Thermodynamics and Chemistry

CHAPTER 9 MIXTURES

9.4 LIQUID ANDSOLIDMIXTURES OFNONELECTROLYTES 248

By eliminatingi(g) between these equations and rearranging, we obtain Eq.9.4.5withxi
replaced byyi.
Thus, anideal mixture, whether solid, liquid, or gas, is a mixture in which the chemical
potential of each constituent at a givenTandpis a linear function of the logarithm of the
mole fraction:

iDiCRTlnxi (9.4.8)

(ideal mixture)

9.4.3 Partial molar quantities in ideal mixtures

With the help of Eq.9.4.8for the chemical potential of a constituent of an ideal mixture,
we will now be able to find expressions for partial molar quantities. These expressions find
their greatest use for ideal liquid and solid mixtures.
For the partial molar entropy of substancei, we haveSiD.@i=@T /p;fnig(from Eq.
9.2.48) or, for the ideal mixture,

SiD



@i

@T



p

RlnxiDSiRlnxi (9.4.9)

(ideal mixture)

Since lnxiis negative in a mixture, the partial molar entropy of a constituent of an ideal
mixture is greater than the molar entropy of the pure substance at the sameTandp.
For the partial molar enthalpy, we haveHiDiCTSi(from Eq.9.2.46). Using the
expressions foriandSigives us

HiDiCTSiDHi (9.4.10)

(ideal mixture)

Thus,Hiin an ideal mixture is independent of the mixture composition and is equal to the
molar enthalpy of pureiat the sameT andpas the mixture. In the case of an idealgas
mixture,Hiis also independent ofp, because the molar enthalpy of an ideal gas depends
only onT.
The partial molar volume is given byViD.@i=@p/T;fnig(Eq.9.2.49), so we have

ViD



@i

@p



T

DVi (9.4.11)

(ideal mixture)

Finally, from Eqs.9.2.50and9.2.52and the expressions above forHiandVi, we obtain

UiDHipViDUi (9.4.12)

(ideal mixture)

and

Cp;iD.@Hi=@T /p;fnigDCp;i (9.4.13)

(ideal mixture)

Note that in an ideal mixture held at constantTandp, the partial molar quantitiesHi,Vi,
Ui, andCp;ido not vary with the composition.