Thermodynamics and Chemistry

CHAPTER 11 REACTIONS AND OTHER CHEMICAL PROCESSES

11.7 GIBBSENERGY ANDREACTIONEQUILIBRIUM 343

of, its rate of change with respect tois zero in the equilibrium state. The condition for
reaction equilibrium, then, is thatÅrGmust be zero:

ÅrGD

X

i

iiD 0 (11.7.4)

(reaction equilibrium)

It is important to realize that this condition is independent of whether or not reaction
equilibrium is approached at constant temperature and pressure. It is a universal criterion
of reaction equilibrium. The value ofÅrGis equal to

P

iiiand depends on the state of
the system. If the state is such thatÅrGis positive, the direction of spontaneous change
is one that, under the existing constraints, allowsÅrGto decrease. IfÅrGis negative,
the spontaneous change increases the value ofÅrG. When the system reaches reaction
equilibrium, whatever the path of the spontaneous process, the value ofÅrGbecomes zero.

11.7.3 General derivation

We can obtain the condition of reaction equilibrium given by Eq.11.7.4in a more general
and rigorous way by an extension of the derivation of Sec.9.2.7, which was for equilibrium
conditions in a multiphase, multicomponent system.
Consider a system with a reference phase,í^0 , and optionally other phases labeled by
í§í^0. Each phase contains one or more species labeled by subscripti, and some or all of
the species are the reactants and products of a reaction.
The total differential of the internal energy is given by Eq.9.2.37on page 236 :

dUDTí

0

dSí

0

pí

0

dVí

0

C

X

i

í

0

i dn

í^0

i

C

X

í§í^0

TídSípídVíC

X

i

íidníi

!

(11.7.5)

The conditions of isolation are

dUD 0 (constant internal energy) (11.7.6)

dVí

0

C

X

í§í^0

dVíD 0 (no expansion work) (11.7.7)

For each speciesi:

dní

0

i C

X

í§í^0

dníi Did (closed system) (11.7.8)

In Eq.11.7.8, dní
00
i^0 should be set equal to zero for a speciesi

(^0) that is excluded from phase
í^00 , andi 00 should be set equal to zero for a speciesi^00 that is not a reactant or product of
the reaction.