2 cellobiase ((3-glucosidase) at several product inhibitor levels. This is an example of noncompetitive inhibition where the product is not only completing for binding in the active site but also binding to a secondary site on the enzyme that alters the enzyme catalytic ability... 

Figure 5. Plot of kinetic data for the curing of PMDA/ODA polyimide using Eq. 1. The slope of the line yields Ea and ln(A) is obtained from the intercept.

A double reciprocal plot of kinetic data for a biochemical reaction that obeys a Monod rate law will yield a value of Pmax from the reciprocal of the intercept of the y-axis. The corresponding slope is equal to At high val-... 

Figure 4.18 Plot of kinetic data for polypropylene according to equation (4..W)...

Figure 4.51 Plots of kinetic data according to equation (4.50).. Mass fraction of PEK-C I, O II, 5 III, 10 IV, 20 V, 40 VI, 60. The indicated compositions correspond to nominal values and not to the actual content of PEK-C in the crystalline pha.se 73)...

Fig. 75. First-order plot of kinetic data on step 1 at O C. (1 M NaBr, pH 5.3) at a citrate thrombin (Seegers) concentration of 100 units per milliliter. Curves A, B, and C correspond to initial fibrinogen concentrations of 30, 20, and 10 mg. per milliliter, respectively. It should be noted that the stated thrombin concentration is that determined at pH 8 at 25 C. the actual activity in the reaction mixture is considerably lower as can be seen from Fig. 62 (Ehrenpreis et al., 1958a).

Fig. 78. Plot of kinetic data for several forward runs on step 1 at 0 according to Eq. (V-ll). The values of (F)o are indicated in the diagram. The average concentration of thrombin is 95 units per milliliter. From the form of Eq. (V-ll), the experimental error in the data would increase as a approaches ae, (Laskowski el al., 19 b).

Linearization. In preliminary screening of reaction mechanisms, it is very useful to construct plots of experimental data transformed in such a way that the plot of the dependent (transformed) variable versus the independent (transformed) variable is a straight line if the rate equation being the basis of transformation has been chosen properly. This is illustrated with the rate expression for a-th order kinetics ... 

The plots of the data according to this equation were rectilinear for polymerisations at -1 °C, 10 °C, 20 °C and 30 °C, so that values of kp and kp+-KDm could be obtained. The authors then used the common-ion salt (n-Bu)4N+ CF3S03 and interpreted the kinetic results by the equation... 

To understand why a Tafel plot of log / against tf has its specific shape, and learn that the central slopes of such plots allow kinetic data to be obtained. 

For a given feed (fixed C o, . ) and using conversion of key component as a measure of the composition and extent of reaction, the versus T plot has the general shape shown in Fig. 9.3. This plot can be prepared either from a thermodynamically consistent rate expression for the reaction (the rate must be zero at equilibrium) or by interpolating from a given set of kinetic data in conjunction with thermodynamic information on the equilibrium. Naturally, the reliability of all the calculations and predictions that follow are directly dependent on the accuracy of this chart. Hence, it is imperative to obtain good kinetic data to construct this chart. 

Plot calculated kinetic data to obtain information about the order of the kinetic reaction. 

Armstrong and Spinks (4) studied the gas phase addition of HBr to ethylene induced by the action of Co60 7-rays. They detected ethyl bromide as the only product. They determined the kinetics of the process in two pressure regions. At lower pressures the rate of the chain process was in agreement with the standard expression for wall termination of Br atoms. The plots of the data gave values of the ratio of the rate constants of the reactions... 

Marcus5 8 taught us that the most appropriate and useful kinetic measure of chemical reactivity is the intrinsic barrier (AG ) rather than the actual barrier (AG ), or the intrinsic rate constant (kQ) rather than the actual rate constant (k) of a reaction. These terms refer to the barrier (rate constant) in the absence of a thermodynamic driving force (AG° = 0) and can either be determined by interpolation or extrapolation of kinetic data or by applying the Marcus equation.5 8 For example, for solution phase proton transfers from a carbon acid activated by a ji-acceptor (Y) to a buffer base, Equation (1), k0 may be determined from Br A ns ted-type plots of logki or... 

Included in the following table are some data points from a hypothetical enzyme kinetics study. Using a spreadsheet program with graphing abilities (such as Excel), generate a Line-weaver-Burk plot of the data points in the table. Determine the best-fit line for the data along with Vnax, ATm, and r2 (the square of the correlation coefficient of the line). Does this enzyme follow Michaelis-Menten kinetics Why or why not ... 

Some calculated temperature profiles from an example problem are plotted in Figure 3. The parameter is water influx ratio (moles H20/mole air fed). Only the combustion and water gas reactions were included in the problem analysis due to lack of kinetics data. This problem was contrived to illustrate the predictive features of the model, and while the physical properties and operating conditions are believed to be representative of the Hanna UCG tests, no effort was made to simulate any particular test. For a complete problem statement see ref. (3). 

The variation of the cathodic peak potential with the scan rate (0.3-0.4 mV precision on each determination, 1 mV reproducibility over the whole set of experiments) allows the determination of the rate constant with a relative error of 3-11%. The results are consistent with those derived from anodic-to-cathodic peak current ratios. Simulation of the whole voltammogram confirms the absence of significant systematic errors that could arise from the assumptions underlying the analysis of kinetic data. Activation parameters derived from weighted regression Arrhenius plots of the data points taken at 5 or 6 tern-... 

One important point to remember when using kinetics to study soil-water processes is that the apparatus chosen for the study is capable of removing or isolating the end product as fast as it is produced. A second point is that unimolecular reactions always produce first-order plots, but fit of kinetic data (representing a process not well understood) to a first-order plot is no proof that the process is unimolecular. Complementary data (e.g., spectroscopic data) are needed to support such a conclusion, On the other hand, rate-law differences between any two reaction systems suggest that the mechanisms involved may represent different elementary reactions. 

Pig. (first) The Lineweaver-Burk method of plotting enzyme kinetic data (second) Eadie-Hofstee method of plotting enzyme kinetic data. 

From simple plots of fraction unreacted vs. time (Figure 1), it was clear that this was an unusually self-consistent set of kinetic data. We therefore have taken it as the basis for our kinetic modeling and used additional data available to confirm and extend. Experiments in the same equipment also were carried out at 2 atm pressure, at 0.13 atm, and, with helium dilution, at 1 atm total pressure and about 0.13 atm initial partial pressure of propane. The effects of pressure and partial pressure observed are discussed briefly. 

Kinetics of Coke Formation. On the basis of the x-ray diffraction data, the QI can be considered equivalent to coke and for the remainder of the discussion the term coke will be used in place of QI. The first-order rate equation was applied to the data for coke formation. The plots of these data in Figure 3 are similar to the curves produced with the / -resin results. A temperature-dependent induction period is obtained, followed by a reaction sequence that shows a reasonable fit with the first-order kinetic equation. Rate constants calculated from the linear portion of each curve are plotted in the Arrhenius equation in Figure 4. From the slope of the best straight line for the data points in Figure 4, the activation energy for coke formation is found to be 61 kcal. 

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