Pressure effect in fractional conversion

In combustion problems, one is interested in the rate of energy conversion or utilization. Thus it is more convenient to deal with the fractional change of a particular substance rather than the absolute concentration. If (M) is used to denote the concentrations in a chemical reacting system of arbitrary order n, the rate expression is 

Since (M) is a concentration, it may be written in terms of the total density p and the mole or mass fraction e that is, 

That is, the fractional change is proportional to the pressure raised to the reaction order — 1. 

For systems with large numbers of species and reactions, the dynamics of the reaction and the interactions between species can become quite complex. In order to analyze the reaction progress of species, various diagnostics techniques have been developed. Two of these techniques are reaction rate-of-production analysis and sensitivity analysis. A sensitivity analysis identifies the rate limiting or controlling reaction steps, while a rate-of-production analysis identifies the dominant reaction paths (i.e., those most responsible for forming or consuming a particular species). 

as mentioned previously, for a system of reactions, Eq. (2.1) can be rewritten as 

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