Initial rate, method

The rate of reaction is measured at the commencement of the reaction, when the concentrations of the reactants are accurately known, indeed predetermined. 

It is apparent from these data that within experimental error the initial rate is proportional to the initial concentration of iron(III) complex, (Runs 1-3) to the square of the initial HjOj concentration [H202]q (4-6) and inversely dependent on both H+ (7-9) and total acetate [OAc].p (10-12) concentrations. A rate law involving the initial rate Fq, 

Initial reaction rates are often estimated from the steepest tangents to absorbance/time traces. These initial gradients (absorbanee units/sec) are easily converted into Ms units by using the known molar absorptlvities of products and reactants. Alternatively, absorbanee (Z))/Time (T) plots can be fit to a funetion (1.9) leading to (1.10) and (1.11) 

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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. 

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. 

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)... 

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... 

One advantage of the initial rate method is that complex rate functions that may be extremely difficult to integrate can be handled in a convenient manner. Moreover, if one uses initial reaction rates, the reverse reactions can be neglected and attention can be focused solely on the reaction rate function for the forward reaction. More complex rate functions may be tested by the choice of appropriate coordinates for plotting the initial rate data. For example, a reaction rate function of the form... 

M. Muratsugu, S. Kurosawa, and N. Kamo, Detection of antistreptolysin O antibody application of an initial rate method of latex piezoelectric immunoassay. Anal. Chem. 64, 2483-2487 (1992). 

Initial-rate method. This method is similar to the previous one, but only uses values of... 

The quantity and quality of experimental information determined by the new techniques call for the use of comprehensive data treatment and evaluation methods. In earlier literature, quite often kinetic studies were simplified by using pseudo-first-order conditions, the steady-state approach or initial rate methods. In some cases, these simplifications were fully justified but sometimes the approximations led to distorted results. Autoxidation reactions are particularly vulnerable to this problem because of strong kinetic coupling between the individual steps and feed-back reactions. It was demonstrated in many cases, that these reactions are very sensitive to the conditions applied and their kinetic profiles and stoichiometries may be significantly altered by changing the pH, the absolute concentrations and concentration ratios of the reactants, and also by the presence of trace amounts of impurities which may act either as catalysts and/or inhibitors. 

Because of the complexity of biological systems, Eq. (1) as the differential form of Michaelis-Menten kinetics is often analyzed using the initial rate method. Due to the restriction of the initial range of conversion, unwanted influences such as reversible product formation, effects due to enzyme inhibition, or side reactions are reduced to a minimum. The major disadvantage of this procedure is that a relatively large number of experiments must be conducted in order to determine the desired rate constants. 

The rate of loss of reactant is negative because the concentration decreases with time The gradient at the start of the reaction is called the initial rate. Analysing the initial rates method is an extremely powerful way of determining the order of a reaction. 

One way to ensure that back reactions are not important is to measure initial rates. The initial rate is the limit of the reaction rate as time reaches zero. With an initial rate method, one plots the concentration of a reactant or product over a short reaction time period during which the concentrations of the reactants change so little that the instantaneous rate is hardly affected. Thus,by measuring initial rates, one can assume that only the forward reaction in Eq. (35) predominates. This would simplify the rate law to that given in Eq. (36) which as written would be a second-order reaction, first-order in reactant A and first-order in reactant B. Equation (35), under these conditions, would represent a second-order irreversible elementary reaction. 

As you have learned, the values of the exponents in a rate law equation must be determined experimentally. Chemists determine the values of m and n by carrying out a series of experiments. Each experiment has a different, known set of initial concentrations. All other factors, such as temperature, remain constant. Chemists measure and compare the initial rate of each reaction. Thus, this method is called the initial rates method. 

To see how the initial rates method works, consider the following reaction ... 

Then, k equals the observed reaction rate divided by the initial reactant concentration i.e., k = Vinitiai/[Ainitiai])-This method is most useful when one has an assay method that is sufficiently sensitive to ensure that only a small fraction, say 3-5%, of the reactant is depleted during the rate measurements. Typically, this is satisfactorily achieved with a UV-visible spectrophotometer, a fluorescence spectrometer, or a radioactively labeled reactant. The initial rate method is extremely convenient, and the preponderance of enzyme rate data has been obtained by initial rate measurements. Finally, one should note that the initial rate method can yield erroneous results if the initial reactant concentration is in doubt. This is not true for the plots of ln ([Ao] - [At]/([Ao] -[Aoo]) versus reaction time because one is considering the fraction of reactant A remaining. 

While requiring the availability of competitive inhibitors for each of the substrates, Fromm s use of competitive inhibitors to distinguish multisubstrate enzyme kinetic pathways represents the most powerful initial rate method. See Alternative Substrate Inhibition... 

An initial-rate method introduced by Fromm to discriminate between rival three-substrate enzyme kinetic mechanisms. See Fromm Method for Ternary Systems. 

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