PHYSICAL CHEMISTRY IN BRIEF

CHAP. 6: THERMODYNAMICS OF HOMOGENEOUS MIXTURES [CONTENTS] 169

whereγ∞i is the limiting activity coefficientγiin a mixture in which componentiis infinitely
diluted.

6.5.5.2 Relation between the activity coefficient and the osmotic coefficient

For mixtures with one prevailing component (e.g. aqueous solutions of salts),osmotic coef-
ficientsare also used in addition to activity coefficients. The osmotic coefficient of a solvent
φ
[c]
1 is defined as
φ[ 1 c]= 1 +

lnγ[ 1 c]

ln(c 1 /cst)

(6.110)

The coefficientsφ[ 1 x]andφ[ 1 m]are defined in a similar way.

6.5.6 Dependence of the excess Gibbs energy and of the activity

coefficients on composition

Various empirical and semi-empirical relations are used for the dependence of ∆GEon compo-
sition and possibly also on temperature. Two of them are presented here.

6.5.6.1 Wilson equation

The Wilson equation is used in practice most often. Its form for ak-component system is

∆GE

RT

= −

∑k

i=1

xiln





∑k

j=1

xjAij



, (6.111)

Aij =

Vm,j•

Vm,i•

exp(−

aij

T

), aij 6 =aji, aii=ajj= 0,

whereVm•, 1 , Vm•, 2 are the molar volumes of components in the liquid state, andaij are the
adjustable constants.
For the activity coefficients we have

lnγi= 1−ln





∑k

j=1

xjAij



−

∑k

j=1

xj

Aji

∑k

`=1x`Aj`

. (6.112)