Page 73 - Instant notes

B6
FREE ENERGY

Key Notes
The Gibbs free energy, G, is defined as G=H−TS and at constant
pressure and temperature, finite changes in G may be expressed as
∆G=∆H−T∆S. A similar function, applied at constant volume, is the
Helmholtz free energy, A, defined as A=U−TS. At constant temperature,
∆G is equal to −T∆S total at constant pressure and ∆A is equal to −T∆S total
at constant volume. For a spontaneous process ∆G<0 (constant pressure),
or ∆A<0 (constant volume). Because most chemical and biochemical
systems operate at constant pressure, the Gibbs free energy is more
commonly encountered.
The Gibbs and Helmholtz free energies are state functions which do not
have measurable absolute values. The free energy change represents the
maximum amount of work, other than volume expansion work, which
may be obtained from a process.
∆G is negative for a spontaneous process. An exothermic reaction
(∆H>0) with a positive entropy (∆S>0) is always spontaneous. A reaction
for which ∆H<0 and ∆S<0 is spontaneous only at low temperatures,
whilst a reaction for which ∆H>0 and ∆S>0 is spontaneous only at high
temperatures. The temperature at which the reaction becomes
spontaneous in each case is given by T=∆H/∆S.
The most useful expression for the temperature dependence of the Gibbs
free energy is the Gibbs-Helmholtz equation:

The Gibbs-Helmholtz 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: