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W

E STARTED THE LAST CHAPTER with the question, “Will a process

occur spontaneously?’’ Although we introduced the concept of en-

tropy as a basis for answering that question, we did not completely answer it.

The second law of thermodynamics is strictly applicable to an isolatedsystem,

in which no other discernible change in a thermodynamic state function occurs.

For such systems, spontaneous processes do occur if they are accompanied by

an increase in the entropy of a system. But most systems are not isolated (in

fact, the only truly isolated system is the entire universe), and most changes

involve more than a change in entropy. Many processes occur with a simulta-

neous change in energy. You may recall the idea that most spontaneous changes

are exothermic. Many endothermic changes are also spontaneous. A proper

thermodynamic definition of a spontaneous process takes bothenergy and

entropy changes into account.

4.1 Synopsis

We will begin the chapter by discussing the limitations of entropy. We will then

define the Gibbs free energy and the Helmholtz energy. What we will ulti-

mately show is that for most chemical processes, the Gibbs free energy provides

a strict test for the spontaneity or nonspontaneity of that process.

The Gibbs and Helmholtz energies, both named after prominent thermo-

dynamicists, are the last energies that will be defined. Their definitions, coupled

with the appropriate use of partial derivation, allow us to derive a rich set of

mathematical relationships. Some of these mathematical relationships let the

full force of thermodynamics be applied to many phenomena, like chemical

reactions and chemical equilibria and—importantly—predictions of chemical

occurrences. These relationships are used by some as proof that physical

chemistry is complicated. Perhaps they are better seen as proof that physical

chemistry is widely applicable to chemistry as a whole.

4.2 Spontaneity Conditions

The derivation of the equation

S 0 (4.1)

4.1 Synopsis

4.2 Spontaneity Conditions

4.3 The Gibbs Free Energy and
the Helmholtz Energy

4.4 Natural Variable Equations
and Partial Derivatives

4.5 The Maxwell Relationships

4.6 Using Maxwell Relationships

4.7 Focusing on G

4.8 The Chemical Potential
and Other Partial
Molar Quantities

4.9 Fugacity

4.10 Summary

Free Energy and

Chemical Potential