Quantum yields independent on reaction time

In Section 1.4.2, in analogy to the thermal rate constants, photochemical quantum yields have been defined. It was mentioned that the amount of light absorbed varies according to Section 1.4.3 during the photoreaction. Accordingly the definitions given in Section 1.4.2 exhibit a dependence on time. 

It is assumed that a simple photoreaction stoichiometrically takes place according to the condition given in eq. (1.4). If the reactant A = A starts a photoreaction, then the degree of advancement is given according to eq. (1.8) and one finds the rate law as given in eq. (1.2) to 

10) the amounts of the stoichiometric coefficients have to be inserted, since the quantum yields are defined always as positive numbers. 

It makes more sense to relate the quantum yield to the degree of advancement X. Therefore by definition 

In principle the superscript refers to the reactant which starts the photoreaction absorbing the radiation. The subscript refers to the reactant under consideration. In the case of the use of the degree of advancement, its subscript is not necessary. Two other true quantum yields can be defined. 

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