PHYSICAL CHEMISTRY IN BRIEF

CHAP. 6: THERMODYNAMICS OF HOMOGENEOUS MIXTURES [CONTENTS] 148

6.3 Differential quantities.

Instead of integral quantities describing a mixture as a whole, we may also use differential
quantities which describe its individual components.

6.3.1 Partial molar quantities

Partial molar quantitiesare most often used for a general description of the behaviour of
individual components of a mixture. For any extensive thermodynamic quantityY, the partial
molar quantity is defined using the relation

Yi=

(

∂Y

∂ni

)

T,p,nj 6 =i

. (6.41)

Note:According to this definition, partial molar quantities are related to one mole ofith

component, but we leave out the subscriptmfor the sake of simplicity.

6.3.2 Properties of partial molar quantities

6.3.2.1 Relations between system and partial molar quantities

For ak−component mixture we have:

Ym=

∑k

i=1

xiYi resp. Y =

∑k

i=1

niYi. (6.42)

TheGibbs-Duhem equation

∑k

i=1

xi

(

∂Yi

∂xj

)

T,p,x` 6 =j

= 0 j= 1. 2 ,... , k− 1. (6.43)

Note:This relation represents a thermodynamic link between partial molar quantities; it

may be used to test the consistency of the measured partial molar data or to calculate one

partial molar quantity provided that we know the others.