Analysis of Initial Rate Data

In the analysis of initial rate data it is imperative to keep the time elapsed between data acquisition and data analysis as short as possible. 

Once the range of substrate concentrations to be used is chosen, the intermediate levels must be decided upon. If substrate concentrations are spaced in an arithmetic series, too many of the points will be in the high concentration range. A geometric series is better, but the best procedure is probably to space the points evenly on a reciprocal plot. 

Fisiire 2. Envelopes of expected errors for data fitting to the linear forms of the Midiadis-Mentm equation, with K and V equal to unity, and a constant ndard error in Uo of j 0.03 V (dotted lines.  

If one fits the data in the form of one of the reciprocal graphs, a linear plot is always obtained. Under no circumstances should one attempt to fit data in reciprocal form for statistical evaluations of kinetic constants, since this requires weighted fits using weights (when equal variance in velocities is assumed) or Uo weights (if the error is proportional). 

The three linear plots in Fig. 2 show that the choice of substrate concentrations above or well above the Km wiU afford a relatively precise estimation of the maximal velocity, but a very poor estimation of the specificity constant, 

The initial rates of the reaction were calculated from the concentration-time data, based on acetic acid consumption during the reaction, following the procedure described in section 2.4.3.1. The initial rate data for all the runs at different reaction conditions are presented in Table 3.3. 

The effect of butanol concentration on the initial rate of reaction showed that the initial rate decreases with increase in the concentration of butanol, as shown in Fig. 3.8. This is due to the fact that an increase in butanol concentration decreases the concentration of acetic acid, since the total volume of the reactants was kept constant (120 cm see also Section 2.4.3.1). 

In order to study the effect of particle size, the resin was sieved to obtain average particle sizes of 0.327, 0.5 and 0.74 mm diameter. The effect of particle size on initial rate of reaction is shown in Fig. 3.9. It was observed that there is significant effect of particle size on initial rate of reaction indicating the presence of intra particle diffusion. 

Following the procedures described in Section 2.4.3.2, the initial rate data was used to analyze the significance of mass transfer effect. It was found that the liquid-solid mass transfer resistance was negligible, as indicated by the value of az (Table 3.3). 

Reaction Conditions Temp = 353 K, Acetic acid-Butanol molar ratio = 1 2, dp = 4.58 X 10 m. 

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In contrast to consecutive reactions, with parallel competitive reactions it is possible to measure not only the initial rate of isolated reactions, but also the initial rate of reactions in a coupled system. This makes it possible to obtain not only the form of the rate equations and the values of the adsorption coefficients, but also the values of the rate constants in two independent ways. For this reason, the study of mutual influencing of the reactions of this type is centered on the analysis of initial rate data of the single and coupled reactions, rather than on the confrontation of data on single reactions with intergal curves, as is usual with consecutive reactions. 

This representation yields the so-called Lineweaver-Burk plot (Fig. 3.5). This is also commonly done in heterogeneous catalysis for analysis of initial rate data [4,5]. This changes, however the error distribution and parameter values may be... 

The analysis of initial rate data is useful in understanding the dependency of the reaction rate on individual reaction parameters and also in the evaluation of mass transfer effects. Initial rates of hydrogenation were calculated from the experimentally observed H2 consumption in the reservoir vessel vs time data. The initial rate data observed are presented in Table 3. The effects of individual parameters on the initial rate are dicussed below. 

For glyceraldehyde-3-phosphate dehydrogenase, conflicting conclusions have been reached by different workers (47 49). From one analysis of initial rate data, for the pig muscle enzyme, it appears that with glycer-aldehyde as substrate the mechanism is random (SO), whereas with glyceraldehyde 3-phosphate there is random combination of this substrate and NAD followed by phosphate as the compulsory third substrate (48). On the other hand, inhibition studies with the rabbit muscle enzyme indicate an ordered mechanism in which NAD is the first and acyl acceptor the last substrate to combine (51). More detailed comparative initial rate studies with the several aldehydes w hich act as substrates (Section II,E), preferably by a fluorimetric method (11,47), and isotope exchange studies at equilibrium are needed for this enzyme. 

The graphical analysis of initial rate data, which is described extensively in this chapter, is useful, especially while the experiment is still in progress. However, it is important to emphasize that, for definitive results, one should always fit the data with appropriate rate equations for statistical analysis (Cleland, 1979). 

It is useful to note the identity of terms in both equations, because both equations wiU be used for the graphical analysis of initial rate data in Section 12.1.3. 

Tlie usual procedure for the graphical analysis of initial rate data would be to treat each substrate as the varied substrate at different fixed concentrations of another substrate, maintaining a fixed concentration of the third substrate. All such plots represent a family of straight lines with a common intersection point to the left of the i/Uo-axis. 

The analysis of initial rate data is performed graphically and statistically. 

In the graphical analysis of initial rate data, it is pradent to use all three plots shown in Figs. 3 and 4. The direct plot of versus [A] wiU show directly the influence of substrate concentration on initial rate of reaction. The two linear plots should be used together, because the Lineweaver-Burk plot serves to visualize the influence of low concentrations whereas the Hanes plot serves to visualize the influence of high concentrations of substrates. The third plot, the Eadie-Hofstee plot, is useful in detecting exceptionally bad measurements (Section 3.11). 

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