Concise Physical Chemistry

(Tina Meador) #1

c09 JWBS043-Rogers September 13, 2010 11:26 Printer Name: Yet to Come


PARTIAL MOLAR VOLUME 133

quantities analogous to the partial molar volume exist for all thermodynamic state
variables. This rule gives us the partial molar energy,

U ̄mi=

(


∂U


∂ni

)


T,p,nj

the partial molar enthalpy,

H ̄mi=

(


∂H


∂ni

)


T,p,nj

the partial molar entropy,

S ̄mi=

(


∂S


∂ni

)


T,p,nj

and the partial molar Gibbs free energy

μmi=

(


∂μ
∂ni

)


T,p,nj

This last partial molar quantity is so important that it is given a unique name and
symbol. It is called theGibbs chemical potentialμmi. It should be clear that in real
(nonideal) systems, each of these functions has a correspondingexcessfunction; the
excess energy, the excess enthalpy, the excess entropy, and so on.
In generalizing thermodynamics to many-component systems, Gibbs brought
about an immense expansion of the scope of the subject. All of the classical ther-
modynamic equations apply to partial molar quantities as well. For example, by
analogy to

d

(


G


T


)


d

(


1


T


)=H


for the Gibbs free energy of ideal components (Section 6.6), we have

d


T

)


d

(


1


T


)=H ̄m

relating the partial molar Gibbs free energy and the partial molar enthalpy.H ̄m.
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