CHAPTER 12 EQUILIBRIUM CONDITIONS IN MULTICOMPONENT SYSTEMS
12.1 EFFECTS OFTEMPERATURE 368
Here is the cubic expansion coefficient of the solution (Eq.7.1.1). If the activity coeffi-
cient is to be unity, the solution must be an ideal-dilute solution, and is then (^) A, the cubic
expansion coefficient of the pure solvent. Eq.12.1.5for a nonelectrolyte becomes
d.c;B=T /
dT
D
HB
T^2
CRA (12.1.8)
12.1.3 Variation of lnKwith temperature
The thermodynamic equilibrium constantK, for a given reaction equation and a given
choice of reactant and product standard states, is a function ofTandonlyofT. By equat-
ing two expressions for the standard molar reaction Gibbs energy,ÅrG D
P
ii
i and
ÅrGD RTlnK(Eqs.11.8.3and11.8.10), we obtain
lnKD
1
RT
X
i
ii (12.1.9)
The rate at which lnKvaries withTis then given by
d lnK
dT
D
1
R
X
i
i
d.i=T /
dT
(12.1.10)
Combining Eq.12.1.10with Eqs.12.1.6or12.1.8, and recognizing that
P
iiH
i is the
standard molar reaction enthalpyÅrH, we obtain the final expression for the temperature
dependence of lnK:
d lnK
dT
D
ÅrH
RT^2