Reaction-progress variables competitive-consecutive reactions

In chemical-engineering applications, the competitive-consecutive reactions are often studied in the limit where k oo. In this limit, the first reaction-progress variable Y can be written in terms of Y2 and f. From the reaction rate expression for Y, it can be seen that the limiting value is given by... 

The chemical compositions of many reacting systems can be expressed in terms of a single reaction progress variable. However, a chemical engineer must often consider systems that cannot be adequately described in terms of a single extent of reaction. In this chapter we are concerned with the development of the mathematical relationships that govern the behavior of such systems. We treat reversible reactions, competitive (parallel) reactions, and consecutive reactions, first in terms of the mathematical relations that govern the behavior of such systems and then in terms of the techniques that may be used to relate the kinetic parameters of the system to the phenomena observed in the laboratory. 

---