Thermodynamics and Chemistry

CHAPTER 12 EQUILIBRIUM CONDITIONS IN MULTICOMPONENT SYSTEMS

12.2 SOLVENTCHEMICALPOTENTIALS FROMPHASEEQUILIBRIA 371

b

b

b

b

b

a

b

c

d

e

Tf Tf T^0

T



=TA

solid

liquid

solution

slopeDH

A(s)

T^2

slopeDH

A(l)

T^2

slopeDHAT(sln) 2

Figure 12.1 Integration path abcde at constant pressure for determiningAA

at temperatureT^0 from the freezing pointTfof a solution (schematic). The dashed

extensions of the curves represent unstable states.

slope d.A=T /=dToverTalong the path abcde:

A.l; T^0 /

T^0

A.sln; T^0 /

T^0

D

ZTf

T^0

HA(sln)

T^2

dT

ZTf

Tf

HA(sln)

T^2

dT

ZTf

Tf

HA(s)

T^2

dT

ZT 0

Tf

HA(l)

T^2

dT (12.2.2)

By combining integrals that have the same range of integration, we turn Eq.12.2.2into

A.l; T^0 /

T^0

A.sln; T^0 /

T^0

D

ZTf

Tf

HA(sln)HA(s)

T^2

dT

C

ZT 0

Tf

HA(sln)HA(l)

T^2

dT (12.2.3)

For convenience of notation, this book will useÅsol,AHto denote the molar enthalpy
differenceHA(sln)HA(s).Åsol,AHis the molar differential enthalpy of solution of solid
A in the solution at constantT andp. The first integral on the right side of Eq.12.2.3
requires knowledge ofÅsol,AHover a temperature range, but the only temperature at which
it is practical to measure this quantity calorimetrically is at the equilibrium transition tem-
peratureTf. It is usually sufficient to assumeÅsol,AHis a linear function ofT:

Åsol,AH.T /DÅsol,AH.Tf/CÅsol,ACp.TTf/ (12.2.4)

The molar differential heat capacity of solutionÅsol,ACpDCp;A(sln)Cp;A(s) is treated
as a constant that can be determined from calorimetric measurements.
The quantityHA(sln)HA(l) in the second integral on the right side of Eq.12.2.3is the
molar differential enthalpy of dilution of the solvent in the solution,ÅdilH(see Eq.11.4.7).