Fixed-time methods

An alternative to a fixed-time method is a variable-time method, in which we measure the time required for a reaction to proceed by a fixed amount. In this case the analyte s initial concentration is determined by the elapsed time, Af, with a higher concentration of analyte producing a smaller Af. For this reason variabletime integral methods are appropriate when the relationship between the detector s response and the concentration of analyte is not linear or is unknown. In the one-point variable-time integral method, the time needed to cause a desired change in concentration is measured from the start of the reaction. With the two-point variable-time integral method, the time required to effect a change in concentration is measured. 

The reaction is now first-order in substrate, and the rate of the reaction can be used to determine the substrate s concentration by a fixed-time method. 

Walash et al. [14] described a kinetic spectrophotometric method for determination of several sulfur containing compounds including penicillamine. The method is based on the catalytic effect on the reaction between sodium azide and iodine in aqueous solution, and entails measuring the decrease in the absorbance of iodine at 348 nm by a fixed time method. Regression analysis of the Beer s law plot showed a linear graph over the range of 0.01 0.1 pg/mL for penicillamine with a detection limit of 0.0094 pg/mL. 

Enzymes are extremely useful analytical tools, primarily because of their specificity. Currently a very large number of enzymes are available commercially in various forms of purity and, although their cost is often high, only small amounts are usually required. Procedure 8.8 describes a fixed time method for the quantitation of D-alanine using D-amino acid oxidase. 

Tomiyasu, T., Sakamoto, H., and Yonehara, N., Catalytic determination of iron by a fixed-time method using the oxidation reaction of chlorpromazine with hydrogen peroxide, Analyt. Sci., 12, 507-509, 1996. 

Integral methods Constant time In the fixed-time method of measurement the change in concentration of the indicator substance I [which could be [R] or [P] in Equation (21-2)] is measured twice to cover a preselected time interval (Figure 21-2). 

Fixed-time methods include those in which the reaction is quenched after a preselected period of time and the solution analyzed by chemical or physical techniques. 

According to Equation (21-13), with a constant enzyme concentration the rate of reaction is linearly proportional to substrate concentration at low concentrations, and fixed-time methods are appropriate. Such methods are commonly used in clinical laboratories. At high concentrations of substrate the rate becomes independent of concentration (Figure 21-7). For measurement of enzyme concentrations, variable-time procedures have advantages. 

Product inhibition is a cause of nonlinearity of reaction progress curves during fixed-time methods of enzyme assay. For example, oxaloacetate produced by the action of aspartate aminotransferase inhibits the enzyme, particularly the mitochondrial isoenzyme. The inhibitory product may be removed as it is formed by a coupled enzymatic reaction malate dehydrogenase converts the oxaloacetate to malate and at the same time oxidizes NADH to NADL... 

Determmation of reaction rate involves the kinetic measurement of the amount of change produced in a defined time interval. Both fixed-time and continuous-monitoring methods are used to measure reaction rates. In the fixed-time method, the amount of change produced by the enzyme is measured after stopping the reaction at the end of a fixedtime interval. In the continuous-monitoring method, the progress of the reaction is monitored continuously. These two methods have different advantages and limitations. To appreciate these, it is necessary to consider the way in which the rate of an enzymatic reaction varies with time. 

Fixed-Time Methods Fixed-time methods are based on Equation 29-7 or 29-9. The former can be rearransed to... 

An important example of an uncatalyzed method is the fixed-time method for the determination of thiocyanate ion based on spectrophotometric measurements of the red iron(III) thiocyanate complex. The reaction in this application is... 

Fixed-time methods are advantageous because the measured quantity is directly proportional to the analyte concentration and because measurements can be made at any time during the progress of first-order reactions. When instrumental methods are used to monitor reactions by means of fixed-time procedures, the precision of the analytical results approaches the precision of the instrnment used. 

Because this method involves counting for a fixed time, the background and low-intensity portions of the diffraction line are measured with less accuracy than the high-intensity portions. The counting time should be chosen so that the low intensities are measured to the accuracy required by the particular problem involved it will then follow that the high intensities are measured with unnecessarily high accuracy, but that is unavoidable in a fixed-time method. 

Equation 18.12 is the basis for the derivative approach to rate-based analysis, which involves directly measuring the reaction rate at a specific time or times and relating this to [A]fl. Equation 18.11 is the basis for the two different integral approaches to kinetic analysis. In one case, the amount of A reacted during a fixed time is measured and is directly proportional to [A]o ( fixed-time method) in the other case, the time required for a fixed amount of A to react is measured and is also proportional to [A]o variable-time method). Details of these methods will be discussed in Section... 

If all measurements are begun at the same value of after the start of the reaction and Ar is constant, the quantity in brackets will be constant for all experiments, and [A]o is directly proportional to This is true for any fixed time-interval during the reaction and, thus, the fixed-time method is not restricted to measurements of initial rates. However, the analysis can be considerably simplified if the measurement is made before 1-2% of A has reacted. 

The use of this equation in the fixed-time method is shown in Figure 18.3. It is clear from the format of the fixed-time method and Equations 18.29 and 18.30 that, if is not directly proportional to A[P] (as is the case with nonlinear-response instruments), the fixed-time method will lead to a nonlinear relation between A and [A]o this virtually rules out the use of this method with such instruments. 

Figure 18.3. The fixed-time method for uncatalyzed reactions, in the case where = 0 and S t=o = 0. (a) Variation of as a function of time for various different initial concentrations of A. (6) Variation of Ay at a fixed time-interval At with change in [/4]q.

With respect to the use of catalyzed reactions, the catalyst concentrations can be determined using the fixed-time method, but strict adherence to pseudo-zero-order conditions (initial reaction-rate measurement) is generally necessary to obtain linear calibration curves. 

The variable-time method, like the fixed-time method, is an integral method which, for short measurement times and small changes in concentration, also gives results approaching the instantaneous reaction-rate. 

The variable-time method, however, is not as well suited for determining substrate concentrations as the fixed-time method there will be a nonlinear relationship between [S]o and 1/Ar unless pseudo-zero-order conditions are used during the interval At and the measurements are begun very close to r = 0. 

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... 

Technetium Color formation with 1,3,5-triphenyl-A -pyrazoline 0.01-12 Initial-rate and fixed-time methods used... 

Hydrazine Reaction with Mo(VI) 10 moir level Use of variable and fixed-time methods. Spectrophotometric detection... 

Differential fixed-time method Implementation of this kinetic method involves measuring the concentration of a reactant or product at a preset time from the start of the reaction according to the following equation... 

Hgure 2 Implemenlation of the fixed-time method. (Reproduced with permission from Perez-Bendito D and Silva M (1988) Kinetic Methods in Analytical Chemistry. Chichester Ellis Honvood.)... 

Af-phenyi-p-phenyienediamine-1- A/, A/-dimethyianiiine -1- HzOi 0.4 Fixed-time method (f=15min)... 

Rhodamine B -i- HzOi 0.04-150 Accelerated by potassium thiocyanate fixed-time method (f=12min)... 

Thionine-i-KBrOa (N02 ) 7xl0 -1.2x10 moir Fixed-time method (f=5min)... 

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