Thermodynamics and Chemistry

CHAPTER 11 REACTIONS AND OTHER CHEMICAL PROCESSES

11.7 GIBBSENERGY ANDREACTIONEQUILIBRIUM 344

We use these conditions of isolation to substitute for dU, dVí
0
, and dní
0
i in Eq.11.7.5,
and make the further substitution dSí
0
DdS

P

í§í^0 dS

í. Solving for dS, we obtain

dSD

X

í§í^0

.Tí

0

Tí/

Tí^0

dSí

X

í§í^0

.pí

0

pí/

Tí^0

dVí

C

X

i

X

í§í^0

.í

0

i 

í

i/

Tí^0

dníi

P

ii

í^0

i

Tí^0

d (11.7.9)

The equilibrium condition is that the coefficient multiplying each differential on the right
side of Eq.11.7.9must be zero. We conclude that at equilibrium the temperature of each
phase is equal to that of phaseí^0 ; the pressure of each phase is equal to that of phaseí^0 ;
the chemical potential of each species, in each phase containing that species, is equal to the
chemical potential of the species in phaseí^0 ; and the quantity

P

ii
í^0
i (which is equal to
ÅrG) is zero.
In short,in an equilibrium state each phase has the same temperature and the same
pressure, each species has the same chemical potential in the phases in which it is present,
and the molar reaction Gibbs energy of each phase is zero.

11.7.4 Pure phases

Consider a chemical process in which each reactant and product is in a separate pure phase.
For example, the decomposition of calcium carbonate, CaCO 3 (s)!CaO(s) + CO 2 (g), in-
volves three pure phases if no other gas is allowed to mix with the CO 2.
As this kind of reaction advances at constantT andp, the chemical potential of each
substance remains constant, andÅrGis therefore constant. The value ofÅrG for this
reaction depends only onTandp. IfÅrGis negative, the reaction proceeds spontaneously
to the right until one of the reactants is exhausted; the reaction is said to “go to completion.”
IfÅrGis positive, the reaction proceeds spontaneously to the left until one of the products
is exhausted.^15 The reactants and products can remain in equilibrium only ifT andpare
such thatÅrGis zero. These three cases are illustrated in Fig.11.14on the next page.

Note the similarity of this behavior to that of an equilibrium phase transition of a pure

substance. Only one phase of a pure substance is present at equilibrium unlessÅtrsG

is zero. A phase transition is a special case of a chemical process.

11.7.5 Reactions involving mixtures

If any of the reactants or products of a chemical process taking place in a closed system is
a constituent of a mixture, a plot ofGversus(at constantTandp) turns out to exhibit a
minimum with a slope of zero; see the example in Fig.11.15on the next page. At constant
T andp,changes spontaneously in the direction of decreasingGuntil the minimum is
reached, at which pointÅrG(the slope of the curve) is zero and the system is in a state of
reaction equilibrium.

(^15) Keep in mind that whether a species is called a reactant or a product depends, not on whether its amount
decreases or increases during a reaction process, but rather on which side of the reaction equation it appears.