PHYSICAL CHEMISTRY IN BRIEF

CHAP. 6: THERMODYNAMICS OF HOMOGENEOUS MIXTURES [CONTENTS] 152

6.3.4 Excess partial molar quantities

For real mixtures we sometimes use excess partial molar quantities:

Y

E

i =Yi−Yi,id.mix. (6.55)

In an ideal mixture, all quantitiesY
E
i thus equal zero while in real mixtures their value expresses
the degree of non-ideal behaviour of the mixture. We obtain relations forY
E
i from those for
partial molar quantities using equation (6.41) by substituting relations (6.46) to (6.51).

Example

Prove that the excess partial molar Gibbs energyG

E

i is a partial molar quantity derived from the

excess Gibbs energy∆GE.

Solution

We proceed from the definition relation (6.27)

∆GE = Gm−Gm,id.mix=

=

∑k

i=1

xiGi−

∑k

i=1

xiG•m,i−RT

∑k

i=1

xilnxi=

=

∑k

i=1

xi(Gi−G•m,i−RTlnxi) =

=

∑k

i=1

xiG

E

i.

By multiplyingnon both sides and subsequent differentiation we obtain

G

E

i =

(

∂n∆GE

∂ni

)

T,p,nj 6 =i

,

which is the definition relation for partial molar quantities [see (6.41)].