Plot of kinetic data for

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

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)...

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).

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 ...

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 3 presents a superposition of kinetic data for the radiation-induced loss of 1,2 unsaturation in VB, the data having been normalized for the different initial vinyl contents in the various polymers. The residual unsaturation-dose data for Polymer A were plotted directly, yielding the solid line shown data for Polymers B, C and 6 were arbitrarily plotted at doses greater than the actual doses by amounts equal to shift factors of 2.0, 2.7 and 3.0 Mrad, respectively. These shift factors correspond to the doses required to decrease the 1,2 unsaturation of Polymer A from 98.5% initially to 90.1, 86.0 and 85.0% (the initial vinyl contents of Polymers B, C and 6), respectively. By this normalization procedure, the data for the three VB polymers used in this work (A, B and C) and the single data point available from the literature (Polymer 6) could be fitted to a common kinetic plot. From the initial slope to the solid line in Figure 3, Gg(-1,2) was found to have the rather high value of t SSO. Taking the tangent to the line at 85% 1,2, we obtain G3.q(-1,2) 270, which compares...

Howard and Miles (1965) have described the enzymic synthesis of inosine-6- 0, inosine 5 -phosphate-6- 0, and guanosine-6- 0. In the course of this work they used infrared spectroscopy of Dj 0 and Dj 0 solutions to evaluate the conversion of 5 -AMP to 5 -IMP and the conversion of 2,6-diamino-9-/S-D-ribofuranosylpurine to guanosine. Kinetic plots of the data for these reactions were made in the same way as already indicated in Fig. 15.5 of Howard and Miles (1964). Figure 15.6 shows spectra for the enzymic conversion of 2,6-diamino-9-) -D-ribofuranosylpurine to guanosine, and Fig. 15.7 shows a plot of the absorbances of certain specific absorption bands during the course of the reaction. 

Herein is the rate constant for a dienophile with substituent x ko is the corresponding rate constant for unsubstituted 2,4c Ox is the substituent constant for substituent x and p is the reaction constant, defined as the slope of the plot of log (k / ko) versus Ox. The parameter p is a measure of the sensitivity of the reactions towards introduction of substituents. Figure 2.3 and Table 2.4 show the results of correlating the kinetic data for the reaction of 2.4a-e with 2.5 with a. ... 

The plotting of Dixon plot and its slope re-plot (see 5.9.5.9) is a commonly used graphical method for verification of kinetics mechanisms in a particular enzymatic reaction.9 The proposed kinetic mechanism for the system is valid if the experimental data fit the rate equation given by (5.9.4.4). In this attempt, different sets of experimental data for kinetic resolution of racemic ibuprofen ester by immobilised lipase in EMR were fitted into the rate equation of (5.7.5.6). The Dixon plot is presented in Figure 5.22. 

Kinetic data for the decomposition of diacetone alcohol, from Table 2-3. were obtained by dilatometry. The nonlinear least-squares fit of the data to Eq. (2-30) is shown on the left. Plots are also shown for two methods presented in Section 2.8 they are the Guggenheim method, center, and the Kezdy-Swinbourne approach, right. 

Nonlinear least-squares programs have made time lag methods much less important. They are less accurate, for one thing. For another, the linearity of the appropriate plots, although a necessary consequence of first-order kinetics, does not constitute a proof of first-order kinetics. Certain other kinetic equations also lead to linear plots of either function. For example, Problem 2-11 presents data for a product-catalyzed reaction. The data in this case can be plotted linearly according to the Guggenheim equation, although the reaction does not follow first-order kinetics and the plot of In [A] versus time is decidedly nonlinear. 

A plot to analyze kinetic data for the exchange of benzyl iodide and iodide ions in ethanol at 27.3 °C. The line shows that log 1 - F) decreases linearly with time according to the McKay equation, Eq. (3-56). The data are given in Table 3-3. 

Enzyme kinetics. Data for reactions that follow the Michaelis-Menten equation are sometimes analyzed by a plot of v,/tA]o versus l/[A]o. This treatment is known as an Eadie-Hofstee plot. Following the style of Fig. 4-7b, sketch this function and label its features. 

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 ... 

In experimental kinetics studies one measures (directly, or indirectly) the concentration of one or more of the reactant and/or product species as a function of time. If these concentrations are plotted against time, smooth curves should be obtained. For constant volume systems the reaction rate may be obtained by graphical or numerical differentiation of the data. For variable volume systems, additional numerical manipulations are necessary, but the process of determining the reaction rate still involves differentiation of some form of the data. For example,... 

Based on the reaction network in Example 18-8, calculate and plot the temperature (7)-volume (V) profile and the concentration (c,)-volume profiles for a set of independent species in a PFR operated adiabatically. Consult the paper by Spencer and Pereira (1987) for appropriate choice of feed conditions and for kinetics data For thermochemical data, consult the compilation of Stull et al. (1969), or an equivalent one. 

Having established the speciation, we now have a very powerful tool for analyzing the kinetic data for the pH dependence of the La3 + catalysis of the alcoholysis of various substrates. Included in the Figs 1 and 2 plots are the second-order rate constants for La3 + -catalysis of the ethanolysis of paraoxon (1) and the methanolysis of /xnitrophenyl acetate (PNPA, 2) as a function of pH in ethanol and methanol, respectively. The kinetic data mainly follow the rise/fall behavior of the Lal+( OR)2 species with some involvement of the other species, La2 + ( OR)i, La2 1 ( OR)3 and Lal+(-OR)4. 

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... 

Fig. 2.6 (a) Desorption kinetic curves at various temperatures under initial hydrogen pressure of 0.1 MPa of the as-received, nonactivated, commercial MgH powder Tego Magnan and (b) the Arrhenius plot of the desorption rate for the estimate of the apparent activation energy, fi, using kinetics data for four temperatures 350, 375, 400, and 420°C (fi -120 kJ/mol). Coefficient of fit = 0.996... 

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