Initial reaction rate method

Determination of a singie species Pseudo-first-order reactions Initial rate method Fixed-time method Variable-time method Second-order reactions Identical reactant concentrations Unequal reactant concentrations Multipoint methods Curve-fitting methods Predictive methods Error-compensated methods... 

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)... 

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... 

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. 

The kinetics of the addition of aniline (PI1NH2) to ethyl propiolate (HC CCChEt) in DMSO as solvent has been studied by spectrophotometry at 399 nm using the variable time method. The initial rate method was employed to determine the order of the reaction with respect to the reactants, and a pseudo-first-order method was used to calculate the rate constant. The Arrhenius equation log k = 6.07 - (12.96/2.303RT) was obtained the activation parameters, Ea, AH, AG, and Aat 300 K were found to be 12.96, 13.55, 23.31 kcalmol-1 and -32.76 cal mol-1 K-1, respectively. The results revealed a first-order reaction with respect to both aniline and ethyl propiolate. In addition, combination of the experimental results and calculations using density functional theory (DFT) at the B3LYP/6-31G level, a mechanism for this reaction was proposed.181... 

Although not very commonly used (with the exception of the initial rate procedure for slow reactions), the differential method has the advantage that it makes no assumption about what the reaction order might be (note the contrast with the method of integration, Section 3.3.2), and it allows a clear distinction between the order with respect to concentration and order with respect to time. However, the rate constant is obtained from an intercept by this method and will, therefore, have a relatively high associated error. The initial rates method also has the drawback that it may miss the effect of products on the global kinetics of the process. 

A reaction which is complete within, say, a day may be monitored for most of its course whereas a slower reaction would usually be studied using the initial rates method (see Section 3.3.1) using data collected during the initial stages - perhaps just the first 1% of the reaction. 

Initial Rate Method. Using integrated equations like Eqs. (2.5), (2.6), or (2.7) to directly determine a rate law and rate constants is risky. This is particularly true if secondary or reverse reactions are important in equations like (2.5) and (2.6). One sound option is to establish these equations directly using initial rates (Skopp, 1986). 

The initial rate is the limit of the reaction rate as time reaches zero. Using the initial rate method, one could ascertain Eqs. (2.5) and (2.6) by finding out how the initial rates (lim d[A]/dt) depend on the initial concentrations (A, B, Y). Experiments are conducted such that initial concentrations of each reactant are altered while the other concentrations are constant. It is desirable with this method to have one reactant in much higher concentration than the other reactant(s). 

Kinetics of the addition of PI13P to p-naphthoquinone in 1,2-dichloromethane, using the initial rate method, revealed the order of reaction with respect to the reactants the rate constant was obtained from pseudo-first-order kinetic studies. A variable time method using UV-visible spectrophotometry (at 400 nm) was employed to monitor this addition, for which the following Arrhenius equation was obtained log k = 9.14- (13.63/2.303RT). The resulting activation parameters a, AH, AG, and Aat 300 K were 13.63, 14.42 and 18.75 kcalmol-1 and —14.54 calmol 1K 1,... 

In another procedure, which we shall call the initial-rate method, the reaction is ran for a time small in comparison with the half-life of the reaction but large in comparison with the time required to attain a steady state, so that the actual value of the initial rate [the initial value of the derivative on the left side of Eq. (3)] can be estimated approximately. Enough different combinations of initial concentrations of the several reactants are employed to enable the exponents to be determined separately. For example the exponent m is determined from two experiments which differ only in the IO3 concentration. 

In the present experiment the rate law for the reaction shown in Eq. (1) will be studied by the initial rate method, at 25°C and a pH of about 5. The initial concentrations of iodate ion, iodide ion, and hydrogen ion will be varied independently in separate experiments, and the time required for the consumption of a definite small amount of the iodate will be measmed. 

Initial-rate methods have several fundamental advantages. Since the amount of product formed during the period of measurement is small, the reverse reaction decreases the overall net rate inappreciably. Complications from slower side reactions usually are minimal. The concentrations of reactants change but little, and pseudozero-order kinetics are obeyed. For reactions whose rates are in the useful range, measurements of initial rate should be more precise than measurements of rates at later times because the rate is highest at the beginning, where the slope of the curve is steepest and the relative signal-to-noise ratio is most favorable. Initial-rate methods permit the use of reactions whose formation constants may be too small for equilibrium methods. 

Initial rate methods Kinetic methods based on measurements made near the onset of a reaction. 

The initial rate method has only rarely been applied to soil kinetics studies. Aringhieri et al. (1985) used the initial rate method to establish that the reaction orders for each reactant (element and soil) were unity for Cu and Cd retention by a soil. The overall reaction was thus second-order. 

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