Photokinetic-thermal equations

A different approximation is based on the use of very dilute solutions in which the absorbance is smaller than 0.02 units (A <0.02). In this case, the photokinetic factor is considered constant as an expansion into series. Accordingly, the factor exhibits a value of 2.303, and the rate depends on the concentration in a similar way as observed in first-order (thermal) reactions. Assuming a partial absorption during the photoreaction and taking into account that the photoproducts will also absorb at the actinic wavelength, the photokinetic equations become more complicated. There are a large number of such different equations, each tailored to a specific problem, as demonstrated in the various examples in the following sections. 

Rate constants are determined by variation of experimental conditions and chemical composition of the reaction mixture. Data are measured by application of a variety of modem analytical methods. Modem numerical approaches of curve fitting and/or solution of differential equations are applied. Results and consequences influence chemical reaction engineering as well as production costs. Many books cover these formal thermal kinetics in detail, but most are restricted to simple mechanisms. In contrast, analogous treatments of photochemical reactions are restricted to publications of special reactions and examinations. Therefore this book aims to supply an overall treatment of formal photokinetics beyond the scope of normal books on kinetics. 

The change in concentration of reactants is at the centre of interest in photokinetics as well as the determination of these partial photochemical quantum yields. The time laws cannot be integrated in a closed form. Therefore to avoid the problems with solving these differential equations, the integrals are numerically calculated - a procedure named formal integration. This method also turns out to be advantageous in thermal and photochemical examinations. 

In contrast to thermal kinetics the photokinetic equations given above cannot be solved in a closed form, since the photokinetic factor depends on the absorbance of the solution itself and is consequently dependent on time. In the literature approximations either with respect to total absorbance or to very dilute solutions are used. The consequences are discussed in detail in Section 3.3.3. Using the conditions... 

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