Gibbs Energy as a Criterion for Chemical Equilibrium

Our objective in this section is to develop a criterion that tells us when two or more phases can coexist at equilibrium or, conversely, when only a single phase is stable. The second law of thermodynamics can give us some insight into answering this question. We 

We would prefer a way to tell if we have phase equilibrium by considering only properties of the system. In this section, we use a combination of the first and the second laws to develop a new property, Gibbs energy, G. This property is useful because by just looking at the Gibbs ener of each phase in the system, we can determine if either phase is more stable or, alternatively, if the two phases can coexist at equilibrium. We will now explore how Gibbs ener provides this information. 

Gonsider a closed system composed of pure species i in mechanical and thermal equilibrium and, therefore, at constant T and P. In most phase equilibria problems, the only work is Pv work. Ifwe assume there is only Pv work, the first law in differential form can be written as  

We introduce the subscript i to denote that the analysis is performed for pure species i. The rationale for this nomenclature will be discussed further when mixtures are addressed in Section 6.3. 

For mechanical equilibrium, we have constant pressure, that is, dP = 0. Therefore, we can subtract VjdP from the right-hand side of the previous equation to get  

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