Thermodynamics and Chemistry

CHAPTER 11 REACTIONS AND OTHER CHEMICAL PROCESSES

11.7 GIBBSENERGY ANDREACTIONEQUILIBRIUM 342

11.7 Gibbs Energy and Reaction Equilibrium

This section begins by examining the way in which the Gibbs energy changes as a chemical
process advances in a closed system at constantT andpwith expansion work only. A
universal criterion for reaction equilibrium is derived involving the molar reaction Gibbs
energy.

11.7.1 The molar reaction Gibbs energy

Applying the general definition of a molar differential reaction quantity (Eq.11.2.15) to the
Gibbs energy of a closed system withT,p, andas the independent variables, we obtain
the definition of themolar reaction Gibbs energyor molar Gibbs energy of reaction,ÅrG:

ÅrG

def

D

X

i

ii (11.7.1)

Equation11.2.16shows that this quantity is also given by the partial derivative

ÅrGD



@G

@



T;p

(11.7.2)

(closed system)

The total differential ofGis then

dGDSdTCVdpCÅrGd (11.7.3)

(closed system)

11.7.2 Spontaneity and reaction equilibrium

In Sec.5.8, we found that the spontaneous direction of a process taking place in a closed
system at constantTandp, with expansion work only, is the direction of decreasingG. In
the case of a chemical process occurring at constantT andp,ÅrGis the rate at whichG
changes with. Thus ifÅrGis positive,spontaneously decreases; ifÅrGis negative,
spontaneously increases. During a spontaneous process dandÅrGhave opposite signs.^14

Note how the equality of Eq.11.7.3agrees with the inequality dG <SdTCVdp,

a criterion of spontaneity in a closed system with expansion work only (Eq.5.8.6on

page 145 ). When dandÅrGhave opposite signs,ÅrGdis negative and dGD

.SdTCVdpCÅrGd/is less than.SdTCVdp/.

If the system is closed and contains at least one phase that is a mixture, a state of reaction
equilibrium can be approached spontaneously at constantTandpin either direction of the
reaction; that is, by both positive and negative changes of. In this equilibrium state,
therefore,Ghas its minimum value for the givenTandp. SinceGis a smooth function

(^14) Sometimes reaction spontaneity at constantTandpis ascribed to the “driving force” of a quantity called
theaffinity of reaction, defined as the negative ofÅrG.increases spontaneously if the affinity is positive and
decreases spontaneously if the affinity is negative; the system is at equilibrium when the affinity is zero.