Thermodynamics and Chemistry

CHAPTER 11 REACTIONS AND OTHER CHEMICAL PROCESSES

11.1 MIXINGPROCESSES 303

A B mixture ofA and B

Figure 11.1 Initial state (left) and final state (right) of mixing process for liquid sub-

stances A and B.

11.1.1 Mixtures in general

First let us consider changes in the Gibbs energyG. Since this is an extensive property,G
in the initial state 1 is the sum ofGfor each pure phase:

G 1 D

X

i

nii (11.1.1)

Hereiis the chemical potential (i.e., the molar Gibbs energy) of pure substanceiat the
initial temperature and pressure. For the final state 2, we use the additivity rule for a mixture

G 2 D

X

i

nii (11.1.2)

whereiis the chemical potential ofiin the mixture at the same temperature and pressure
as the initial state. The overall change ofG, theGibbs energy of mixing, is then

ÅG(mix)DG 2 G 1 D

X

i

ni.ii/ (11.1.3)

Themolar Gibbs energy of mixingis the Gibbs energy of mixing per amount of mix-
ture formed; that is,ÅGm(mix)DÅG(mix)=n, wherenis the sum

P

ini. Dividing both
sides of Eq.11.1.3byn, we obtain

ÅGm(mix)D

X

i

xi.ii/ (11.1.4)

wherexiis the mole fraction of substanceiin the final mixture.
Following the same procedure for an extensive state functionX, we derive the following
general relation for its molar mixing quantity:

ÅXm(mix)D

X

i

xi.XiXi/ (11.1.5)

11.1.2 Ideal mixtures

When the mixture formed is an ideal mixture (gas, liquid, or solid), and the pure con-
stituents have the same physical state as the mixture, the expressions for various molar
mixing quantities are particularly simple. An ideal molar mixing quantity will be indicated