Reaction rate method

A reaction rate model was first used by Tobolsky and Eyring to describe the viscoelastic mechanical properties of rubber-like materials. Zhurkov and Korsukov showed that the same model could be used to account for the degradation of a number of polymers under an applied stress. They derived Eq. (10) for the time to failure, tf, in which A and are the Arrhenius constants for the fracture process, a is a constant (sometimes called the activation volume), and a is the applied stress. 

Their treatment assumes that mechanical fracture can be considered as a thermally activated process involving the degradation of stressed chemical bonds. 

The application of reaction rate theory has been extended to predict the failure times of adhesive bonds. This approach is reasonable if bond failure involves fracture within the adhesive layer. One form of the integrated rate equation, suitable for bonds under constant stress, is shown in Eq. (11).  

In this equation, tf is the time for bond failure at absolute temperature r, under constant stress cr. The terms C and b are constants and a = Ea/2303R all three terms can be found by graphical procedures. A comparison of experimentally determined failure times for different stress levels and those predicted by Eq. (11), for epoxy/aluminum lap shear joints at 140°F/95% RH, is presented in Table X. These and other results indicate that the reaction rate method is satisfactory for predicting the effect of 

It is known that the humidity of the environment also effects the rate of loss of strength of adhesive joints and thus the time to failure, but this is not allowed for in the above treatment. The reaction rate approach has been modified by treating the terms C, a, and b in Eq. (11) as fitting parameters that account for the temperature and stress dependence of the fracture process. 

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

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

Fabiny, P.L. and Ertingshausen, E., Automated reaction rates method for determination of serum creatinine with the centrifichem, Clinical Chemistry, 17, 696-700, 1971. 

Figure of merit Maximum reaction-rate method Peak-height method... 

Figure 3.8 — (A) Biosensors used in different FI manifolds to perform reaction-rate measurements (I) stopped-flow manifold (II) iterative flow-reversal system (III) open-closed configuration S sample B buffer P pump IV injection valve PC personal computer IMEC immobilized enzyme cell D detector W waste SV switching valve. (B) Types of recordings obtained by using the three types of biosensors and measurements to be performed on them in order to develop reaction-rate methods. (Reproduced from [50] with permission of Elsevier Science Publishers).

Figure 1-5 Determination of the order of hypothetical reactions with respect to species A. (a) The initial reaction rate method is used. The initial rate versus the initial concentration of A is plotted on a log-log diagram. The slope 2 is the order of the reaction with respect to A. The intercept is related to k. (b) The concentration evolution method is used. Because the exponential function (dashed curve) does not fit the data (points) well, the order is not 1. The solution for the second-order reaction equation (solid curve) fits the data well. Hence, the order of the reaction is 2.

To obtain products that are more homogeneous as well as better reaction rates, methods involving smaller particles than can be obtained by grinding have been introduced and these methods are described in the next section. 

Initial reaction rate method Again the decrease in the concentration of A over time is measured for two different initial concentrations. The reaction rate r for / — 0 is calculated with the help of a tangent at the steepest region of the curve, intersecting ca at t = 0, and the following equation (see Figure 4-lc) ... 

Figure 4-1 Method of half-life (a and b) and initial reaction rate method (c)...

Reaction-rate method A method independent of linear extrapolation but requiring more observations is to determine the rate of change in total concentration dCJdt, which approaches A b[B], as the concentration of A approaches zero ... 

Within each of the classifications of reaction-rate methods, there are many different methods of display or mathematical manipulation of the data or equations used to calculate the initial concentration of the species being determined. The calculating technique used can have very significant effects on the accuracy of the analysis. For example, the kinetic role of the species being determined in methods employing first-order or enzymatic or other catalyzed reactions has a strong effect on the choice of measurement of the reaction rate. For the simultaneous, in situ, analysis of several components of a mixture, the choice of method is even more critical with respect to accuracy. Both the relative and absolute values of the rate constants, as well as the initial concentrations of the species to be determined, dictate the choice of method. Furthermore, within the mathematical framework of each of these calculation procedures, there are generally optimum or limited times at which rate data should be taken in order to minimize the effects of random and absolute error in measurement. The choice of procedure and optimization of the measurement... 

