CHAPTER 12 EQUILIBRIUM CONDITIONS IN MULTICOMPONENT SYSTEMS
12.5 SOLID–LIQUIDEQUILIBRIA 388
då(s)=T çD
Hm(s)
T^2
dT (12.5.16)
When we substitute these expressions in Eq.12.5.13and solve for dT=dxA, settingTequal
toTf, we obtain
dTf
dxA
D
Tf
aHACbHB Hm(s)
"
a
@A
@xA
T;p
Cb
@B
@xA
T;p
(12.5.17)
The quantityaHACbHB Hm(s) in the denominator on the right side of Eq.12.5.17
isÅsolH, the molar differential enthalpy of solution of the solid compound in the liquid
mixture. The two partial derivatives on the right side are related through the Gibbs–Duhem
equationxAdACxBdB D 0 (Eq.9.2.27on page 233 ), which applies to changes at
constantTandp. We rearrange the Gibbs–Duhem equation to dBD .xA=xB/dAand
divide by dxA:
@B
@xA
T;p
D
xA
xB
@A
@xA
T;p
(12.5.18)
Making this substitution in Eq.12.5.17, we obtain the equation
dTf
dxA
D
xATf
ÅsolH
a
xA