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

The differential of the Gibbs function (GHTS) at constant tempera-

ture and pressure is

(16–3)

From Eqs. 16–2 and 16–3, we have (dG)T,P0. Therefore, a chemical reac-

tion at a specified temperature and pressure proceeds in the direction of a

decreasing Gibbs function. The reaction stops and chemical equilibrium is

established when the Gibbs function attains a minimum value (Fig. 16–4).

Therefore, the criterion for chemical equilibrium can be expressed as

(16–4)

A chemical reaction at a specified temperature and pressure cannot proceed

in the direction of the increasing Gibbs function since this will be a viola-

tion of the second law of thermodynamics. Notice that if the temperature or

the pressure is changed, the reacting system will assume a different equilib-

rium state, which is the state of the minimum Gibbs function at the new

temperature or pressure.

To obtain a relation for chemical equilibrium in terms of the properties of

the individual components, consider a mixture of four chemical components

A,B,C, and Dthat exist in equilibrium at a specified temperature and pres-

sure. Let the number of moles of the respective components be NA,NB,NC,

and ND. Now consider a reaction that occurs to an infinitesimal extent

during which differential amounts of Aand B(reactants) are converted to C

and D(products) while the temperature and the pressure remain constant

(Fig. 16–5):

The equilibrium criterion (Eq. 16–4) requires that the change in the Gibbs

function of the mixture during this process be equal to zero. That is,

(16–5)

or

(16–6)

where the g–’s are the molar Gibbs functions (also called the chemical poten-

tials) at the specified temperature and pressure and the dN’s are the differen-

tial changes in the number of moles of the components.

To find a relation between the dN’s, we write the corresponding stoichio-

metric (theoretical) reaction

(16–7)

where the n’s are the stoichiometric coefficients, which are evaluated easily

once the reaction is specified. The stoichiometric reaction plays an impor-

tant role in the determination of the equilibrium composition of the reacting

nAAnBB∆nCCnDD

gC¬dNCgD¬dNDgA¬dNAgB¬dNB 0

1 dG (^2) T,Pa 1 dGi (^2) T,Pa 1 gi¬dNi (^2) T,P 0
dNAAdNBB¬¡¬dNCCdNDD
1 dG (^2) T,P 0
dUP dVT dS
 1 dUP dVV dP 2 T dSS dT
1 dG (^2) T,PdHT dSS dT
Chapter 16 | 795
100%
products
Violation of
second law
G
Equilibrium
composition
100%
reactants
dG = 0
dG < 0 dG > 0
FIGURE 16–4
Criteria for chemical equilibrium for a
fixed mass at a specified temperature
and pressure.
REACTION
CHAMBER
T, P
NA moles of A
NB moles of B
NC moles of C
ND moles of D
dNAA + dNBB → dNCC + dNDD
FIGURE 16–5
An infinitesimal reaction in a chamber
at constant temperature and pressure.
→
0
→
0
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