Spontaneity and equilibrium

The most familiar transformations occur under conditions of constant temperamre and pressure, so it will be particularly useful to have a criterion of spontaneity and equilibrium that applies to these conditions. 

Thus far we have observed that the Gibbs and Planck functions provide the criteria of spontaneity and equilibrium in isothermal changes of state at constant pressure. If we extend our analysis to systems in which other constraints are placed on the system, and therefore work other than mechanical work can be performed, we find that the Gibbs and Helmholtz functions also supply a means for calculating the maximum magnitude of work obtainable from an isothermal change. 

Skill 11.5 Relating cell potentials to spontaneity and equilibrium constants... 

The result of Example 4 above applies, strictly speaking, only to the standard states of the substances involved. (It is beyond the scope of this text to extend the calculations to other conditions of temperature and pressure. Such calculations are straightforward and are covered in courses in Physical Chemistry.) Calculations of A/f° are nonetheless extremely useful because A/f is not very sensitive to conditions (except in the extreme) and A//° provides us with a valid qualitative assessment of the reaction energy in most situations. For example, the result of Example 4 tells us to beware of a violent reaction when you open a PCI5 container in moist air The A//° calculation is important also because it is the first step in calculating AT/ at other conditions, and in calculating AG° (see Chapter 16), which in turn determines spontaneity, and equilibrium states. 

Note that we have merely organized the expression for the entropy change of the universe and equating the free-energy change of the system (AG) with -TA univ. so that we can focus on changes in the system. We can now summarize the conditions for spontaneity and equilibrium at constant temperature and pressure in terms of AG as follows ... 

In later chapters, the inequality of Eq. 4.6.6 will turn out to be one of the most useful for deriving conditions for spontaneity and equilibrium in chemical systems The entropy of an isolated system continuously increases during a spontaneous, irreversible process until it reaches a maximum value at equilibrium. 

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