PHYSICAL CHEMISTRY IN BRIEF

CHAP. 6: THERMODYNAMICS OF HOMOGENEOUS MIXTURES [CONTENTS] 150

6.3.3 Determination of partial molar quantities.

While determining the partial molar quantities of a real mixture we proceed from

• Respective system quantities by applying thedefinition relation(6.41).


• Dependence ofmolar quantitiesYmon the mole fraction.
  In this case we have the following relations for the partial molar quantitiesY 1 andY 2
  in a binary system

Y 1 =Ym+x 2

(

∂Ym

∂x 1

)

T,p

, Y 2 =Ym−x 1

(

∂Ym

∂x 1

)

T,p

. (6.52)

Note:Figure6.1shows why the graphical version of this method is called the method of

intercepts.

• Dependence ofexcess quantitieson the mole fraction
  In this case we have for a binary mixture

Y 1 = Y 1 ,id.mix+ ∆YE+x 2

(

∂∆YE

∂x 1

)

T,p

, (6.53)

Y 2 = Y 2 ,id.mix+ ∆YE−x 1

(

∂∆YE

∂x 1

)

T,p

(6.54)

andYi,id.mixare defined by relations (6.46) to (6.51).

Example

Dependence of the molar volume of a mixture of acetone and benzene on composition at tem-

perature 25◦C is expressed by the equation

Vm= 73. 936 x 1 + 89.412(1−x 1 )− 0. 272 x 1 (1−x 1 )cm^3 mol−^1 ,

wherex 1 is the mole fraction of acetone. Calculate the partial molar volumes of both components

at this temperature andx 1 = 0.4.