Concepts from Chemical Reaction Kinetics - Elements of Environmental Engineering: Thermodynamics and Kinetics - page 192

G

Equilibrium position

d G
d

= 0

ξ

0 1

ξ

FIGURE 5.1 Gibbs function variation with the extent of reaction.

Hence,

G 0 Δ G = Δ + RT ln K . (5.14)

Note that only at equilibrium (i.e., Δ G = 0) does K equal K eq , at which point we

have

G 0 Δ =− RT ln K eq . (5.15)

K is called the reaction quotient and K eq the equilibrium constant . Therefore, we can
write

RT ln K
K eq

.

d G
d

Δ G =

ξ =

(5.16)

The approach to equilibrium for a chemical reaction is measured by the above equa-
tion. The activity of a compound is given by a = γ[ i ] , where [ i ] represents the

concentration and represents

the molar concentration C i (mol/L) for reactions in solution or the partial pressures
P i (atm or kPa) for reactions in the gas phase. Hence,

γ is the activity coefficient. Note that in this chapter [ i ]

y
Y

X γ

x y

K eq = [

X ] [ Y ]

b γ

. (5.17)

[ A ]

a

[ B ]

A γ B

γ

From the relation for < 0,

K < K eq , the reaction will be spontaneous and will proceed from left to right in Equa-
tion 5.1, whereas if

Δ G or d G/ d ξ , one can conclude that if Δ G = d G/ d ξ

Δ G = d G/ d ξ > 0, K > K eq , the reaction will be spontaneous in