Thermodynamics and Chemistry

CHAPTER 11 REACTIONS AND OTHER CHEMICAL PROCESSES

11.8 THETHERMODYNAMICEQUILIBRIUMCONSTANT 351

For instance, for the ammonia synthesis reaction N 2 (g) + 3 H 2 (g)!2 NH 3 (g) the reac-
tion quotient is given by

QrxnD

a^2 NH 3

aN 2 a^3 H 2

(11.8.7)

Qrxnis a dimensionless quantity. It is a function ofT,p, and the mixture composition, so
its value changes as the reaction advances.
The expression for the molar reaction Gibbs energy given by Eq.11.8.4can now be
written
ÅrGDÅrGCRTlnQrxn (11.8.8)

The value ofQrxnunder equilibrium conditions is thethermodynamic equilibrium con-
stant,K. The general definition ofKis

K

def

D

Y

i

.ai/eqi (11.8.9)

where the subscript eq indicates an equilibrium state. Note thatK, likeQrxn, is dimension-
less.

The IUPAC Green Book^19 givesK as an alternative symbol for the thermodynamic

equilibrium constant, the appended superscript denoting “standard.” An IUPAC Com-

mission on Thermodynamics^20 has furthermore recommended the name “standard

equilibrium constant,” apparently because its value depends on the choice of stan-

dard states. Using this alternative symbol and name could cause confusion, since the

quantity defined by Eq.11.8.9does not refer to reactants and products in their standard

states but rather to reactants and products in anequilibriumstate.

Substituting the equilibrium conditionsÅrGD 0 andQrxnDKin Eq.11.8.8gives an im-
portant relation between the standard molar reaction Gibbs energy and the thermodynamic
equilibrium constant:
ÅrGDRTlnK (11.8.10)

We can solve this equation forKto obtain the equivalent relation

KDexp



ÅrG

RT



(11.8.11)

We have seen that the value ofÅrGdepends only onTand the choice of the standard
states of the reactants and products. This being so, Eq.11.8.11shows that the value ofKfor
a given reaction depends only onT and the choice of standard states. No other condition,
neither pressure nor composition, can affect the value ofK. We also see from Eq.11.8.11
thatKis less than 1 ifÅrGis positive and greater than 1 ifÅrGis negative. At a fixed
temperature, reaction equilibrium is attained only if and only if the value ofQrxnbecomes
equal to the value ofKat that temperature.
The thermodynamic equilibrium constantKis the proper quotient of the activities of
species in reaction equilibrium. At typical temperatures and pressures, an activity cannot be

(^19) Ref. [ 36 ], p. 58.
(^20) Ref. [ 52 ].