The integrals for simple non-uniform reactions

In the case of non-uniform reactions, the relationship between the absorbances at the wavelength of irradiation and the degrees of advancement is given by 

In this case all the s linear independent degrees of advancement have to be summed up. The relationship between the different values of can be calculated for simple photoreactions under these conditions. A typical example is a parallel photoreaction as demonstrated in Section 3.1.2. 

A photoreaction is given in Example 3.17 in which both partial steps of the reaction are induced by absorption of the reactant A  

The following relationships are necessary to be able to integrate the rate equation 

The consecutive photoreaction is discussed in Example 3.25 in Section 3.2.3. Instead of eq. (3.40) derived there, eq. (3.83) can be used. In this case the parameter x has a different meaning. As demonstrated above it becomes 

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