REACTIONS: THERMODYNAMIC ASPECTS, KINETICS, AND CATALYSIS - Biomass as a Sustainable Energy Source for the Future - page 139

reactions that occur at constant pressure. The mathematical definition of this function
of state is

G=H − TS ð Eq : 5 : 15 Þ

For spontaneous processes, the entropy will increase, i.e.,

Δ S tot = Δ S syst + Δ S env >0 ð Eq : 5 : 16 Þ

Considering that

− Δ

H
T

Δ S env = ð Eq : 5 : 17 Þ

substitution of Equation (5.17) in Equation (5.16)

S s yst − Δ

H
T >0

: :

Δ S tot = Δ ð Eq 5 18 Þ

and referring only to the system yields

T Δ S − Δ H>0 ð Eq : 5 : 19 Þ

Differentiating under the condition that the temperature is constant (dT = 0) and con-
sidering a finite increment, we can conclude that for spontaneous processes, the free
energy decreases, i.e.,

Δ G T,P <0 ð Eq : 5 : 20 Þ

Considering the general reaction equation (RX. 5.20), the reaction rates of A and B ( r f )
will be the highest at the beginning and will decrease in time with the formation of the
products C and D ; the reverse reaction rates ( r b ) will increase from zero to r f . When r b
is equal to r f , we can say that the reaction has reached chemical equilibrium (

G T,P =0)
and the concentrations of all species are constant. This is called dynamic equilibrium:
the rates of the forward and reverse reactions are not zero, but they are equal (forward
and reverse reactions occur continuously at the same rate). From a thermodynamic
point of view, we can say that if the sum of the standard free energies G 0 (at the stand-
ard temperature of 298.15 K and at the standard pressure of 1 bar) of the products is
less than that of the reactants,

Δ

G 0 for the reaction is negative, and the reaction will
proceed to the right spontaneously.
For a reversible process, the infinitesimal change of the free energy of the system is
given by (Moran and Shapiro, 2010; Smith et al., 2005)

Δ

SdT + X

j
i =1 μ i dn i

dG =Vd p − ð Eq : 5 : 21 Þ