Response Experiments and Lifetime Distributions

We consider that the chemical process studied takes place in an isothermal, continuous-flow stirred tank reactor (CSTR) operated with a constant total flow rate and with constant input concentrations. We assume that at least one of the chemicals entering the system is available in two different forms, unlabeled and labeled, respectively, and that the kinetic isotope effect can be neglected, that is, the kinetic parameters are the same for the labeled 

For a given reaction intermediate, which may exist in an unlabeled form Xj as well as in a labeled form, Xf, we assume that it is possible to measure the time dependence of the following fractions  

The ratio a, (f) between the rate [x (f)] of generation of the labeled compound 

In order to extract the information about the lifetime distributions from these two functions, o, (t) and Pt (t), we derive an evolution equation for the concentration xf (t) of labeled intermediate in the system  

Balance equations of this type were introduced in chemical kinetics by Neiman and Gal [18]. Equations (12.18) must be supplemented by the kinetic equations (12.2)  

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