Comparison of reaction-rate methods of analysis for systems following first-order kinetics

Wentzell, Peter D.; Crouch, S. R.

doi:10.1021/ac00126a059

Cited by 34 publications

(9 citation statements)

References 44 publications

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“…Davis and Pevnick (3) considered coupled enzyme reactions and obtained optimum times for several cases of variations in one or both of the rate constants. Most recently, Wentzell and Crouch presented a two-rate method (4) and compared the accuracy and precision of their method and several other methods under various conditions (5). In an earlier report, we used propagation of error theory to show that the relative standard deviation of the rate of a first-order reaction is zero at t = 1/k = and presented experimental evidence verifying this result (6).…”

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confidence: 83%

Improvement of reaction rate measurement precision using the temporally optimized fixed-time ratemeter

Engh¹,

Holler²

1988

Anal. Chem.

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The domain of application of the flxed-time integrating ratemeter method is extended to ail times during first-order and pseudo-first-order reactlons. Propagation of error theory is applied to rate expressions to glve the optimum tlme for rate measurement as a function of Integration wldth. The maximum integration wldth consistent with the optimum measurement time is determined. Experimental data collected with a stopped-flow mixer uslng the iron( I I I)-thlocyanate reaction show excellent agreement with theory. The relative standard deviation of concentration of flve determlnations of a thlocyanate unknown was 0.16% under conditions of random varlabie temperature.It has been shown previously that the precision of reaction rate measurements can be improved by selection of the optimum time at which to make these measurements (1-6). To make best use of an optimum time for measurement, a reliable method of obtaining the rate at a single time is needed. The fixed-time integrating ratemeter method (7) gives an estimate of the rate a t a time at the center of an interval over which the reaction curve can be considered to be linear. In contrast to many methods of rate estimation, this approach is highly resistant to instrumental noise. In this paper we will show that this method is valid under first-order and pseudo-firstorder conditions at any time during the reaction, that the precision of the rate obtained by this method can be temporally optimized, and that there is a maximum integration width consistent with temporal optimization. Finally, we present experimental verification of temporal optimization and signal-to-noise-ratio enhancement resulting from optimum use of the integrating ratemeter.Several strategies have been proposed to temporally optimize reaction rate measurements. Landis et al. (I) recognized that a measurement time o f t = l / k = T is optimum, where k is the first-order or pseudo-first-order rate constant for the reaction, but only used this result for error analysis. Davis and Renoe (2) developed equations to obtain optimum times for wide-interval fixed-time rate measurements. Davis and Pevnick (3) considered coupled enzyme reactions and obtained optimum times for several cases of variations in one or both of the rate constants. Most recently, Wentzell and Crouch presented a two-rate method (4) and compared the accuracy and precision of their method and several other methods under various conditions (5). In an earlier report, we used propagation of error theory to show that the relative standard deviation of the rate of a first-order reaction is zero at t = l / k = 7 and presented experimental evidence verifying this result (6). Three assumptions were made in that development: (1) the reaction of interest is first order or pseudo first order, (2) sources of error other than variation in the rate constant are negligible, and (3) the rate can be estimated by instrumental or numerical methods at any time during the reaction. To take full advantage of the simplicity of a single-rate measurement at t ...

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confidence: 83%

Improvement of reaction rate measurement precision using the temporally optimized fixed-time ratemeter

Engh¹,

Holler²

1988

Anal. Chem.

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“…Linearized Rate Equation. As described earlier (6), it is assumed that the rate of change of concentration can be represented by the equation -dct/df = kctn (1) in which k is a rate constant, n is the reaction order, and ct is the concentration of the species monitored (reactant or product) at time, t. It is also assumed that the time-dependent concentration is related to measured signal by ct = (D/q)(S" -SO (2) in which D is ±1 and accounts for the direction of signal change and q accounts for stoichiometry (6) and St and S" are values of signal at time t and at t = ", respectively.…”

Section: Mathematical Descriptionmentioning

confidence: 99%

Linearized model for error-compensated kinetic determinations without prior knowledge of reaction order or rate constant

Larsson¹,

Pardue²

1989

Anal. Chem.

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This paper describes a new algorithm for calculation of reaction orders, rate constants, and initial and final values of detector signal from several signal vs time data points. The algorithm utilizes a linearized version of the rate equation and is intended primarily to provide initial estimates of these kinetic parameters for other curve-fitting methods. However, under some circumstances, the linearized model can provide sufficiently reliable results that subsequent processing by other methods is not needed. Simulated data with different levels of superimposed noise, data densities, reaction orders, rate constants, and signal change are used to evaluate the algorithm both for its primary purpose of providing initial estimates for other curve-fitting methods and as an independent method. Results are compared with those obtained with a nonlinear least-squares method and two initial-rate methods. The new algorithm provides less reliable results than those obtained by the nonlinear curve-fitting method for some situations (e.g. reaction orders greater than two, low data densities) but has the advantage that it is applicable to reaction orders at and near unity where the nonlinear method to which it is compared fails.

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“…They record the spectra after the reaction reaches equilibrium. A number of differential kinetic methods [21][22][23][24] have been developed for resolving mixtures of analytes with similar or identical spectra, which cannot be resolved by equilibrium-based methods. The simultaneous kinetic determination of such analytes is usually based on the difference in their reaction rate constants.…”

Section: Introductionmentioning

confidence: 99%

Application of principal component-artificial neural network models for simultaneous determination of phenolic compounds by a kinetic spectrophotometric method

Hasani

Moloudi

2008

Journal of Hazardous Materials

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Comparison of reaction-rate methods of analysis for systems following first-order kinetics

Cited by 34 publications

References 44 publications

Improvement of reaction rate measurement precision using the temporally optimized fixed-time ratemeter

Improvement of reaction rate measurement precision using the temporally optimized fixed-time ratemeter

Linearized model for error-compensated kinetic determinations without prior knowledge of reaction order or rate constant

Application of principal component-artificial neural network models for simultaneous determination of phenolic compounds by a kinetic spectrophotometric method

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