Thermodynamics and Chemistry

CHAPTER 11 REACTIONS AND OTHER CHEMICAL PROCESSES

11.8 THETHERMODYNAMICEQUILIBRIUMCONSTANT 349

D 0

DnA, 0

bc

b

0:2

0:4

0:6

0:8

1:0

1:2

1:4

0 0:5 1:0 1:5 2 :0 2 :5 3:0

V=V 0

p=p

Æ

Figure 11.17 Dependence of Gibbs energy on volume and pressure, at constant tem-

perature, in a closed system containing an ideal gas mixture of A and B. The reaction is

A!2 B withÅrGD 0. Solid curves: contours of constantGplotted at an interval of

0:5nA;0RT. Dashed curve: states of reaction equilibrium (ÅrGD 0 ). Dotted curves:

limits of possible values of the advancement. Open circle: position of minimumG

(and an equilibrium state) at the constant pressurepD1:02p. Filled circle: position

of minimumGfor a constant volume of1:41V 0 , whereV 0 is the initial volume at

pressurep.

volumein which the pressure changes, the point of reaction equilibrium is not the point of
minimumG. Instead, the point of reaction equilibrium in this case is at the minimum of the
Helmholtz energyA(Sec.11.7.5).

11.8 The Thermodynamic Equilibrium Constant

11.8.1 Activities and the definition ofK

Equation10.1.9gives the general relation between the chemical potentialiand the activity
aiof speciesiin a phase of electric potential:

iDiCRTlnaiCziF (11.8.1)

The electric potential affectsionly if the charge numberziis nonzero, i.e., only if species
iis an ion.
Consider a reaction in which any reactants and products that are ions are in a single
phase of electric potential^0 , or in several phases of equal electric potential^0. Under these