PHYSICAL CHEMISTRY IN BRIEF

CHAP. 6: THERMODYNAMICS OF HOMOGENEOUS MIXTURES [CONTENTS] 149

6.3.2.2 Relations between partial molar quantities.

The relations between partial molar quantities are analogous to those applying between system
quantities, e.g.

Hi = Ui+pVi, (6.44)

Gi = Hi−TSi. (6.45)

Example

For a certain substance at temperature 400 K and pressure 10 MPa we have Vi =

280 cm^3 mol−^1 , Hi = − 1000 J mol−^1 , Si = 250J mol−^1 K−^1. Using this data calculate the

partial molar internal energy and the partial molar Gibbs energy.

Solution

Substituting into (6.44) and (6.45) gives

Ui = Hi−pVi=− 1000 − 10 ×280 =− 3800 J mol−^1 ,

Gi = Hi−TSi=− 1000 − 400 ×250 =− 101000 J mol−^1.

6.3.2.3 Partial molar quantities of an ideal mixture

From relations (6.2) to (6.9) we obtain

Vi,id.mix = Vm•,i, (6.46)

Hi,id.mix = Hm•,i, (6.47)

Ui,id.mix = Um•,i, (6.48)

Si,id.mix = Sm•,i−Rlnxi, (6.49)

Gi,id.mix = G•m,i+RTlnxi, (6.50)

Fi,id.mix = Fm•,i+RTlnxi. (6.51)