Free energy

The free energy is derived from the entropy and is, in many ways, a more useful function to use. The free energy which is referred to when we are discussing processes at constant pressure is the Gibbs free energy (G). This is defined by

The change in the free energy at constant temperature arises from changes in enthalpy and entropy and is

Thus, at constant temperature and pressure,

from which we can see that the change in free energy is another way of expressing the change in overall entropy of a process occurring at constant temperature and pressure.

In view of this relationship we can now consider changes in free energy which occur during a spontaneous process. From equation (3.13) we can see that AG will decrease during a spontaneous process at constant temperature and pressure. This decrease will occur until the system reaches an equilibrium state when AG becomes zero. This process can be thought of as a gradual using up of the system's ability to perform work as equilibrium is approached. Free energy can therefore be looked at in another way in that it represents the maximum amount of work, wmax (other than the work of expansion), which can be extracted from a system undergoing a change at constant temperature and pressure; i.e.

at constant temperature and pressure

This nonexpansion work can be extracted from the system as electrical work, as in the case of a chemical reaction taking place in an electrochemical cell, or the energy can be stored in biological molecules such as adenosine triphosphate (ATP).

When the system has attained an equilibrium state it no longer has the ability to reverse itself. Consequently all spontaneous processes are irreversible. The fact that all spontaneous processes taking place at constant temperature and pressure are accompanied by a negative free energy change provides a useful criterion of the spontaneity of any given process.

By applying these concepts to chemical equilibria we can derive (see Box 3.2) the following simple relationship between free energy change and the equilibrium constant of a reversible reaction, K:

where the standard free energy G ® is the free energy of 1 mole of gas at a pressure of 1 bar.

A similar expression may be derived for reactions in solutions using the activities (see

Box 3.2 Relationship between free energy change and the equilibrium constant

Consider the following reversible reaction taking place in the gaseous phase aA + bB ecC + d D

According to the law of mass action, the equilibrium constant, K, can be expressed as

where p' terms represent the partial pressures of the components of the reaction at equilibrium. The relationship between the free energy of a perfect gas and its partial pressure is given by

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