As [R] decreases further, the kinetics again approach pseudo-first-order rates (Region VI), but now with respect to R. As [R] ([A] + [B]) (Region VII), a pseudo-first-order rate again applies, and general differential reaction-rate methods have been developed for this situation. There are also differential methods based on measurements of initial reaction-rates, where the kinetics become pseudo-zero-order. 

The rate of chemical reaction is considerably more sensitive to temperature variation than is the position of equilibrium (provided the formation constant is very large and the reaction can be considered quantitative ). Thus, temperature control is critical in reaction-rate methods. 

Most transducers converting chemical concentration into an electrical signal have a nonlinear response for example, electrode potential and optical transmission are not directly proportional to concentration. In general, this nonlinearity is easily and simply corrected in equilibrium analytical measurements. However, it is considerably more difficult to instrumentally correct the response-versus-concentration function in reaction-rate methods, and often the correction itself can introduce significant errors in the analytical results. For example, the simple nonlinear feedback elements employed in log-response operational-amplifier circuits are not sufficiently accurate in transforming transmittance into absorbance to be used for many analytical purposes. 

Figure 18.10. Block diagram of completely automated system for reaction-rate methods. From H. V. Malmstadt, E. A. Cordos, and C. J. Delaney, Anal. Chem., 44 2), 26A (1972), by permission of the senior author and the publisher. Copyright 1972 by the American Chemical Society.

In most equilibrium-based analytical methods, the success or failure of a determination is not affected by the reaction mechanism, provided that the reaction is either quantitative or the measured parameter at equilibrium is linearly proportional to the initial concentration of the species of interest. This is not the case in reaction-rate methods. Any development of a kinetic method should include, if possible, a complete study of the reaction mechanisms involved in the procedure. (Unfortunately, some reactions, such as catalytic reactions, are so complicated that complete elucidation of the mechanism is impossible.) It should also include a detailed study of the effects of typical sample-matrix components, which can act as catalysts, induce side-reactions, alter the activity of the reactants, and so on. The rates and rate constants for chemical reactions are very sensitive to low concentrations of such spectator species hence, samples containing the same true initial composition of the species of interest but coming from different sources can very often give quite different apparent concentrations. Unless the experimenter is aware of the total reaction mechanism and of all possible factors that can affect either the activation energy or the reaction path, erroneous analytical results can be obtained. A detailed investigation of the simultaneous, in situ, analysis of binary amine mixtures illustrates this point. (Most systems, by the way, are less error-prone than this one.) The rate constants for the reaction of many individual organic amines with methyl iodide in acetone solvent... 

In a narrower sense, however, the term kinetic method is confined to methods based on direct or indirect measurements of the rate of a chemical reaction, which ought to be called reaction-rate methods . This view is followed in this article. 

In the next section, the general principles of the analytical use of reaction-rate methods are described in the subsequent sections the application of noncatalytic and catalytic techniques are treated. Several methods, instruments, and techniques for which separate entries can be found in this encyclopedia are only briefly mentioned, e.g., enzymatic catalysis, chemiluminescence, sensors, data processing. 

Kinetic methods have been classified according to a number of criteria. One classification distinguishes between catalytic and noncatalytic methods (see Table 1). The former are further divided according to the type of reaction involved, while the latter are categorized according to whether they are used to determine a single species or several components in mixtures (differential reaction-rate methods)... 

For determination of multicomponents (differential reaction-rate methods)... 

Differential reaction-rate methods are based on the different rate at which two or more species react with a common reagent and allow the determination of several components without the need for a prior separation. 

Noncatalytic reactions are less frequently used in kinetic-based determinations than are those involving a catalytic effect. However, recent advances in instrumentation mean that noncatalytic kinetic methods are powerful alternatives to equilibrium (nonkinetic) methods. This type of reaction is of especial relevance to the analysis of mixtures of closely related compounds, for which a munber of differential reaction rate methods have been developed. Whether for individual or joint determinations of species, the main field of application of noncatalytic reactions is organic analysis, unlike catalytic reactions, where a metal ion usually acts as the catalyst this has also contributed to their current wide acceptance. 

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