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

where g–i* (T) represents the Gibbs function of component iat 1 atm pres-

sure and temperature T, and Pirepresents the partial pressure of component

iin atmospheres. Substituting the Gibbs function expression for each com-

ponent into Eq. 16–9, we obtain

For convenience, we define the standard-state Gibbs function changeas

(16–11)

Substituting, we get

(16–12)

Now we define the equilibrium constantKPfor the chemical equilibrium

of ideal-gas mixtures as

(16–13)

Substituting into Eq. 16–12 and rearranging, we obtain

(16–14)

Therefore, the equilibrium constant KPof an ideal-gas mixture at a specified

temperature can be determined from a knowledge of the standard-state

Gibbs function change at the same temperature. The KPvalues for several

reactions are given in Table A–28.

Once the equilibrium constant is available, it can be used to determine the

equilibrium composition of reacting ideal-gas mixtures. This is accom-

plished by expressing the partial pressures of the components in terms of

their mole fractions:

where Pis the total pressure and Ntotalis the total number of moles present

in the reaction chamber, including any inert gases.Replacing the partial

pressures in Eq. 16–13 by the above relation and rearranging, we obtain

(Fig. 16–7)

(16–15)

where

Equation 16–15 is written for a reaction involving two reactants and two

products, but it can be extended to reactions involving any number of reac-

tants and products.

¢nnCnDnAnB

KP

NCnCNDnD

NAnANBnB

a

P

Ntotal

b

¢n

Piyi P

Ni

Ntotal

P

KPe¢G*^1 T2>RuT

KP

PCnCPDnD

PAnAPBnB

¢G* 1 T 2 RuT 1 nC ln PCnD ln PDnA ln PAnB ln PB 2 RuT ln

PCnCPDnD

PAnAPBnB

¢G* 1 T 2 nCgC* 1 T 2 nDg*D 1 T 2 nAg*A 1 T 2 nBgB* 1 T 2

nA 3 g*A 1 T 2 RuT ln PA 4 nB 3 gB* 1 T 2 RuT ln PB 4  0

nC 3 g*C 1 T 2 RuT ln PC 4 nD 3 gD* 1 T 2 RuT ln PD 4

Chapter 16 | 797

(1) In terms of partial pressures

KP =

PC CDPD

PA ABPB

(3) In terms of the equilibrium

composition

KP =

NC ND

N (

A NB

A B Ntotal (

P ∆

(2) In terms of ∆G*(T)

KP= e–∆G*(T)/R T

C D

u

nn

nn

nn

nn

n

FIGURE 16–7

Three equivalent KPrelations for

reacting ideal-gas mixtures.

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