The Extent of Reaction or Progress Variable

For the sake of argument, assume that case 1 above actually occurs. We can speak of the extent to which this reaction has progressed from the initial nonequilibrium conditions towards its final state for example, when half the initial Fe is oxidized, the reaction has progressed halfway. You can regard some of this material as a concrete example of the theory discussed in Chapter 14. For any balanced chemical reaction, 

Assume that the chemical system is completely closed so that no material can enter or leave. As our initial system of Fe and O2 begins to react it will form a small amount of Fc203 we can express the change in mass of each species for this small amount of reaction by the equation 

You can get a better intuitive feeling for the physical significance of the progress variable by rearranging (19.73) to express explicitly the change in mass of any species with extent of reaction  

It is often more convenient to deal with moles (and concentrations) rather than masses in typical applications. For this, simply divide masses of all species i by then-molecular weights Mi. 

The relationship between reaction progress, change in moles of different species, and the overall reaction stoichiometry as in (19.72) now simplifies to 

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