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Physical Chemistry 62

Temperature dependence of the Gibbs free energy

For a closed system doing no work other than that due to volume expansion, it is possible
to show that dG=Vdp−SdT and so it follows that, at constant pressure,

which provides one relationship between the Gibbs free energy and temperature.
However, it is possible to take this further, and in doing so obtain a more useful
relationship. Since, by definition, G=H−TS, then −S=(G−H)/T, which may be
substituted in the previous expression and the result rearranged to give:

The left hand side of this expression simplifies to to give the
Gibbs-Helmholtz equation:

This expression is most useful when applied to changes in G at constant pressure, such as
in the course of a chemical reaction, when it may be written in the form:

Properties and applications of the Gibbs free energy
The Gibbs free energy can be applied in a similar manner to other state functions, and
many of the expressions which are encountered are similar in form to those seen for the
enthalpy, for example (see Topic B2).
The standard reaction free energy, , is the change in the Gibbs free energy
which accompanies the conversion of reactants in their standard states into products in
their standard states. It is possible to calculate the free energy of a reaction from the
standard enthalpy and energy changes for the reaction: , with
and being obtained either from tabulated data or direct measurement. An

alternative is to use the standard free energy of formation, . This is defined as
the free energy which accompanies the formation of a substance in its standard state from