Microsoft Word - Cengel and Boles TOC _2-03-05_.doc

16–1 ■ CRITERION FOR CHEMICAL EQUILIBRIUM

Consider a reaction chamber that contains a mixture of CO, O 2 , and CO 2 at

a specified temperature and pressure. Let us try to predict what will happen

in this chamber (Fig. 16–1). Probably the first thing that comes to mind is a

chemical reaction between CO and O 2 to form more CO 2 :

This reaction is certainly a possibility, but it is not the only possibility. It is

also possible that some CO 2 in the combustion chamber dissociated into CO

and O 2. Yet a third possibility would be to have no reactions among the

three components at all, that is, for the system to be in chemical equi-

librium. It appears that although we know the temperature, pressure, and

composition (thus the state) of the system, we are unable to predict whether

the system is in chemical equilibrium. In this chapter we develop the neces-

sary tools to correct this.

Assume that the CO, O 2 , and CO 2 mixture mentioned above is in chemical

equilibrium at the specified temperature and pressure. The chemical compo-

sition of this mixture does not change unless the temperature or the pressure

of the mixture is changed. That is, a reacting mixture, in general, has differ-

ent equilibrium compositions at different pressures and temperatures. There-

fore, when developing a general criterion for chemical equilibrium, we

consider a reacting system at a fixed temperature and pressure.

Taking the positive direction of heat transfer to be to the system, the

increase of entropy principle for a reacting or nonreacting system was

expressed in Chapter 7 as

(16–1)

A system and its surroundings form an adiabatic system, and for such systems

Eq. 16–1 reduces to dSsys
0. That is, a chemical reaction in an adiabatic

chamber proceeds in the direction of increasing entropy. When the entropy

reaches a maximum, the reaction stops (Fig. 16–2). Therefore, entropy is a

very useful property in the analysis of reacting adiabatic systems.

When a reacting system involves heat transfer, the increase of entropy

principle relation (Eq. 16–1) becomes impractical to use, however, since it

requires a knowledge of heat transfer between the system and its surround-

ings. A more practical approach would be to develop a relation for the

equilibrium criterion in terms of the properties of the reacting system only.

Such a relation is developed below.

Consider a reacting (or nonreacting) simple compressible system of fixed

mass with only quasi-equilibrium work modes at a specified temperature T

and pressure P (Fig. 16–3). Combining the first- and the second-law

relations for this system gives

(16–2)

dQP dVdU

dS

dQ

T

¶ dUP dVT ds 0

dSsys

dQ

T

CO^12 O 2 ¬S¬CO 2

794 | Thermodynamics

CO 2

CO

O 2

O 2

O 2

CO 2

CO 2

CO

CO

FIGURE 16–1

A reaction chamber that contains a

mixture of CO 2 , CO, and O 2 at a

specified temperature and pressure.

100%

products

Violation of

second law

S

Equilibrium

composition

100%

reactants

dS = 0

dS > 0

dS < 0

FIGURE 16–2

Equilibrium criteria for a chemical

reaction that takes place adiabatically.

Wb

REACTION

CHAMBER

δ

δ

Control

mass

T, P

Q

FIGURE 16–3

A control mass undergoing a chemical

reaction at a specified temperature and

pressure.

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