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Free energy 61

in solids. However, because most chemical and biochemical systems take place at
constant pressure, the Gibbs free energy is by far the more commonly encountered
property.

General properties of the free energies

Because they are wholly derived from state functions, it follows that both the Gibbs and
Helmholtz free energies are also state functions. Both of the free energies do not have
measurable absolute values, and calculations involving free energy changes may be
manipulated in the same manner as, for example, enthalpy changes. Hess’s law may be
applied to free energies, and it is similarly useful to define free energies of formation for
substances.
A most important property of the free energy is that it not only provides an indication
of the spontaneity of a process but it also represents the maximum amount of work, other
than volume expansion work, which may be obtained from a process. This differs from
the heat which may be obtained from a process, because the total entropy change must be
greater than zero. For example, in the case of a reaction for which ∆S system is negative,
some heat must be lost to the surroundings and contribute to ∆S surroundings in order that
∆S totalis greater than zero. The value of the heat which is then unavailable for conversion
into work is given by T∆S system.

Free energy and spontaneity

For a spontaneous process, ∆S total is positive and ∆G is therefore negative. The
relationship ∆G=∆H−T∆S system allows prediction of the conditions under which a reaction
is spontaneous. As T must be positive, the relationships may be summarized in Table 1.
Table 1. Free energy and the spontaneity of
reactions

∆H ∆S Spontaneous? Spontaneity favored by
Negative Positive Under all conditions All conditions
Negative Negative If |T∆S|<|∆H| Low temperatures
Positive Positive If |T∆S|>|∆H| High temperatures
Positive Negative Never No conditions

Temperature has a major impact on the spontaneity of some reactions as indicated in
Table 1. For a reaction where ∆H<0 and ∆S<0, |T∆S| will be less than |∆H| provided that
T is small, and such a reaction will be spontaneous at lower temperatures. Conversely,
when ∆H>0 and ∆S>0, |T∆S| will be greater than |∆H| provided that T is large, and such a
reaction will become spontaneous at higher temperatures. In both cases, the temperature
at which the reaction becomes spontaneous (when ∆G=0) is simply given by T=∆H/∆S.