Overall reaction progress variable

In section 2.12 we recalled the significance of the overall reaction progress variable I which represents the extent of advancement of simultaneous irreversible processes in heterogeneous systems (Temkin, 1963). The overall progress variable is related to progress variables of individual reactions by... 

Delany et al., 1986). The relative rate of theyth reaction o) with respect to the overall reaction progress variable f is given by... 

The essential goal is to locate the transition state on the RIP diagram. This involves specifying two coordinates, so two quantitative progress variables are required. One approach, fairly widely applied, can be illustrated with the study by Hill et al. of the general acid-catalyzed addition of substituted anilines to dicy-anamide. The overall reaction is... 

We have tried to show that the affinity is a convenient representation of how far a system is from stable equilibrium, and increments in the progress variable allows us to consider the system at various stages as it progresses towards stable equilibrium. This progress is a part of the model we call a quasistatic reaction—a continuous succession of metastable equilibrium states in an overall irreversible reaction. 

The second and third groups include slow chemical processes, for which the relaxation time is significantly different from 0 (At > 0). Over the time At values of chemical affinity A., saturation index SI. and rate of reaction tend to 0. That is why the considered closed models of mass transfer may be considered titration models, in which added portions of minerals sequentially lower values A., SI. or A. (equation (1.112)). Usually in a study of interaction between water and rock the researcher uses the overall progress variable of mass transfer (equation (2.256)), which in the course of computation sequentially lowered to 0. 

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