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Entropy and chemical equilibrium 151

equilibrium. An imbalance between the external forces would initiate
motion of the body.
Likewise, chemical equilibrium is the state of a reactive system at which
the quantity (e.g., mole, concentration) of the individual components (reac-
tants and products) does not vary with time. Fig. 10.1c1 shows a reactive
system that initially (t ¼ 0) contains reactants (filled circles) and products
(empty circles). The system approaches equilibrium at t¼t eq beyond which
the composition of the species will no longer be dependent on time, so all
reactants and products will have uniform concentrations. As depicted in
Fig. 10.1c2, between t¼0 and t¼t eq , the quantity of individual species
may continuously change in time.
For a reactive system comprising k species, the condition of chemical
equilibrium may analytically be expressed as

ΔX j tðÞ ¼ ε t > t eq ; j ¼ 1,2,…,k (10.2)

where X j denotes the conversion of species j, and ε is a negligible real
number.
Eq. (10.2) states that after a chemical equilibrium has been established in a
reactive system, the change in the quantity of any species like j is negligible at
any instant beyond the equilibrium time, t eq . One may also express the con-
dition of chemical equilibrium described in Eq. (10.2) in terms of concen-
tration C, mole fraction y, or mass fraction x, i.e.,

ΔC j tðÞ ¼ ε 1 t > t eq (10.2a)

Δy j tðÞ ¼ ε 2 t > t eq (10.2b)

(10.2c)
Δx j tðÞ ¼ ε 3 t > t eq
Whether the state of chemical equilibrium characterized by Eq. (10.2) may
also be determined by minimization of Gibbs function, Eq. (10.1), is a ques-
tion that we aim to answer in the following sections.

10.3 Experimental examination of theory

Equilibrium-based modeling approaches have been used widely,
mainly due to their simplicity compared to the coupled transport-kinetic
models, for prediction of the composition of reactive mixtures. In general,
an equilibrium model consists of three main parts: (i) conservation of
elements, e.g. carbon, hydrogen, oxygen, (ii) conservation of energy assum-
ing a uniform temperature, and (iii) Gibbs criterion of equilibrium,