Thermodynamics and Chemistry

CHAPTER 12 EQUILIBRIUM CONDITIONS IN MULTICOMPONENT SYSTEMS

12.3 BINARYMIXTURE INEQUILIBRIUM WITH APUREPHASE 374

Substitution from Eq.12.2.7changes this to

A.p^0 /A.p^0 /D

Zp (^0) C
p^0
VAdp (12.2.10)
(constantT)
which is the desired expression forAAat a single temperature and pressure. To evaluate
the integral, we need an experimental value of the osmotic pressureof the solution. If
we assumeVAis constant in the pressure range fromp^0 top^0 C, Eq.12.2.10becomes
simply
A.p^0 /A.p^0 /DVA (12.2.11)

12.3 Binary Mixture in Equilibrium with a Pure Phase

This section considers a binary liquid mixture of components A and B in equilibrium with
either pure solid A or pure gaseous A. The aim is to find general relations among changes of
temperature, pressure, and mixture composition in the two-phase equilibrium system that
can be applied to specific situations in later sections.
In this section,Ais the chemical potential of component A in the mixture andAis
for the pure solid or gaseous phase. We begin by writing the total differential ofA=T
withT,p, andxAas the independent variables. These quantities refer to the binary liquid
mixture, and we have not yet imposed a condition of equilibrium with another phase. The
general expression for the total differential is

d.A=T /D



@.A=T /

@T



p;xA

dTC



@.A=T /

@p



T;xA

dpC



@.A=T /

@xA



T;p

dxA (12.3.1)

With substitutions from Eqs.9.2.49and12.1.3, this becomes

d.A=T /D

HA

T^2

dTC

VA

T

dpC



@.A=T /

@xA



T;p

dxA (12.3.2)

Next we write the total differential ofA=Tfor pure solid or gaseous A. The indepen-
dent variables areTandp; the expression is like Eq.12.3.2with the last term missing:

d.A=T /D

HA

T^2

dTC

VA

T

dp (12.3.3)

When the two phases are in transfer equilibrium,AandAare equal. If changes occur
inT,p, orxAwhile the phases remain in equilibrium, the condition d.A=T /Dd.A=T /
must be satisfied. Equating the expressions on the right sides of Eqs.12.3.2and12.3.3and
combining terms, we obtain the equation

HAHA

T^2

dT

VAVA

T

dpD



@.A=T /

@xA



T;p

dxA (12.3.4)