Thermodynamics and Chemistry

CHAPTER 12

12 Equilibrium Conditions in Multicomponent Systems

MULTICOMPONENT SYSTEMS

This chapter applies equilibrium theory to a variety of chemical systems of more than one
component. Two different approaches will be used as appropriate: one based on the relation
íi Dìi for transfer equilibrium, the other based on

P

iii D^0 orK D

Q

ia

i
i for
reaction equilibrium.

12.1 Effects of Temperature

For some of the derivations in this chapter, we will need an expression for the rate at which
the ratioi=Tvaries with temperature in a phase of fixed composition maintained at con-
stant pressure. This expression leads, among other things, to an important relation between
the temperature dependence of an equilibrium constant and the standard molar reaction
enthalpy.

12.1.1 Variation ofi=T with temperature

In a phase containing speciesi, either pure or in a mixture, the partial derivative ofi=T
with respect toTat constantpand a fixed amount of each species is given by^1

@ .i=T /
@T



p;fnig

D

1

T



@i

@T



p;fnig

i

T^2

(12.1.1)

This equality comes from a purely mathematical operation; no thermodynamics is involved.
The partial derivative.@i=@T /p;fnigis equal toSi(Eq.9.2.48), so that Eq.12.1.1be-
comes 
@ .i=T /
@T



p;fnig

D

Si

T

i

T^2

D

TSiCi

T^2

(12.1.2)

The further substitutioniDHiTSi(Eq.9.2.46) gives finally

@ .i=T /
@T



p;fnig

D

Hi

T^2

(12.1.3)

(^1) This relation is obtained from the formula d.uv/=dxDu.dv=dx/Cv.du=dx/(AppendixE), whereuis
1=T,visi, andxisT.
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