REACTIONS: THERMODYNAMIC ASPECTS, KINETICS, AND CATALYSIS - Biomass as a Sustainable Energy Source for the Future - page 138

5.2 CHEMICAL EQUILIBRIUM

In principle, all chemical reactions are reversible: they comprise a forward and
a reverse reaction. When the concentrations of the reactants and products have
no further tendency to change with time, this is called chemical equilibrium: the
reaction results in an equilibrium mixture of reactants and products. The condi-
tion of no variation of concentrations is necessary but not sufficient for equilib-
rium. We can speak about chemical equilibrium only when the forward reaction
proceeds at the same rate as the reverse reaction. Since at equilibrium, the
rates of the forward and reverse reactions are equal, given the general reaction
equation:

aA + bB !

cC + dD

ð RX : 5 : 20 Þ

the ratio of the rate coefficients is constant and known as the equilibrium constant:

c D d

K eq = C

½ ½

ð Eq : 5 : 14 Þ

a B b

½ A ½

The relation in Equation (5.14) is known as the law of mass action and is valid only
for concerted one-step reactions that proceed through a single transition state. It is
not generally valid because rate equations do not, in general, follow the stoichiom-
etry of the reaction as Guldberg and Waage proposed. Caused by the existence of
the elementary reactions, the kinetics of the global rate law cannot be theoretically
deduced but only experimentally. Therefore, also the relation between rates and
equilibrium constants is not valid like shown in Equation (5.14), but has to be
defined thermodynamically. Despite the failure of this derivation, the equilibrium
constant for a reaction is indeed a constant, independent of the activities of the
various species involved, though it does depend on temperature. Given a reaction
at a certain temperature, the numerical value of the equilibrium constant depends
on the units of measurement chosen. That is, depending on whether the concentra-
tions are indicated as mol L − 1 , atm, or mole fractions, K eq is symbolized, respec-

tively, by K c , K p ,or K x .
Adding a catalyst, a substance capable of changing the rate of a chemical reaction,
will affect both the forward reaction and the reverse reaction in the same way but will
not have an effect on the equilibrium constant. The catalyst will speed up both reac-
tions, thereby increasing the rate at which equilibrium is reached.

5.2.1 Equilibrium Calculations Based on the Gibbs Free Energy

Let us investigate the thermodynamic conditions for chemical equilibrium.
To measure the spontaneity of chemical phenomena, the extensive thermodynamic
property ”

systems. To overcome this difficulty, a new thermodynamic function has been
defined: the Gibbs free energy also called Gibbs function , which is suitable for

“ entropy ” cannot be used as the reactions usually take place in “ nonisolated