Rate Method

Let the rate equation be v = kc%,. We initiate the reaction and measure Ca as a function of time during the first few percentage of reaction. The slope of the plot 

Thus by measuring Vq at several values of c , the log-log plot yields the reaction order. This method also works if the rate equation includes the concentrations of other reactants, provided their concentrations are held constant throughout the series of measurements. 

Casado et al. have analyzed the error of estimating the initial rate from a tangent to the concentration-time curve at t = 0 and conclude that the error is unimportant if the extent of reaction is less than 5%. Chandler et al. ° fit the kinetic data to a polynomial in time to obtain initial rate estimates. 

One advantage of the initial rate method is that it avoids any complications arising from product inhibition or catalysis or from subsequent reactions. Another advantage is that it is applicable to veiy slow reactions whose study by other methods might be impractical. 

The initial rate method yields the reaction order with respect to concentration. 

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Direct-Computation Rate Methods Rate methods for analyzing kinetic data are based on the differential form of the rate law. The rate of a reaction at time f, (rate)f, is determined from the slope of a curve showing the change in concentration for a reactant or product as a function of time (Figure 13.5). For a reaction that is first-order, or pseudo-first-order in analyte, the rate at time f is given as... 

Sensitivity The sensitivity for a one-point fixed-time integral method of analysis is improved by making measurements under conditions in which the concentration of the monitored species is larger rather than smaller. When the analyte s concentration, or the concentration of any other reactant, is monitored, measurements are best made early in the reaction before its concentration has substantially decreased. On the other hand, when a product is used to monitor the reaction, measurements are more appropriately made at longer times. For a two-point fixed-time integral method, sensitivity is improved by increasing the difference between times t and f2. As discussed earlier, the sensitivity of a rate method improves when using the initial rate. 

Malmstadt, H. V. Delaney, C. J. Cordos, E. A. Reaction-Rate Methods of Chemical Analysis, Crit. Rev. Anal. Chem. 1972, 2, 559-619. 

A variation on the use of pseudo-ordered reactions is the initial rate method. In this approach to determining a reaction s rate law, a series of experiments is conducted in which the concentration of those species expected to affect the reaction s rate are changed one at a time. The initial rate of the reaction is determined for each set of conditions. Comparing the reaction s initial rate for two experiments in which the concentration of only a single species has been changed allows the reaction order for that species to be determined. The application of this method is outlined in the following example. 

The heat-transfer surface area determined by the basic sizing or rating method described herein is considered the minimum required area. There are also additional surface area requirements in the final sizing of a heat exchanger. 

If exchanger shell diameter is in doubt, see Chapter 2, Heat Exchangers, the Shell Diameter section. In addition, this book provides a rough rating method for air-cooled heat exchangers. 

Initial rate method. Consider a first-order reaction studied by the method of initial rates. If AY/At represents the slope of the initial linear portion of the recording of Y against time, show that the rate constant is given by... 

Induced reactions, 102 Induction period, 72 Inhibitor competitive, 92 noncompetitive, 93 Initial rates, method of, 8, 32 from power series, 8 Initiation step, 182 Inverse dependences, 130-131 Isokinetic relationship, 164—165 Isokinetic temperature, 163, 238 Isolation, method of (see Flooding, method of)... 

Method of initial rates (see Initial rates, method of)... 

This result is experimentally indistinguishable from the general form, Equation (10.12), derived in Example 10.1 using the equality of rates method. Thus, assuming a particular step to be rate-controlling may not lead to any simplification of the intrinsic rate expression. Furthermore, when a simplified form such as Equation (10.15) is experimentally determined, it does not necessarily justify the assumptions used to derive the simplified form. Other models may lead to the same form. 

Bimolecular Reactions. Models of surface-catalyzed reactions involving two gas-phase reactants can be derived using either the equal rates method or the method of rate-controlling steps. The latter technique is algebraically simpler and serves to illustrate general principles. 

Automated reaction rate methods of anaylsis. Anal. Chem. (1972), 44 (12), 26A- 41A. 

The Controlled Shear Rate Method - Testing on Aqueous Pectin Solutions... 

Table 3), Enantioselective reaction was of order 0 7 in hydrogen by the initial rate method (over the range 2 to 50 bar, 293 K, cinchonine modifier) and 0 2 in pyruvate (0 1 to 3.0 M, 293 K, 10 bar pressure, cinchonine modifier) Enantiomeric excess was independent of reactant concentrations within these ranges Reactions exhibited self-poisoning so that complete conversion was not achieved within 20 h reaction time. As the quantity of cinchonine modifier added to the catalyst was increased from zero to 1 gram per gram so the... 

This method is basically a rating method, suitable for determining the performance of an existing column, rather than a design method, as the number of stages must be known. 

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