The Affinity and Chemical Potentials

It is appropriate at this point to expand on a concept introduced in Chapter 5—the affinity. We said that irreversible processes begin from some metastable state and end either at stable equilibrium (or on the stable equilibrium surface ) or perhaps in another metastable state closer to stable equilibrium than the first one. As an example we used a binary alloy with varying degrees of disorder (f , and we concluded that the expression 

To see what this means, we need a relationship between drii and d. We have already mentioned reaction increments in this chapter, although we didn t call them that. We said ( 14.2.4) that because reactant and product constituents are related by fixed stoichiometries, changes in their masses are related by (14.24), 

But the only natural cause of such changes in these masses is a spontaneous or irreversible reaction such as we are now considering, so it appears natural to identify the increments in (14.24) with increments in the progress variable, d. Thus 

In other words, increments of are now in moles rather than degree of disorder and the rate of change of each constituent in a reaction is its (dimensionless) stoichiometric coefficient. This may be quite opaque on first reading, but will become almost trivial when understanding dawns. If for example we have a mole of A that wants to change spontaneously into 5 moles of B, the reaction is A = 5B, and (dnA/d ) = — 1 (dn /d ) = 5. This just says that for every mole of A that disappears, 5 moles of B must appear. This fairly obvious relation now allows us to link with the chemical potentials. From (5.39) we have 

In a metastable mixture of oxygen and hydrogen, A then expresses the amount by which the chemical potentials could be lowered by spontaneous reaction on release of the metastable constraint, and is in fact the driving force of the reaction. The driving force becomes zero when IfiUi + M02 = 2/iH20- 

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