Criteria for Chemical Reaction Equilibrium
The general criterion for thermodynamic equilibrium was derived in section 6.3 as:
As already explained, the above equation implies that if a closed system undergoes a process of change while being under thermal and mechanical equilibrium, for all incremental changes associated with the compositions of each species, the total Gibbs free energy of the system would decrease. At complete equilibrium the equality sign holds; or, in other words, the Gibbs free energy of the system corresponds to the minimum value possible under the constraints of constant (and uniform) temperature and pressure. Since the criterion makes no assumptions as to the nature of the system in terms of the number of species or phases, or if reactions take place between the species, it may also be applied to determine a specific criterion for a reactive system under equilibrium.
As has been explained in the opening a paragraph of this chapter, at the initial state of a reaction, when the reactants are brought together a state of non-equilibrium ensues as reactants begin undergoing progressive transformation to products. However, a state of equilibrium must finally attain when the rates of forward and backward reactions equalize. Under such a condition, no further change in the composition of the residual reactants or products formed occurs. However, if we consider this particular state, we may conclude that while in a macroscopic sense the system is in a state of static equilibrium, in the microscopic sense there is dynamic equilibrium as reactants convert to products and vice versa. Thus the system is subject to minute fluctuations of concentrations of each species.
However, by the necessity of maintenance of the dynamic equilibrium the system always returns to the state of stable thermodynamic equilibrium. In a macroscopic sense then the system remains under the under equilibrium state described by eqn. 6.36b. It follows that in a reactive system at the state of chemical equilibrium the Gibbs free energy is minimum subject to the conditions of thermal and mechanical equilibrium.
The above considerations hold regardless of the number of reactants or the reactions occurring in the system. Since the reaction co-ordinate is the single parameter that relates the compositions of all the species, the variation of the total Gibbs free energy of the system as a function of the reaction coordinate may be shown schematically as in fig. 8.3; here ξ e is the value of the reaction co-ordinate at equilibrium.
Fig. 8.3 Variation of system Gibbs free energy with equilibrium conversion