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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Abstract. The integrating ratemeter is used in concert with the two-rate parameter to form the integrating ratemeter two-rate parameter. Propagation of error theory is applied to the integrating ratemeter two-rate parameter to yield expressions for the precision of rates calculated from the integrating ratemeter two-rate parameter in terms of the precision of the rates measured with the integrating ratemeter. Simulations and experimental results show that in cases where the standard deviation of the rate is relatively constant, the optimum time to make a rate measurement using the integrating ratemeter is also the optimum time to measure either of the rates in the two-rate parameter. If either of the two rates comprising the two-rate parameter is measured at the optimum time, then the precision and accuracy of concentrations measured with this technique are optimized.Key words" kinetics, rates, integrating ratemeter, optimization, first-order.Recent efforts to improve the precision and accuracy of reaction-rate methods of analysis have concentrated on the reduction of the effects of variations in experimental variables that affect the first-order or pseudo-first-order rate constant of an analytical reaction [1][2][3][4][5]. Temporal optimization of reaction rate measurement [1] and the temporally optimized fixed-time integrating ratemeter [2,3] have been shown to improve the precision of rate measurements. Wentzell and Crouch devised the two-rate-parameter Ptr, which is insensitive to between-run variations in the rate constant [4], and compared its performance with other reaction rate measurement techniques [-5]. Love and Pardue [6] have shown that the two-rate-parameter has considerable advantage in minimizing between-run errors relative to other data enhancement methods, but noise inherent in acquiring instantaneous rates at two different times leads to imprecision in measured concentrations. The use of the integrating ratemeter method in the computation of Ptr should provide a powerful