Absorption rate constant worked example

Equation (41.11) represents the (deterministic) system equation which describes how the concentrations vary in time. In order to estimate the concentrations of the two compounds as a function of time during the reaction, the absorbance of the mixture is measured as a function of wavelength and time. Let us suppose that the pure spectra (absorptivities) of the compounds A and B are known and that at a time t the spectrometer is set at a wavelength giving the absorptivities h (0- The system and measurement equations can now be solved by the Kalman filter given in Table 41.10. By way of illustration we work out a simplified example of a reaction with a true reaction rate constant equal to A , = 0.1 min and an initial concentration a , (0) = 1. The concentrations are spectrophotometrically measured every 5 minutes and at the start of the reaction after 1 minute. Each time a new measurement is performed, the last estimate of the concentration A is updated. By substituting that concentration in the system equation xff) = JC (0)exp(-A i/) we obtain an update of the reaction rate k. With this new value the concentration of A is extrapolated to the point in time that a new measurement is made. The results for three cycles of the Kalman filter are given in Table 41.11 and in Fig. 41.7. The... 

Confirmation was provided by the observation that the species produced by the photolysis of two different carbene sources (88 and 89) in acetonitrile and by photolysis of the azirine 92 all had the same strong absorption band at 390 nm and all reacted with acrylonitrile at the same rate (fc=4.6 x 10 Af s" ). Rate constants were also measured for its reaction with a range of substituted alkenes, methanol and ferf-butanol. Laser flash photolysis work on the photolysis of 9-diazothioxan-threne in acetonitrile also produced a new band attributed the nitrile ylide 87 (47). The first alkyl-substituted example, acetonitrilio methylide (95), was produced in a similar way by the photolysis of diazomethane or diazirine in acetonitrile (20,21). This species showed a strong absorption at 280 nm and was trapped with a variety of electron-deficient olefinic and acetylenic dipolarophiles to give the expected cycloadducts (e.g., 96 and 97) in high yields. When diazomethane was used as the precursor, the reaction was carried out at —40 °C to minimize the rate of its cycloaddition to the dipolarophile. In the reactions with unsymmetrical dipolarophiles such as acrylonitrile, methyl acrylate, or methyl propiolate, the ratio of regioisomers was found to be 1 1. 

In order to investigate the kinetics of a reaction with the stirred cell, firstly experiments are carried out using a suitably related system in which gas absorption takes place by a purely physical mass transfer process (i.e. no reaction occurs). This establishes values of the physical mass transfer coeffient kL for the range of stirrer speeds employed. Then the rate of gas absorption into the liquid with the reaction occurring is measured. Finding the rate constant for a fast first-order reaction, for example, is then a matter of working back through equation 4.13 to find the value of P and hence of kt. 

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