Fixed-time integral methods measurement

In Example 13.1 the initial concentration of analyte is determined by measuring the amount of unreacted analyte at a fixed time. Sometimes it is more convenient to measure the concentration of a reagent reacting with the analyte or the concentration of one of the reaction s products. The one-point fixed-time integral method can still be applied if the stoichiometry is known between the analyte and the species being monitored. For example, if the concentration of the product in the reaction... 

The one-point fixed-time integral method has the advantage of simplicity since only a single measurement is needed to determine the analyte s initial concentration. As with any method relying on a single determination, however, a... 

Sensitivity The sensitivity for a one-point fixed-time integral method of analysis is improved by making measurements under conditions in which the concentration of the monitored species is larger rather than smaller. When the analyte s concentration, or the concentration of any other reactant, is monitored, measurements are best made early in the reaction before its concentration has substantially decreased. On the other hand, when a product is used to monitor the reaction, measurements are more appropriately made at longer times. For a two-point fixed-time integral method, sensitivity is improved by increasing the difference between times t and f2. As discussed earlier, the sensitivity of a rate method improves when using the initial rate. 

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. 

FIGURE 21-2 Fixed-time (teft) and variable-time (right) integral methods of measurement of reaction rates. 

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). 

Integral methods Variable time In the variable-time method of measurement of the initial slope, the concentration of the indicator substance I is measured twice, and the time interval At required to bring about a preselected change in concentration A[I] is the important quantity (Figure 21-2, right). Since the change in concentration is a fixed preselected value, it can be incorporated with the constant in Equation (21-5) to give... 

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... 

Two types of techniques are employed for analyzing a single-component system. The most straightforward is the derivative or slope method in which one obtains the derivative of the electrical signal by electronically differentiating the signal from the transducer. The second approach uses the integral forms of the rate equations, and one of two possible types of measurement the fixed-time or constant-time method... 

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. 

Figure 8. A plot of measured upconverted signal intensity (PMT voltage) vs. fluorescence intensity at fixed delay time. The data were acquired using Method A, and the fluorescence intensity was varied with neutral density filters. PMT voltage was monitored by integrator and hold electronics followed by an analog to digital converter.

Isothermal Method 2. This method is necessary to obtain cure data at low temperatures where the rate of heat evolution is too small for method 1 to be reliable. It is also recommended for nth-order reactions where the maximum rate of cure occurs at f = 0, and to obtain simultaneous Tg and conversion data to construct Jg-conversion plots. The conversion-time data can be fit to integrated forms of the rate equation, such as Eqs. (2.83)-(2.85). Several samples are cured isothermally, for example, in an oven, in the calorimeter or at ambient temperature, for various times until no additional curing can be detected. The samples are subsequently scanned in the DSC at a fixed heating rate, from which Tg and the residual heat of cure (A//res) the heat evolved during completion of the reaction, are measured, as illustrated in Fig. 2.69. 

Because multielement detection capability is probably the major reason why most laboratories invest in ICP-MS, it is important to understand the impact of measurement criteria on detection limits. We know that in a multielement analysis, the qua-drupole s RF-to-DC ratio is driven or scanned to mass regions, which represent the elements of interest. The electronics are allowed to settle and then sit or dwell on the peak and take measurements for a fixed period of time This is usually performed a number of times until the total integration time is fulfilled. For example, if a dwell time of 50 ms is selected for all masses and the total integration time is 1 s, then the quadrupole will carry out 20 complete sweeps per mass, per replicate. It will then repeat the same routine for as many replicates that have been built into the method. This is shown in a simplified manner in Figure 12.8, which displays the scanning protocol of a multielement scan of three different masses. 

---