Thermodynamics and Chemistry

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
ÅrGDRTlnK(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

A

X

solutes,

conc. basis

i (12.1.11)

The sum on the right side includes only solute species whose standard states are based on
concentration. The expression is simpler if all solute standard states are based on mole
fraction or molality:

d lnK

dT

D

ÅrH

RT^2

(12.1.12)

(no solute standard states

based on concentration)

We can rearrange Eq.12.1.12to

ÅrHDRT^2

d lnK

dT

(12.1.13)

(no solute standard states

based on concentration)

We can convert this expression forÅrHto an equivalent form by using the mathematical
identity d.1=T /D.1=T^2 /dT:

ÅrHDR

d lnK

d.1=T /

(12.1.14)

(no solute standard states

based on concentration)