Approximation photokinetic factor

A successful approximation for Eq. (8) is the introduction of total (complete) absorption. Under such conditions, the photokinetic factor F t) is replaced by A, and Eq. (8) reduces to... 

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. 

Approximate integration of Equation 3.22 is possible by linear interpolation of the reciprocal photokinetic factor,222 F(Xia,t) (Equation 3.23). 

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... 

An approximation using the photokinetic factor given by eq. (3.69) supplies an even better evaluation using azobenzene as an actinometric system. Using a linear interpolation between two points of measurement at time ti and 2 the photokinetic factor according to eq. (5.108) can be approximated within this time domain as... 

To reduce the dependence on the geometric properties in fluorescence spectroscopy usually very dilute solutions are used. The photokinetic factor F(t) is approximated according to eq. (5.111). Under these conditions neither the change in absorbance at the wavelengths of irradiation E nor changes in the factors r(E ) and r(E ) have to be taken into account. Thus eq. (5.136) can be rewritten as... 

The photoisomerisation of azobenzene in methanolic solution is a preferable photoreaction to be used in actinometry, since the mechanism has been well examined. The trans-cis photoreaction is photoreversible. The thermal reaction cis trans will not disturb photokinetics at normal conditions because of a half-life of approximately 1 week. Therefore a concentrated solution of trans-azobenzene in methanol at 6.4 x 1(H mol h, which totally absorbs radiation between 345 and 240 nm, can be used taking eq. (5.107) and the approximation given by eq. (5.109). In a first approximation the change in absorbance with time at a wavelength of observation is proportional to the intensity of radiation. This proportionality includes the photochemical quantum yields of the trans cis isomerisation step, the factor 1000 and the absorption coefficients at the observation wavelengths of the trans and cis isomers. 

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