Concise Physical Chemistry

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

(μ

T

)

d

(

1

T

)=H ̄m

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